Python_EDA_Book3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we will explore several methods to see if certain characteristics or features can be used to predict car price. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Table of content</h2>\n",
    "\n",
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "<ol>\n",
    "    <li><a href=\"#import_data\">Import Data </a></li>\n",
    "    <li><a href=\"#pattern_visualization\">Analyzing Individual Feature Patterns using Visualization</a></li>\n",
    "    <li><a href=\"#discriptive_statistics\">Descriptive Statistical Analysis</a></li>\n",
    "    <li><a href=\"#basic_grouping\">Basics of Grouping</a></li>\n",
    "    <li><a href=\"#correlation_causation\">Correlation and Causation</a></li>\n",
    "    <li><a href=\"#anova\">ANOVA</a></li>\n",
    "</ol>\n",
    "    \n",
    "</div>\n",
    " \n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What are the main characteristics which have the most impact on the car price?</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"import_data\">1. Import Data </h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "pd.set_option('display.max_rows', None)\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " load data and store in dataframe df:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-type</th>\n",
       "      <th>num-of-cylinders</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>fuel-system</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>highway-L/100km</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "      <th>std</th>\n",
       "      <th>turbo</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>122.0</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>0.816054</td>\n",
       "      <td>2548</td>\n",
       "      <td>dohc</td>\n",
       "      <td>four</td>\n",
       "      <td>130</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.47</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>8.703704</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Low HP</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>122.0</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>0.816054</td>\n",
       "      <td>2548</td>\n",
       "      <td>dohc</td>\n",
       "      <td>four</td>\n",
       "      <td>130</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.47</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>8.703704</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Low HP</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>122.0</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>0.909722</td>\n",
       "      <td>0.876254</td>\n",
       "      <td>2823</td>\n",
       "      <td>ohcv</td>\n",
       "      <td>six</td>\n",
       "      <td>152</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>2.68</td>\n",
       "      <td>3.47</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>9.038462</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium HP</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>164.0</td>\n",
       "      <td>audi</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>0.919444</td>\n",
       "      <td>0.908027</td>\n",
       "      <td>2337</td>\n",
       "      <td>ohc</td>\n",
       "      <td>four</td>\n",
       "      <td>109</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>7.833333</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Low HP</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>164.0</td>\n",
       "      <td>audi</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>0.922222</td>\n",
       "      <td>0.908027</td>\n",
       "      <td>2824</td>\n",
       "      <td>ohc</td>\n",
       "      <td>five</td>\n",
       "      <td>136</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>10.681818</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Low HP</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "   Unnamed: 0  symboling  normalized-losses         make num-of-doors  \\\n",
       "0           0          3              122.0  alfa-romero          two   \n",
       "1           1          3              122.0  alfa-romero          two   \n",
       "2           2          1              122.0  alfa-romero          two   \n",
       "3           3          2              164.0         audi         four   \n",
       "4           4          2              164.0         audi         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length     width  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  0.890278   \n",
       "1  convertible          rwd           front        88.6  0.811148  0.890278   \n",
       "2    hatchback          rwd           front        94.5  0.822681  0.909722   \n",
       "3        sedan          fwd           front        99.8  0.848630  0.919444   \n",
       "4        sedan          4wd           front        99.4  0.848630  0.922222   \n",
       "\n",
       "     height  curb-weight engine-type num-of-cylinders  engine-size  \\\n",
       "0  0.816054         2548        dohc             four          130   \n",
       "1  0.816054         2548        dohc             four          130   \n",
       "2  0.876254         2823        ohcv              six          152   \n",
       "3  0.908027         2337         ohc             four          109   \n",
       "4  0.908027         2824         ohc             five          136   \n",
       "\n",
       "  fuel-system  bore  stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "0        mpfi  3.47    2.68                9.0         111    5000.0   \n",
       "1        mpfi  3.47    2.68                9.0         111    5000.0   \n",
       "2        mpfi  2.68    3.47                9.0         154    5000.0   \n",
       "3        mpfi  3.19    3.40               10.0         102    5500.0   \n",
       "4        mpfi  3.19    3.40                8.0         115    5500.0   \n",
       "\n",
       "   city-mpg  highway-mpg    price  highway-L/100km  city-L/100km  \\\n",
       "0        21           27  13495.0         8.703704     11.190476   \n",
       "1        21           27  16500.0         8.703704     11.190476   \n",
       "2        19           26  16500.0         9.038462     12.368421   \n",
       "3        24           30  13950.0         7.833333      9.791667   \n",
       "4        18           22  17450.0        10.681818     13.055556   \n",
       "\n",
       "  horsepower-binned  diesel  gas  std  turbo  \n",
       "0            Low HP       0    1    1      0  \n",
       "1            Low HP       0    1    1      0  \n",
       "2         Medium HP       0    1    1      0  \n",
       "3            Low HP       0    1    1      0  \n",
       "4            Low HP       0    1    1      0  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path='automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"pattern_visualization\">2. Analyzing Individual Feature Patterns using Visualization</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To install seaborn we use the pip which is the python package manager."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "#! pip install seaborn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import visualization packages \"Matplotlib\" and \"Seaborn\", don't forget about \"%matplotlib inline\" to plot in a Jupyter notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>How to choose the right visualization method?</h4>\n",
    "<p>When visualizing individual variables, it is important to first understand what type of variable you are dealing with. This will help us find the right visualization method for that variable.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unnamed: 0             int64\n",
      "symboling              int64\n",
      "normalized-losses    float64\n",
      "make                  object\n",
      "num-of-doors          object\n",
      "body-style            object\n",
      "drive-wheels          object\n",
      "engine-location       object\n",
      "wheel-base           float64\n",
      "length               float64\n",
      "width                float64\n",
      "height               float64\n",
      "curb-weight            int64\n",
      "engine-type           object\n",
      "num-of-cylinders      object\n",
      "engine-size            int64\n",
      "fuel-system           object\n",
      "bore                 float64\n",
      "stroke               float64\n",
      "compression-ratio    float64\n",
      "horsepower             int64\n",
      "peak-rpm             float64\n",
      "city-mpg               int64\n",
      "highway-mpg            int64\n",
      "price                float64\n",
      "highway-L/100km      float64\n",
      "city-L/100km         float64\n",
      "horsepower-binned     object\n",
      "diesel                 int64\n",
      "gas                    int64\n",
      "std                    int64\n",
      "turbo                  int64\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "# list the data types for each column\n",
    "print(df.dtypes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for example, we can calculate the correlation between variables  of type \"int64\" or \"float64\" using the method \"corr\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
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       "      <td>-0.196735</td>\n",
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       "      <td>0.054615</td>\n",
       "      <td>-0.054615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>normalized-losses</td>\n",
       "      <td>-0.241092</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055045</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217300</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.181189</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>0.006911</td>\n",
       "      <td>-0.006911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>wheel-base</td>\n",
       "      <td>0.125517</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158018</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371178</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.577576</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.256889</td>\n",
       "      <td>0.256889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>length</td>\n",
       "      <td>0.161848</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.123952</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579795</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.707108</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.230085</td>\n",
       "      <td>0.230085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>width</td>\n",
       "      <td>0.043976</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188822</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615056</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.736728</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.305732</td>\n",
       "      <td>0.305732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>height</td>\n",
       "      <td>0.252015</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.060663</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087001</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.084301</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.090336</td>\n",
       "      <td>0.090336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>curb-weight</td>\n",
       "      <td>0.064820</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167438</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757981</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.836921</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.321955</td>\n",
       "      <td>0.321955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>engine-size</td>\n",
       "      <td>-0.047764</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.205928</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822668</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.783465</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.110040</td>\n",
       "      <td>0.110040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>bore</td>\n",
       "      <td>0.244734</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566903</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.559112</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.227816</td>\n",
       "      <td>0.227816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>stroke</td>\n",
       "      <td>-0.162490</td>\n",
       "      <td>-0.008153</td>\n",
       "      <td>0.055045</td>\n",
       "      <td>0.158018</td>\n",
       "      <td>0.123952</td>\n",
       "      <td>0.188822</td>\n",
       "      <td>-0.060663</td>\n",
       "      <td>0.167438</td>\n",
       "      <td>0.205928</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187871</td>\n",
       "      <td>0.098128</td>\n",
       "      <td>-0.063561</td>\n",
       "      <td>-0.033956</td>\n",
       "      <td>-0.034636</td>\n",
       "      <td>0.082269</td>\n",
       "      <td>0.047089</td>\n",
       "      <td>0.036133</td>\n",
       "      <td>0.241064</td>\n",
       "      <td>-0.241064</td>\n",
       "      <td>-0.218233</td>\n",
       "      <td>0.218233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>compression-ratio</td>\n",
       "      <td>0.144301</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187871</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214489</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.223361</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>-0.307522</td>\n",
       "      <td>0.307522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>horsepower</td>\n",
       "      <td>-0.022505</td>\n",
       "      <td>0.075810</td>\n",
       "      <td>0.217300</td>\n",
       "      <td>0.371178</td>\n",
       "      <td>0.579795</td>\n",
       "      <td>0.615056</td>\n",
       "      <td>-0.087001</td>\n",
       "      <td>0.757981</td>\n",
       "      <td>0.822668</td>\n",
       "      <td>0.566903</td>\n",
       "      <td>0.098128</td>\n",
       "      <td>-0.214489</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107884</td>\n",
       "      <td>-0.822192</td>\n",
       "      <td>-0.804579</td>\n",
       "      <td>0.809607</td>\n",
       "      <td>0.840627</td>\n",
       "      <td>0.889482</td>\n",
       "      <td>-0.169030</td>\n",
       "      <td>0.169030</td>\n",
       "      <td>-0.251159</td>\n",
       "      <td>0.251159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>peak-rpm</td>\n",
       "      <td>-0.195662</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.063561</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107884</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.017694</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>0.190057</td>\n",
       "      <td>-0.190057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>city-mpg</td>\n",
       "      <td>0.027956</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.033956</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822192</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.909024</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>0.189237</td>\n",
       "      <td>-0.189237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>highway-mpg</td>\n",
       "      <td>0.020344</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.034636</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804579</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.951100</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>0.241851</td>\n",
       "      <td>-0.241851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\n",
       "      <td>-0.118214</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082269</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809607</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.801118</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>-0.179578</td>\n",
       "      <td>0.179578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>highway-L/100km</td>\n",
       "      <td>-0.078346</td>\n",
       "      <td>-0.029807</td>\n",
       "      <td>0.181189</td>\n",
       "      <td>0.577576</td>\n",
       "      <td>0.707108</td>\n",
       "      <td>0.736728</td>\n",
       "      <td>0.084301</td>\n",
       "      <td>0.836921</td>\n",
       "      <td>0.783465</td>\n",
       "      <td>0.559112</td>\n",
       "      <td>0.047089</td>\n",
       "      <td>-0.223361</td>\n",
       "      <td>0.840627</td>\n",
       "      <td>0.017694</td>\n",
       "      <td>-0.909024</td>\n",
       "      <td>-0.951100</td>\n",
       "      <td>0.801118</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.958306</td>\n",
       "      <td>-0.158091</td>\n",
       "      <td>0.158091</td>\n",
       "      <td>-0.210720</td>\n",
       "      <td>0.210720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>city-L/100km</td>\n",
       "      <td>-0.099157</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.036133</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889482</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.958306</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-0.157578</td>\n",
       "      <td>0.157578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>diesel</td>\n",
       "      <td>0.121454</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241064</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169030</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.158091</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-0.408228</td>\n",
       "      <td>0.408228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>gas</td>\n",
       "      <td>-0.121454</td>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241064</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169030</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.158091</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.408228</td>\n",
       "      <td>-0.408228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>-0.082739</td>\n",
       "      <td>0.054615</td>\n",
       "      <td>0.006911</td>\n",
       "      <td>-0.256889</td>\n",
       "      <td>-0.230085</td>\n",
       "      <td>-0.305732</td>\n",
       "      <td>-0.090336</td>\n",
       "      <td>-0.321955</td>\n",
       "      <td>-0.110040</td>\n",
       "      <td>-0.227816</td>\n",
       "      <td>-0.218233</td>\n",
       "      <td>-0.307522</td>\n",
       "      <td>-0.251159</td>\n",
       "      <td>0.190057</td>\n",
       "      <td>0.189237</td>\n",
       "      <td>0.241851</td>\n",
       "      <td>-0.179578</td>\n",
       "      <td>-0.210720</td>\n",
       "      <td>-0.157578</td>\n",
       "      <td>-0.408228</td>\n",
       "      <td>0.408228</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>turbo</td>\n",
       "      <td>0.082739</td>\n",
       "      <td>-0.054615</td>\n",
       "      <td>-0.006911</td>\n",
       "      <td>0.256889</td>\n",
       "      <td>0.230085</td>\n",
       "      <td>0.305732</td>\n",
       "      <td>0.090336</td>\n",
       "      <td>0.321955</td>\n",
       "      <td>0.110040</td>\n",
       "      <td>0.227816</td>\n",
       "      <td>0.218233</td>\n",
       "      <td>0.307522</td>\n",
       "      <td>0.251159</td>\n",
       "      <td>-0.190057</td>\n",
       "      <td>-0.189237</td>\n",
       "      <td>-0.241851</td>\n",
       "      <td>0.179578</td>\n",
       "      <td>0.210720</td>\n",
       "      <td>0.157578</td>\n",
       "      <td>0.408228</td>\n",
       "      <td>-0.408228</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Unnamed: 0  symboling  normalized-losses  wheel-base  \\\n",
       "Unnamed: 0           1.000000  -0.162764          -0.241092    0.125517   \n",
       "symboling           -0.162764   1.000000           0.466264   -0.535987   \n",
       "normalized-losses   -0.241092   0.466264           1.000000   -0.056661   \n",
       "wheel-base           0.125517  -0.535987          -0.056661    1.000000   \n",
       "length               0.161848  -0.365404           0.019424    0.876024   \n",
       "width                0.043976  -0.242423           0.086802    0.814507   \n",
       "height               0.252015  -0.550160          -0.373737    0.590742   \n",
       "curb-weight          0.064820  -0.233118           0.099404    0.782097   \n",
       "engine-size         -0.047764  -0.110581           0.112360    0.572027   \n",
       "bore                 0.244734  -0.140019          -0.029862    0.493244   \n",
       "stroke              -0.162490  -0.008153           0.055045    0.158018   \n",
       "compression-ratio    0.144301  -0.182196          -0.114713    0.250313   \n",
       "horsepower          -0.022505   0.075810           0.217300    0.371178   \n",
       "peak-rpm            -0.195662   0.279740           0.239543   -0.360305   \n",
       "city-mpg             0.027956  -0.035527          -0.225016   -0.470606   \n",
       "highway-mpg          0.020344   0.036233          -0.181877   -0.543304   \n",
       "price               -0.118214  -0.082391           0.133999    0.584642   \n",
       "highway-L/100km     -0.078346  -0.029807           0.181189    0.577576   \n",
       "city-L/100km        -0.099157   0.066171           0.238567    0.476153   \n",
       "diesel               0.121454  -0.196735          -0.101546    0.307237   \n",
       "gas                 -0.121454   0.196735           0.101546   -0.307237   \n",
       "std                 -0.082739   0.054615           0.006911   -0.256889   \n",
       "turbo                0.082739  -0.054615          -0.006911    0.256889   \n",
       "\n",
       "                     length     width    height  curb-weight  engine-size  \\\n",
       "Unnamed: 0         0.161848  0.043976  0.252015     0.064820    -0.047764   \n",
       "symboling         -0.365404 -0.242423 -0.550160    -0.233118    -0.110581   \n",
       "normalized-losses  0.019424  0.086802 -0.373737     0.099404     0.112360   \n",
       "wheel-base         0.876024  0.814507  0.590742     0.782097     0.572027   \n",
       "length             1.000000  0.857170  0.492063     0.880665     0.685025   \n",
       "width              0.857170  1.000000  0.306002     0.866201     0.729436   \n",
       "height             0.492063  0.306002  1.000000     0.307581     0.074694   \n",
       "curb-weight        0.880665  0.866201  0.307581     1.000000     0.849072   \n",
       "engine-size        0.685025  0.729436  0.074694     0.849072     1.000000   \n",
       "bore               0.608971  0.544885  0.180449     0.644060     0.572609   \n",
       "stroke             0.123952  0.188822 -0.060663     0.167438     0.205928   \n",
       "compression-ratio  0.159733  0.189867  0.259737     0.156433     0.028889   \n",
       "horsepower         0.579795  0.615056 -0.087001     0.757981     0.822668   \n",
       "peak-rpm          -0.285970 -0.245800 -0.309974    -0.279361    -0.256733   \n",
       "city-mpg          -0.665192 -0.633531 -0.049800    -0.749543    -0.650546   \n",
       "highway-mpg       -0.698142 -0.680635 -0.104812    -0.794889    -0.679571   \n",
       "price              0.690628  0.751265  0.135486     0.834415     0.872335   \n",
       "highway-L/100km    0.707108  0.736728  0.084301     0.836921     0.783465   \n",
       "city-L/100km       0.657373  0.673363  0.003811     0.785353     0.745059   \n",
       "diesel             0.211187  0.244356  0.281578     0.221046     0.070779   \n",
       "gas               -0.211187 -0.244356 -0.281578    -0.221046    -0.070779   \n",
       "std               -0.230085 -0.305732 -0.090336    -0.321955    -0.110040   \n",
       "turbo              0.230085  0.305732  0.090336     0.321955     0.110040   \n",
       "\n",
       "                       bore    stroke  compression-ratio  horsepower  \\\n",
       "Unnamed: 0         0.244734 -0.162490           0.144301   -0.022505   \n",
       "symboling         -0.140019 -0.008153          -0.182196    0.075810   \n",
       "normalized-losses -0.029862  0.055045          -0.114713    0.217300   \n",
       "wheel-base         0.493244  0.158018           0.250313    0.371178   \n",
       "length             0.608971  0.123952           0.159733    0.579795   \n",
       "width              0.544885  0.188822           0.189867    0.615056   \n",
       "height             0.180449 -0.060663           0.259737   -0.087001   \n",
       "curb-weight        0.644060  0.167438           0.156433    0.757981   \n",
       "engine-size        0.572609  0.205928           0.028889    0.822668   \n",
       "bore               1.000000 -0.055390           0.001263    0.566903   \n",
       "stroke            -0.055390  1.000000           0.187871    0.098128   \n",
       "compression-ratio  0.001263  0.187871           1.000000   -0.214489   \n",
       "horsepower         0.566903  0.098128          -0.214489    1.000000   \n",
       "peak-rpm          -0.267392 -0.063561          -0.435780    0.107884   \n",
       "city-mpg          -0.582027 -0.033956           0.331425   -0.822192   \n",
       "highway-mpg       -0.591309 -0.034636           0.268465   -0.804579   \n",
       "price              0.543155  0.082269           0.071107    0.809607   \n",
       "highway-L/100km    0.559112  0.047089          -0.223361    0.840627   \n",
       "city-L/100km       0.554610  0.036133          -0.299372    0.889482   \n",
       "diesel             0.054458  0.241064           0.985231   -0.169030   \n",
       "gas               -0.054458 -0.241064          -0.985231    0.169030   \n",
       "std               -0.227816 -0.218233          -0.307522   -0.251159   \n",
       "turbo              0.227816  0.218233           0.307522    0.251159   \n",
       "\n",
       "                   peak-rpm  city-mpg  highway-mpg     price  highway-L/100km  \\\n",
       "Unnamed: 0        -0.195662  0.027956     0.020344 -0.118214        -0.078346   \n",
       "symboling          0.279740 -0.035527     0.036233 -0.082391        -0.029807   \n",
       "normalized-losses  0.239543 -0.225016    -0.181877  0.133999         0.181189   \n",
       "wheel-base        -0.360305 -0.470606    -0.543304  0.584642         0.577576   \n",
       "length            -0.285970 -0.665192    -0.698142  0.690628         0.707108   \n",
       "width             -0.245800 -0.633531    -0.680635  0.751265         0.736728   \n",
       "height            -0.309974 -0.049800    -0.104812  0.135486         0.084301   \n",
       "curb-weight       -0.279361 -0.749543    -0.794889  0.834415         0.836921   \n",
       "engine-size       -0.256733 -0.650546    -0.679571  0.872335         0.783465   \n",
       "bore              -0.267392 -0.582027    -0.591309  0.543155         0.559112   \n",
       "stroke            -0.063561 -0.033956    -0.034636  0.082269         0.047089   \n",
       "compression-ratio -0.435780  0.331425     0.268465  0.071107        -0.223361   \n",
       "horsepower         0.107884 -0.822192    -0.804579  0.809607         0.840627   \n",
       "peak-rpm           1.000000 -0.115413    -0.058598 -0.101616         0.017694   \n",
       "city-mpg          -0.115413  1.000000     0.972044 -0.686571        -0.909024   \n",
       "highway-mpg       -0.058598  0.972044     1.000000 -0.704692        -0.951100   \n",
       "price             -0.101616 -0.686571    -0.704692  1.000000         0.801118   \n",
       "highway-L/100km    0.017694 -0.909024    -0.951100  0.801118         1.000000   \n",
       "city-L/100km       0.115830 -0.949713    -0.930028  0.789898         0.958306   \n",
       "diesel            -0.475812  0.265676     0.198690  0.110326        -0.158091   \n",
       "gas                0.475812 -0.265676    -0.198690 -0.110326         0.158091   \n",
       "std                0.190057  0.189237     0.241851 -0.179578        -0.210720   \n",
       "turbo             -0.190057 -0.189237    -0.241851  0.179578         0.210720   \n",
       "\n",
       "                   city-L/100km    diesel       gas       std     turbo  \n",
       "Unnamed: 0            -0.099157  0.121454 -0.121454 -0.082739  0.082739  \n",
       "symboling              0.066171 -0.196735  0.196735  0.054615 -0.054615  \n",
       "normalized-losses      0.238567 -0.101546  0.101546  0.006911 -0.006911  \n",
       "wheel-base             0.476153  0.307237 -0.307237 -0.256889  0.256889  \n",
       "length                 0.657373  0.211187 -0.211187 -0.230085  0.230085  \n",
       "width                  0.673363  0.244356 -0.244356 -0.305732  0.305732  \n",
       "height                 0.003811  0.281578 -0.281578 -0.090336  0.090336  \n",
       "curb-weight            0.785353  0.221046 -0.221046 -0.321955  0.321955  \n",
       "engine-size            0.745059  0.070779 -0.070779 -0.110040  0.110040  \n",
       "bore                   0.554610  0.054458 -0.054458 -0.227816  0.227816  \n",
       "stroke                 0.036133  0.241064 -0.241064 -0.218233  0.218233  \n",
       "compression-ratio     -0.299372  0.985231 -0.985231 -0.307522  0.307522  \n",
       "horsepower             0.889482 -0.169030  0.169030 -0.251159  0.251159  \n",
       "peak-rpm               0.115830 -0.475812  0.475812  0.190057 -0.190057  \n",
       "city-mpg              -0.949713  0.265676 -0.265676  0.189237 -0.189237  \n",
       "highway-mpg           -0.930028  0.198690 -0.198690  0.241851 -0.241851  \n",
       "price                  0.789898  0.110326 -0.110326 -0.179578  0.179578  \n",
       "highway-L/100km        0.958306 -0.158091  0.158091 -0.210720  0.210720  \n",
       "city-L/100km           1.000000 -0.241282  0.241282 -0.157578  0.157578  \n",
       "diesel                -0.241282  1.000000 -1.000000 -0.408228  0.408228  \n",
       "gas                    0.241282 -1.000000  1.000000  0.408228 -0.408228  \n",
       "std                   -0.157578 -0.408228  0.408228  1.000000 -1.000000  \n",
       "turbo                  0.157578  0.408228 -0.408228 -1.000000  1.000000  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The diagonal elements are always one; we will study correlation more precisely Pearson correlation in-depth at the end of the notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>bore</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>stroke</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187871</td>\n",
       "      <td>0.098128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>compression-ratio</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187871</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>horsepower</td>\n",
       "      <td>0.566903</td>\n",
       "      <td>0.098128</td>\n",
       "      <td>-0.214489</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       bore    stroke  compression-ratio  horsepower\n",
       "bore               1.000000 -0.055390           0.001263    0.566903\n",
       "stroke            -0.055390  1.000000           0.187871    0.098128\n",
       "compression-ratio  0.001263  0.187871           1.000000   -0.214489\n",
       "horsepower         0.566903  0.098128          -0.214489    1.000000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['bore','stroke' ,'compression-ratio','horsepower']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Continuous numerical variables:</h2> \n",
    "\n",
    "<p>Continuous numerical variables are variables that may contain any value within some range. Continuous numerical variables can have the type \"int64\" or \"float64\". A great way to visualize these variables is by using scatterplots with fitted lines.</p>\n",
    "\n",
    "<p>In order to start understanding the (linear) relationship between an individual variable and the price. We can do this by using \"regplot\", which plots the scatterplot plus the fitted regression line for the data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see several examples of different linear relationships:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Positive linear relationship</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find the scatterplot of \"engine-size\" and \"price\" "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 56128.03502910951)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Engine size as potential predictor variable of price\n",
    "sns.regplot(x=\"engine-size\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the engine-size goes up, the price goes up: this indicates a positive direct correlation between these two variables. Engine size seems like a pretty good predictor of price since the regression line is almost a perfect diagonal line.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can examine the correlation between 'engine-size' and 'price' and see it's approximately  0.87"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>engine-size</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>engine-size</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.872335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             engine-size     price\n",
       "engine-size     1.000000  0.872335\n",
       "price           0.872335  1.000000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Highway mpg is a potential predictor variable of price "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the highway-mpg goes up, the price goes down: this indicates an inverse/negative relationship between these two variables. Highway mpg could potentially be a predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'highway-mpg' and 'price' and see it's approximately  -0.704"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Weak Linear Relationship</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if \"Peak-rpm\" as a predictor variable of \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fac9c2e0510>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Peak rpm does not seem like a good predictor of the price at all since the regression line is close to horizontal. Also, the data points are very scattered and far from the fitted line, showing lots of variability. Therefore it's it is not a reliable variable.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'peak-rpm' and 'price' and see it's approximately -0.101616 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>peak-rpm</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          peak-rpm     price\n",
       "peak-rpm  1.000000 -0.101616\n",
       "price    -0.101616  1.000000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>stroke</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>stroke</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.082269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\n",
       "      <td>0.082269</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          stroke     price\n",
       "stroke  1.000000  0.082269\n",
       "price   0.082269  1.000000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute\n",
    "df[[\"stroke\",\"price\"]].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fac9c4119d0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Categorical variables</h3>\n",
    "\n",
    "<p>These are variables that describe a 'characteristic' of a data unit, and are selected from a small group of categories. The categorical variables can have the type \"object\" or \"int64\". A good way to visualize categorical variables is by using boxplots.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the relationship between \"body-style\" and \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fac9c50f490>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"body-style\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We see that the distributions of price between the different body-style categories have a significant overlap, and so body-style would not be a good predictor of price. Let's examine engine \"engine-location\" and \"price\":</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fac9c292e90>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Ipr1Nsa1FJWZmZkPfQHsi95AVjR6NwN37Ph0zMxtOBlpEDoqI13pW0vLB/e0gaZyk+yQ9KelxSXNS/CuSNkhanT4zKvaZK6lT0m8lnVURb0mxTklXVsSPkfSQpHWSbk0zHJqZWY0MtIj8QdIJPSuSTgT2NIzrDuALEfFesrnVL5E0KW27LiImp8/SdMxJZLMZvg9oAW6Q1JAunX0HmA5MAi6oOM616VgTgZeBiwd4PmZmtg8M9J7I54CfStqY1o8CPt7fDhGxCdiUll+V9CTQ3+QTM4HFEbEdeCZNk3ty2tYZEU8DSFoMzEzHOx34RGrTBnwFuHGA52RmZntpQD2RiFgJHAt8Bvgs8N6IWDXQL5E0HvgA8FAKXSppjaSFkg5PsTHACxW7rU+xvuKjgFciYkeveLXvny2pQ1JHV1fXQNM2M7M96LeISDo9/fxvwNnAe4CJwNkptkeSDgH+BfhcRPyerKfwbmAyWU/ln3qaVtk9csR3D0YsiIjmiGhuamoaSNpmZjYAe7qc9SHgXrIC0lsAP+tvZ0n7kxWQWyLiZwAR8WLF9u8Dd6bV9cC4it3HAj2Xz6rFfwccJmlE6o1Utjczsxrot4hExFWS9gOWRcRtgzmwJAE3AU9GxLcq4kel+yUAfwk8lpaXAD+W9C3gHWQ9nofJehwTJR0DbCC7+f6JiAhJ9wHnAYuBVuCOweRoZmZ7Z4831iPiDUmXAoMqImQDNn4KWCtpdYp9kezpqslkPZlnyd6AJyIel3Qb8ATZk12XRMROgPT9K4AGspceH0/HuwJYLOnrwKNkRcvMzGpkoE9ntUv6e+BW4A89wYjY3NcOEfErqt+3WNrPPtcA11SJL622X3pi6+TecTMzq42BFpG/Jus5fLZX/F37Nh0zMxtOBlpEJpEVkNPIiskvge8WlZSZmQ0PAy0ibWQTUs1L6xek2P8oIikzMxseBlpE/lNEvL9i/T5JvykiITMzGz4GOnbWo5Km9KxIOgX492JSMjOz4WKgPZFTgFmSnk/rRwNPSloLRET8eSHZmZnZkDbQItJSaBZmZjYsDaiIRMRzRSdiZmbDz0DviZiZme3GRcTMzHJzETEzs9xcRMzMLDcXETMzy81FxMzMcnMRMTOz3FxEzMwst8KKiKRxku6T9KSkxyXNSfGRktolrUs/D09xSZonqVPSGkknVByrNbVfJ6m1In6ipLVpn3lpSl4zM6uRInsiO4AvRMR7gSnAJZImAVcC90TEROCetA4wnWxe9YnAbOBGyIoOcBXZ+F0nA1f1FJ7UZnbFfh6excyshgorIhGxKSIeScuvAk8CY4CZZHORkH6em5ZnAosi8yBwmKSjgLOA9ojYHBEvA+1AS9p2aET8OiICWFRxLDMzq4Ga3BORNB74APAQMDoiNkFWaIAjU7MxwAsVu61Psf7i66vEq33/bEkdkjq6urr29nTMzCwpvIhIOgT4F+BzEfH7/ppWiUWO+O7BiAUR0RwRzU1NTXtK2czMBqjQIiJpf7ICcktE/CyFX0yXokg/X0rx9cC4it3HAhv3EB9bJW5mZjVS5NNZAm4CnoyIb1VsWgL0PGHVCtxREZ+VntKaAmxJl7tWANMkHZ5uqE8DVqRtr0qakr5rVsWxzMysBgY6KVUepwKfAtZKWp1iXwS+Cdwm6WLgeeBjadtSYAbQCWwFLgKIiM2SvgasTO2ujojNafkzwM1AI7AsfczMrEYKKyIR8Suq37cAOKNK+wAu6eNYC4GFVeIdwHF7kaaZme0Fv7FuZma5uYiYmVluLiJmZpabi4iZmeXmImJmZrm5iJiZWW4uImZmlpuLiJmZ5eYiYmZmubmImJlZbi4iZmaWW5EDML7lzJ8/n87OzrLTGBJ6fg9z5swpOZOhYcKECVx22WVlp2FWcy4ig9DZ2cnqx55k58Ejy06ldPv9MZv/a9XTL5acSfkatm7ecyOztygXkUHaefBIth07o+w0bAhpfGpp2SmYlcb3RMzMLLciZzZcKOklSY9VxL4iaYOk1ekzo2LbXEmdkn4r6ayKeEuKdUq6siJ+jKSHJK2TdKukA4o6FzMzq67InsjNQEuV+HURMTl9lgJImgScD7wv7XODpAZJDcB3gOnAJOCC1Bbg2nSsicDLwMUFnouZmVVRWBGJiAeAgd5xnAksjojtEfEM2RS5J6dPZ0Q8HRF/BBYDM9Oc6qcDt6f924Bz9+kJmJnZHpVxT+RSSWvS5a7DU2wM8EJFm/Up1ld8FPBKROzoFa9K0mxJHZI6urq69tV5mJnVvVoXkRuBdwOTgU3AP6V4tbnYI0e8qohYEBHNEdHc1NQ0uIzNzKxPNX3ENyLefKlA0veBO9PqemBcRdOxwMa0XC3+O+AwSSNSb6SyvZmZ1UhNeyKSjqpY/Uug58mtJcD5kg6UdAwwEXgYWAlMTE9iHUB2831JRARwH3Be2r8VuKMW52BmZn9SWE9E0k+ADwNHSFoPXAV8WNJksktPzwJ/CxARj0u6DXgC2AFcEhE703EuBVYADcDCiHg8fcUVwGJJXwceBW4q6lzMzKy6wopIRFxQJdznP/QRcQ1wTZX4UmC3V4Ij4mmyp7fMzKwkfmPdzMxycxExM7PcXETMzCw3FxEzM8vNRcTMzHJzETEzs9xcRMzMLDcXETMzy81FxMzMcnMRMTOz3FxEzMwsNxcRMzPLzUXEzMxycxExM7PcXETMzCw3FxEzM8utsCIiaaGklyQ9VhEbKald0rr08/AUl6R5kjolrZF0QsU+ran9OkmtFfETJa1N+8yTpKLOxczMqitsZkPgZuDbwKKK2JXAPRHxTUlXpvUrgOlk86pPBE4BbgROkTSSbFrdZrIpdVdJWhIRL6c2s4EHyWY+bAGWFXg+bNiwgYatW2h8areJFq2ONWztZsOGHWWnYVaKwnoiEfEAsLlXeCbQlpbbgHMr4osi8yBwmKSjgLOA9ojYnApHO9CSth0aEb+OiCArVOdiZmY1VWRPpJrREbEJICI2SToyxccAL1S0W59i/cXXV4lXJWk2Wa+Fo48+OnfyY8aM4f9tH8G2Y2fkPoa99TQ+tZQxY0aXnYZZKYbKjfVq9zMiR7yqiFgQEc0R0dzU1JQzRTMz663WReTFdCmK9POlFF8PjKtoNxbYuIf42CpxMzOroVoXkSVAzxNWrcAdFfFZ6SmtKcCWdNlrBTBN0uHpSa5pwIq07VVJU9JTWbMqjmVmZjVS2D0RST8BPgwcIWk92VNW3wRuk3Qx8DzwsdR8KTAD6AS2AhcBRMRmSV8DVqZ2V0dEz836z5A9AdZI9lRWoU9mmZnZ7gorIhFxQR+bzqjSNoBL+jjOQmBhlXgHcNze5GhmZntnqNxYNzOzYchFxMzMcnMRMTOz3FxEzMwst1q/sT7sNWzd7LGzgP3+4/cAvHHQoSVnUr6GrZsBv7Fu9clFZBAmTJhQdgpDRmfnqwBMeJf/8YTR/tuwuuUiMgiXXXZZ2SkMGXPmzAHg+uuvLzkTMyuT74mYmVluLiJmZpabi4iZmeXmImJmZrm5iJiZWW4uImZmlpuLiJmZ5eYiYmZmuZVSRCQ9K2mtpNWSOlJspKR2SevSz8NTXJLmSeqUtEbSCRXHaU3t10lq7ev7zMysGGX2RD4SEZMjojmtXwncExETgXvSOsB0YGL6zAZuhKzokM2WeApwMnBVT+ExM7PaGErDnswkm04XoA24H7gixRel2Q8flHSYpKNS2/ae6XIltQMtwE9qm3btzZ8/n87OzlJz6Pn+nuFPyjRhwgQPSWNWkrJ6IgHcJWmVpNkpNjoiNgGkn0em+BjghYp916dYX/HdSJotqUNSR1dX1z48jfrV2NhIY2Nj2WmYWcnK6omcGhEbJR0JtEt6qp+2qhKLfuK7ByMWAAsAmpubq7YZTvy/bjMbKkrpiUTExvTzJeBfye5pvJguU5F+vpSarwfGVew+FtjYT9zMzGqk5kVE0tskvb1nGZgGPAYsAXqesGoF7kjLS4BZ6SmtKcCWdLlrBTBN0uHphvq0FDMzsxop43LWaOBfJfV8/48jYrmklcBtki4Gngc+ltovBWYAncBW4CKAiNgs6WvAytTu6p6b7GZmVhvKHnqqH83NzdHR0VF2GmZmw4qkVRWvZLzJb6ybmVluLiJmZpabi4iZmeXmImJmZrnV3Y11SV3Ac2Xn8RZxBPC7spMw64P/Pvetd0ZEU+9g3RUR23ckdVR7WsNsKPDfZ234cpaZmeXmImJmZrm5iNjeWFB2Amb98N9nDfieiJmZ5eaeiJmZ5eYiYmZmubmI2G4kXS7pSUm37INjfXFf5GRmQ5Pvidhu0kyT0yPimYrYiIjYkeNYr0XEIfs0QbNE2ZwSiog3cu6f6+/a/sQ9EduFpO8C7wKWSNoiaYGku4BFkg6S9ENJayU9KukjaZ8LJf1M0nJJ6yT9rxT/JtAoafW+6NWYAUgan3rKNwCPAJ+S9GtJj0j6qaRDUrsvS1op6bH0d6wUv1/SNyT9AphT4qm8JbgnYruR9CzQDFwKnA2cFhHbJH0BOC4iLpJ0LHAX8B7gfODLwAeA7cBv0z4vuCdi+5qk8cDTwH8hm6zuZ2Q95z9IugI4MCKuljSyZ6I6ST8CbouIn0u6H3giIj5bygm8xbgnYnuyJCK2peXTgB8BRMRTZGOQvSdtuycitkTEfwBPAO+seaZWT56LiAeBKcAk4N8lrSabWrvnb+8jkh6StBY4HXhfxf631jTbt7Aypse14eUPFcvqp932iuWd+G/LitXzdymgPSIuqNwo6SDgBqA59Yi/AhxUZX/bS+6J2GA8AHwSQNJ7gKPJLl3153VJ+xedmNWtB4FTJU0AkHRw+tvsKRi/S/dIzisrwbc6FxEbjBuAhnR54FbgwojYvod9FgBrfGPdihARXcCFwE8krSErKsdGxCvA94G1wL8BK0tL8i3ON9bNzCw390TMzCw3FxEzM8vNRcTMzHJzETEzs9xcRMzMLDcXEbOcJL1D0u376FjjJT22L45VccwLJb2jYv0Hkibty+8w81vFZjlFxEaG9ktsFwKPARsBIuJ/lpqNvSW5J2J1SdJfSXo4jTD8PUkNkl6TdI2k30h6UNLo1PbdaX2lpKslvZbib/Ye+hrJOG2bVm2U2X5y62u05AZJ/zvF10i6LMV3G61W0nlkg2jeks6xMY1e25z2uSAd5zFJ11Z8d9XfgVlfXESs7kh6L/Bx4NSImEw21tcngbcBD0bE+8mGePmbtMv1wPURcRLpf/V9mJyOezzwcUnjJB0BfAmYGhEnAB3A3+0hxUsAIuJ44AKgLY0FNRs4BvhARPw50DMKwLcj4qSIOA5oBD4aEben7/pkREyuGESTdInrWrJBCScDJ0k6N23u63dgVpWLiNWjM4ATgZVp5NczyOZQ+SNwZ2qzChiflv8z8NO0/ON+jlttJOP+RpntS1+jJU8FvtsziVLPMOf0P1ptNScB90dEVzrWLcB/Tdv6+h2YVeV7IlaPBLRFxNxdgtLfx5/GAcozEnG1kYz7GmX2FOB7afXLwJpe+fWV9y7jFA1gtNq+jtOX1/fyd2B1xj0Rq0f3AOdJOhJA0khJ/fUOHgT+e1o+f5DfVXWU2Yh4KF1mmhwRS3rt09doyXcBn5Y0oidv+h+t9lXg7VVyegj4kKQjJDWQXTL7xSDPywxwEbE6FBFPkN2nuCuN/NoOHNXPLp8D/k7Sw6ndlkF8V9VRZvewW1+jJf8AeJ5sVOTfAJ/Yw2i1NwPf7bmxXpHTJmAucB/wG+CRiLhjoOdkVsmj+JrtgaSDgW0REZLOBy6IiJll52U2FPh6p9menQh8W5KAV4C/LjkfsyHDPREzM8vN90TMzCw3FxEzM8vNRcTMzHJzETEzs9xcRMzMLLf/D6YwSPoMxrFZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"engine-location\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here we see that the distribution of price between these two engine-location categories, front and rear, are distinct enough to take engine-location as a potential good predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine \"drive-wheels\" and \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fac9c89cd50>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# drive-wheels\n",
    "sns.boxplot(x=\"drive-wheels\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here we see that the distribution of price between the different drive-wheels categories differs; as such drive-wheels could potentially be a predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"discriptive_statistics\">3. Descriptive Statistical Analysis</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Let's first take a look at the variables by utilizing a description method.</p>\n",
    "\n",
    "<p>The <b>describe</b> function automatically computes basic statistics for all continuous variables. Any NaN values are automatically skipped in these statistics.</p>\n",
    "\n",
    "This will show:\n",
    "<ul>\n",
    "    <li>the count of that variable</li>\n",
    "    <li>the mean</li>\n",
    "    <li>the standard deviation (std)</li> \n",
    "    <li>the minimum value</li>\n",
    "    <li>the IQR (Interquartile Range: 25%, 50% and 75%)</li>\n",
    "    <li>the maximum value</li>\n",
    "<ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can apply the method \"describe\" as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>highway-L/100km</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "      <th>std</th>\n",
       "      <th>turbo</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.00000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mean</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>0.840796</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>98.797015</td>\n",
       "      <td>0.837102</td>\n",
       "      <td>0.915126</td>\n",
       "      <td>0.899108</td>\n",
       "      <td>2555.666667</td>\n",
       "      <td>126.875622</td>\n",
       "      <td>3.330692</td>\n",
       "      <td>3.256874</td>\n",
       "      <td>10.164279</td>\n",
       "      <td>103.402985</td>\n",
       "      <td>5117.665368</td>\n",
       "      <td>25.179104</td>\n",
       "      <td>30.686567</td>\n",
       "      <td>13207.129353</td>\n",
       "      <td>8.044957</td>\n",
       "      <td>9.944145</td>\n",
       "      <td>0.099502</td>\n",
       "      <td>0.900498</td>\n",
       "      <td>0.820896</td>\n",
       "      <td>0.179104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>58.167861</td>\n",
       "      <td>1.254802</td>\n",
       "      <td>31.99625</td>\n",
       "      <td>6.066366</td>\n",
       "      <td>0.059213</td>\n",
       "      <td>0.029187</td>\n",
       "      <td>0.040933</td>\n",
       "      <td>517.296727</td>\n",
       "      <td>41.546834</td>\n",
       "      <td>0.268072</td>\n",
       "      <td>0.316048</td>\n",
       "      <td>4.004965</td>\n",
       "      <td>37.365650</td>\n",
       "      <td>478.113805</td>\n",
       "      <td>6.423220</td>\n",
       "      <td>6.815150</td>\n",
       "      <td>7947.066342</td>\n",
       "      <td>1.840739</td>\n",
       "      <td>2.534599</td>\n",
       "      <td>0.300083</td>\n",
       "      <td>0.300083</td>\n",
       "      <td>0.384397</td>\n",
       "      <td>0.384397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>min</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-2.000000</td>\n",
       "      <td>65.00000</td>\n",
       "      <td>86.600000</td>\n",
       "      <td>0.678039</td>\n",
       "      <td>0.837500</td>\n",
       "      <td>0.799331</td>\n",
       "      <td>1488.000000</td>\n",
       "      <td>61.000000</td>\n",
       "      <td>2.540000</td>\n",
       "      <td>2.070000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>48.000000</td>\n",
       "      <td>4150.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>5118.000000</td>\n",
       "      <td>4.351852</td>\n",
       "      <td>4.795918</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25%</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>101.00000</td>\n",
       "      <td>94.500000</td>\n",
       "      <td>0.801538</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>0.869565</td>\n",
       "      <td>2169.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>3.150000</td>\n",
       "      <td>3.110000</td>\n",
       "      <td>8.600000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>4800.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>7775.000000</td>\n",
       "      <td>6.911765</td>\n",
       "      <td>7.833333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50%</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>97.000000</td>\n",
       "      <td>0.832292</td>\n",
       "      <td>0.909722</td>\n",
       "      <td>0.904682</td>\n",
       "      <td>2414.000000</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>3.310000</td>\n",
       "      <td>3.290000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>5125.369458</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>10295.000000</td>\n",
       "      <td>7.833333</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>75%</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>137.00000</td>\n",
       "      <td>102.400000</td>\n",
       "      <td>0.881788</td>\n",
       "      <td>0.925000</td>\n",
       "      <td>0.928094</td>\n",
       "      <td>2926.000000</td>\n",
       "      <td>141.000000</td>\n",
       "      <td>3.580000</td>\n",
       "      <td>3.410000</td>\n",
       "      <td>9.400000</td>\n",
       "      <td>116.000000</td>\n",
       "      <td>5500.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>16500.000000</td>\n",
       "      <td>9.400000</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>max</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>256.00000</td>\n",
       "      <td>120.900000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4066.000000</td>\n",
       "      <td>326.000000</td>\n",
       "      <td>3.940000</td>\n",
       "      <td>4.170000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>262.000000</td>\n",
       "      <td>6600.000000</td>\n",
       "      <td>49.000000</td>\n",
       "      <td>54.000000</td>\n",
       "      <td>45400.000000</td>\n",
       "      <td>14.687500</td>\n",
       "      <td>18.076923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Unnamed: 0   symboling  normalized-losses  wheel-base      length  \\\n",
       "count  201.000000  201.000000          201.00000  201.000000  201.000000   \n",
       "mean   100.000000    0.840796          122.00000   98.797015    0.837102   \n",
       "std     58.167861    1.254802           31.99625    6.066366    0.059213   \n",
       "min      0.000000   -2.000000           65.00000   86.600000    0.678039   \n",
       "25%     50.000000    0.000000          101.00000   94.500000    0.801538   \n",
       "50%    100.000000    1.000000          122.00000   97.000000    0.832292   \n",
       "75%    150.000000    2.000000          137.00000  102.400000    0.881788   \n",
       "max    200.000000    3.000000          256.00000  120.900000    1.000000   \n",
       "\n",
       "            width      height  curb-weight  engine-size        bore  \\\n",
       "count  201.000000  201.000000   201.000000   201.000000  201.000000   \n",
       "mean     0.915126    0.899108  2555.666667   126.875622    3.330692   \n",
       "std      0.029187    0.040933   517.296727    41.546834    0.268072   \n",
       "min      0.837500    0.799331  1488.000000    61.000000    2.540000   \n",
       "25%      0.890278    0.869565  2169.000000    98.000000    3.150000   \n",
       "50%      0.909722    0.904682  2414.000000   120.000000    3.310000   \n",
       "75%      0.925000    0.928094  2926.000000   141.000000    3.580000   \n",
       "max      1.000000    1.000000  4066.000000   326.000000    3.940000   \n",
       "\n",
       "           stroke  compression-ratio  horsepower     peak-rpm    city-mpg  \\\n",
       "count  201.000000         201.000000  201.000000   201.000000  201.000000   \n",
       "mean     3.256874          10.164279  103.402985  5117.665368   25.179104   \n",
       "std      0.316048           4.004965   37.365650   478.113805    6.423220   \n",
       "min      2.070000           7.000000   48.000000  4150.000000   13.000000   \n",
       "25%      3.110000           8.600000   70.000000  4800.000000   19.000000   \n",
       "50%      3.290000           9.000000   95.000000  5125.369458   24.000000   \n",
       "75%      3.410000           9.400000  116.000000  5500.000000   30.000000   \n",
       "max      4.170000          23.000000  262.000000  6600.000000   49.000000   \n",
       "\n",
       "       highway-mpg         price  highway-L/100km  city-L/100km      diesel  \\\n",
       "count   201.000000    201.000000       201.000000    201.000000  201.000000   \n",
       "mean     30.686567  13207.129353         8.044957      9.944145    0.099502   \n",
       "std       6.815150   7947.066342         1.840739      2.534599    0.300083   \n",
       "min      16.000000   5118.000000         4.351852      4.795918    0.000000   \n",
       "25%      25.000000   7775.000000         6.911765      7.833333    0.000000   \n",
       "50%      30.000000  10295.000000         7.833333      9.791667    0.000000   \n",
       "75%      34.000000  16500.000000         9.400000     12.368421    0.000000   \n",
       "max      54.000000  45400.000000        14.687500     18.076923    1.000000   \n",
       "\n",
       "              gas         std       turbo  \n",
       "count  201.000000  201.000000  201.000000  \n",
       "mean     0.900498    0.820896    0.179104  \n",
       "std      0.300083    0.384397    0.384397  \n",
       "min      0.000000    0.000000    0.000000  \n",
       "25%      1.000000    1.000000    0.000000  \n",
       "50%      1.000000    1.000000    0.000000  \n",
       "75%      1.000000    1.000000    0.000000  \n",
       "max      1.000000    1.000000    1.000000  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The default setting of \"describe\" skips variables of type object. We can apply the method \"describe\" on the variables of type 'object' as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>make</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>engine-type</th>\n",
       "      <th>num-of-cylinders</th>\n",
       "      <th>fuel-system</th>\n",
       "      <th>horsepower-binned</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>unique</td>\n",
       "      <td>22</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>top</td>\n",
       "      <td>toyota</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>ohc</td>\n",
       "      <td>four</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>Low HP</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>freq</td>\n",
       "      <td>32</td>\n",
       "      <td>115</td>\n",
       "      <td>94</td>\n",
       "      <td>118</td>\n",
       "      <td>198</td>\n",
       "      <td>145</td>\n",
       "      <td>157</td>\n",
       "      <td>92</td>\n",
       "      <td>153</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          make num-of-doors body-style drive-wheels engine-location  \\\n",
       "count      201          201        201          201             201   \n",
       "unique      22            2          5            3               2   \n",
       "top     toyota         four      sedan          fwd           front   \n",
       "freq        32          115         94          118             198   \n",
       "\n",
       "       engine-type num-of-cylinders fuel-system horsepower-binned  \n",
       "count          201              201         201               201  \n",
       "unique           6                7           8                 3  \n",
       "top            ohc             four        mpfi            Low HP  \n",
       "freq           145              157          92               153  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=['object'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Value Counts</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Value-counts is a good way of understanding how many units of each characteristic/variable we have. We can apply the \"value_counts\" method on the column 'drive-wheels'. Don’t forget the method \"value_counts\" only works on Pandas series, not Pandas Dataframes. As a result, we only include one bracket \"df['drive-wheels']\" not two brackets \"df[['drive-wheels']]\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can convert the series to a Dataframe as follows :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>fwd</td>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>rwd</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4wd</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     drive-wheels\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts().to_frame()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the above steps but save the results to the dataframe \"drive_wheels_counts\" and rename the column  'drive-wheels' to 'value_counts'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>fwd</td>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>rwd</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4wd</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     value_counts\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts = df['drive-wheels'].value_counts().to_frame()\n",
    "drive_wheels_counts.rename(columns={'drive-wheels': 'value_counts'}, inplace=True)\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Now let's rename the index to 'drive-wheels':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>fwd</td>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>rwd</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4wd</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              value_counts\n",
       "drive-wheels              \n",
       "fwd                    118\n",
       "rwd                     75\n",
       "4wd                      8"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts.index.name = 'drive-wheels'\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can repeat the above process for the variable 'engine-location'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-location</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>front</td>\n",
       "      <td>198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>rear</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 value_counts\n",
       "engine-location              \n",
       "front                     198\n",
       "rear                        3"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# engine-location as variable\n",
    "engine_loc_counts = df['engine-location'].value_counts().to_frame()\n",
    "engine_loc_counts.rename(columns={'engine-location': 'value_counts'}, inplace=True)\n",
    "engine_loc_counts.index.name = 'engine-location'\n",
    "engine_loc_counts.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Examining the value counts of the engine location would not be a good predictor variable for the price. This is because we only have three cars with a rear engine and 198 with an engine in the front, this result is skewed. Thus, we are not able to draw any conclusions about the engine location.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"basic_grouping\">4. Basics of Grouping</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The \"groupby\" method groups data by different categories. The data is grouped based on one or several variables and analysis is performed on the individual groups.</p>\n",
    "\n",
    "<p>For example, let's group by the variable \"drive-wheels\". We see that there are 3 different categories of drive wheels.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>If we want to know, on average, which type of drive wheel is most valuable, we can group \"drive-wheels\" and then average them.</p>\n",
    "\n",
    "<p>We can select the columns 'drive-wheels', 'body-style' and 'price', then assign it to the variable \"df_group_one\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_group_one = df[['drive-wheels','body-style','price']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then calculate the average price for each of the different categories of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>4wd</td>\n",
       "      <td>10241.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9244.779661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>rwd</td>\n",
       "      <td>19757.613333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  drive-wheels         price\n",
       "0          4wd  10241.000000\n",
       "1          fwd   9244.779661\n",
       "2          rwd  19757.613333"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_group_one = df_group_one.groupby(['drive-wheels'],as_index=False).mean()\n",
    "df_group_one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From our data, it seems rear-wheel drive vehicles are, on average, the most expensive, while 4-wheel and front-wheel are approximately the same in price.</p>\n",
    "\n",
    "<p>You can also group with multiple variables. For example, let's group by both 'drive-wheels' and 'body-style'. This groups the dataframe by the unique combinations 'drive-wheels' and 'body-style'. We can store the results in the variable 'grouped_test1'.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>4wd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7603.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12647.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>4wd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>fwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>8249.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8396.387755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9811.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>23949.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>24202.714286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>14337.777778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21711.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   drive-wheels   body-style         price\n",
       "0           4wd    hatchback   7603.000000\n",
       "1           4wd        sedan  12647.333333\n",
       "2           4wd        wagon   9095.750000\n",
       "3           fwd  convertible  11595.000000\n",
       "4           fwd      hardtop   8249.000000\n",
       "5           fwd    hatchback   8396.387755\n",
       "6           fwd        sedan   9811.800000\n",
       "7           fwd        wagon   9997.333333\n",
       "8           rwd  convertible  23949.600000\n",
       "9           rwd      hardtop  24202.714286\n",
       "10          rwd    hatchback  14337.777778\n",
       "11          rwd        sedan  21711.833333\n",
       "12          rwd        wagon  16994.222222"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_gptest = df[['drive-wheels','body-style','price']]\n",
    "grouped_test1 = df_gptest.groupby(['drive-wheels','body-style'],as_index=False).mean()\n",
    "grouped_test1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This grouped data is much easier to visualize when it is made into a pivot table. A pivot table is like an Excel spreadsheet, with one variable along the column and another along the row. We can convert the dataframe to a pivot table using the method \"pivot \" to create a pivot table from the groups.</p>\n",
    "\n",
    "<p>In this case, we will leave the drive-wheel variable as the rows of the table, and pivot body-style to become the columns of the table:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>4wd</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>fwd</td>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>rwd</td>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  NaN           NaN   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_test1.pivot(index='drive-wheels',columns='body-style')\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <td>drive-wheels</td>\n",
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       "      <td>4wd</td>\n",
       "      <td>4wd</td>\n",
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       "      <td>fwd</td>\n",
       "      <td>fwd</td>\n",
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       "      <td>rwd</td>\n",
       "      <td>rwd</td>\n",
       "      <td>rwd</td>\n",
       "      <td>rwd</td>\n",
       "      <td>rwd</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>body-style</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>sedan</td>\n",
       "      <td>wagon</td>\n",
       "      <td>convertible</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>sedan</td>\n",
       "      <td>wagon</td>\n",
       "      <td>convertible</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>sedan</td>\n",
       "      <td>wagon</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\n",
       "      <td>7603</td>\n",
       "      <td>12647.3</td>\n",
       "      <td>9095.75</td>\n",
       "      <td>11595</td>\n",
       "      <td>8249</td>\n",
       "      <td>8396.39</td>\n",
       "      <td>9811.8</td>\n",
       "      <td>9997.33</td>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.7</td>\n",
       "      <td>14337.8</td>\n",
       "      <td>21711.8</td>\n",
       "      <td>16994.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     0        1        2            3        4          5   \\\n",
       "drive-wheels        4wd      4wd      4wd          fwd      fwd        fwd   \n",
       "body-style    hatchback    sedan    wagon  convertible  hardtop  hatchback   \n",
       "price              7603  12647.3  9095.75        11595     8249    8396.39   \n",
       "\n",
       "                  6        7            8        9          10       11  \\\n",
       "drive-wheels     fwd      fwd          rwd      rwd        rwd      rwd   \n",
       "body-style     sedan    wagon  convertible  hardtop  hatchback    sedan   \n",
       "price         9811.8  9997.33      23949.6  24202.7    14337.8  21711.8   \n",
       "\n",
       "                   12  \n",
       "drive-wheels      rwd  \n",
       "body-style      wagon  \n",
       "price         16994.2  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test1.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Often, we won't have data for some of the pivot cells. We can fill these missing cells with the value 0, but any other value could potentially be used as well. It should be mentioned that missing data is quite a complex subject and is an entire course on its own.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
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       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
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       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
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       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>4wd</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>fwd</td>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>rwd</td>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  0.0      0.000000   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_pivot.fillna(0) #fill missing values with 0\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>convertible</td>\n",
       "      <td>21890.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>22208.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9957.441176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>sedan</td>\n",
       "      <td>14459.755319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>wagon</td>\n",
       "      <td>12371.960000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    body-style         price\n",
       "0  convertible  21890.500000\n",
       "1      hardtop  22208.500000\n",
       "2    hatchback   9957.441176\n",
       "3        sedan  14459.755319\n",
       "4        wagon  12371.960000"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_gptesta = df[['body-style','price']]\n",
    "grouped_test2 = df_gptesta.groupby(['body-style'],as_index=False).mean()\n",
    "grouped_test2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you did not import \"pyplot\" let's do it again. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Variables: Drive Wheels and Body Style vs Price</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use a heat map to visualize the relationship between Body Style vs Price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>4wd</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>fwd</td>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>rwd</td>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  0.0      0.000000   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['convertible', 'hardtop', 'hatchback', 'sedan', 'wagon'], dtype='object', name='body-style')"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot.columns.levels[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'drive-wheels'"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot.index.name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#use the grouped results\n",
    "plt.pcolor(grouped_pivot, cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The heatmap plots the target variable (price) proportional to colour with respect to the variables 'drive-wheel' and 'body-style' in the vertical and horizontal axis respectively. This allows us to visualize how the price is related to 'drive-wheel' and 'body-style'.</p>\n",
    "\n",
    "<p>The default labels convey no useful information to us. Let's change that:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.pcolor(grouped_pivot, cmap='RdBu')\n",
    "\n",
    "#label names\n",
    "row_labels = grouped_pivot.columns.levels[1]\n",
    "col_labels = grouped_pivot.index\n",
    "\n",
    "#move ticks and labels to the center\n",
    "ax.set_xticks(np.arange(grouped_pivot.shape[1]) + 0.5, minor=False)\n",
    "ax.set_yticks(np.arange(grouped_pivot.shape[0]) + 0.5, minor=False)\n",
    "\n",
    "#insert labels\n",
    "ax.set_xticklabels(row_labels, minor=False)\n",
    "ax.set_yticklabels(col_labels, minor=False)\n",
    "\n",
    "#rotate label if too long\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "fig.colorbar(im)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Visualization is very important in data science, and Python visualization packages provide great freedom. We will go more in-depth in a separate Python Visualizations course.</p>\n",
    "\n",
    "<p>The main question we want to answer in this module, is \"What are the main characteristics which have the most impact on the car price?\".</p>\n",
    "\n",
    "<p>To get a better measure of the important characteristics, we look at the correlation of these variables with the car price, in other words: how is the car price dependent on this variable?</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"correlation_causation\">5. Correlation and Causation</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Correlation</b>: a measure of the extent of interdependence between variables.</p>\n",
    "\n",
    "<p><b>Causation</b>: the relationship between cause and effect between two variables.</p>\n",
    "\n",
    "<p>It is important to know the difference between these two and that correlation does not imply causation. Determining correlation is much simpler  the determining causation as causation may require independent experimentation.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p3>Pearson Correlation</p>\n",
    "<p>The Pearson Correlation measures the linear dependence between two variables X and Y.</p>\n",
    "<p>The resulting coefficient is a value between -1 and 1 inclusive, where:</p>\n",
    "<ul>\n",
    "    <li><b>1</b>: Total positive linear correlation.</li>\n",
    "    <li><b>0</b>: No linear correlation, the two variables most likely do not affect each other.</li>\n",
    "    <li><b>-1</b>: Total negative linear correlation.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Pearson Correlation is the default method of the function \"corr\".  Like before we can calculate the Pearson Correlation of the of the 'int64' or 'float64'  variables.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>highway-L/100km</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "      <th>std</th>\n",
       "      <th>turbo</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <td>Unnamed: 0</td>\n",
       "      <td>1.000000</td>\n",
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       "      <td>0.125517</td>\n",
       "      <td>0.161848</td>\n",
       "      <td>0.043976</td>\n",
       "      <td>0.252015</td>\n",
       "      <td>0.064820</td>\n",
       "      <td>-0.047764</td>\n",
       "      <td>0.244734</td>\n",
       "      <td>-0.162490</td>\n",
       "      <td>0.144301</td>\n",
       "      <td>-0.022505</td>\n",
       "      <td>-0.195662</td>\n",
       "      <td>0.027956</td>\n",
       "      <td>0.020344</td>\n",
       "      <td>-0.118214</td>\n",
       "      <td>-0.078346</td>\n",
       "      <td>-0.099157</td>\n",
       "      <td>0.121454</td>\n",
       "      <td>-0.121454</td>\n",
       "      <td>-0.082739</td>\n",
       "      <td>0.082739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>symboling</td>\n",
       "      <td>-0.162764</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008153</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075810</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>-0.029807</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.054615</td>\n",
       "      <td>-0.054615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>normalized-losses</td>\n",
       "      <td>-0.241092</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055045</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217300</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.181189</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>0.006911</td>\n",
       "      <td>-0.006911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>wheel-base</td>\n",
       "      <td>0.125517</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158018</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371178</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.577576</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.256889</td>\n",
       "      <td>0.256889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>length</td>\n",
       "      <td>0.161848</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.123952</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579795</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.707108</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.230085</td>\n",
       "      <td>0.230085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>width</td>\n",
       "      <td>0.043976</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188822</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615056</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.736728</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.305732</td>\n",
       "      <td>0.305732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>height</td>\n",
       "      <td>0.252015</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.060663</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087001</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.084301</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.090336</td>\n",
       "      <td>0.090336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>curb-weight</td>\n",
       "      <td>0.064820</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167438</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757981</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.836921</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.321955</td>\n",
       "      <td>0.321955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>engine-size</td>\n",
       "      <td>-0.047764</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.205928</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822668</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.783465</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.110040</td>\n",
       "      <td>0.110040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>bore</td>\n",
       "      <td>0.244734</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566903</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.559112</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.227816</td>\n",
       "      <td>0.227816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>stroke</td>\n",
       "      <td>-0.162490</td>\n",
       "      <td>-0.008153</td>\n",
       "      <td>0.055045</td>\n",
       "      <td>0.158018</td>\n",
       "      <td>0.123952</td>\n",
       "      <td>0.188822</td>\n",
       "      <td>-0.060663</td>\n",
       "      <td>0.167438</td>\n",
       "      <td>0.205928</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187871</td>\n",
       "      <td>0.098128</td>\n",
       "      <td>-0.063561</td>\n",
       "      <td>-0.033956</td>\n",
       "      <td>-0.034636</td>\n",
       "      <td>0.082269</td>\n",
       "      <td>0.047089</td>\n",
       "      <td>0.036133</td>\n",
       "      <td>0.241064</td>\n",
       "      <td>-0.241064</td>\n",
       "      <td>-0.218233</td>\n",
       "      <td>0.218233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>compression-ratio</td>\n",
       "      <td>0.144301</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187871</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214489</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.223361</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>-0.307522</td>\n",
       "      <td>0.307522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>horsepower</td>\n",
       "      <td>-0.022505</td>\n",
       "      <td>0.075810</td>\n",
       "      <td>0.217300</td>\n",
       "      <td>0.371178</td>\n",
       "      <td>0.579795</td>\n",
       "      <td>0.615056</td>\n",
       "      <td>-0.087001</td>\n",
       "      <td>0.757981</td>\n",
       "      <td>0.822668</td>\n",
       "      <td>0.566903</td>\n",
       "      <td>0.098128</td>\n",
       "      <td>-0.214489</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107884</td>\n",
       "      <td>-0.822192</td>\n",
       "      <td>-0.804579</td>\n",
       "      <td>0.809607</td>\n",
       "      <td>0.840627</td>\n",
       "      <td>0.889482</td>\n",
       "      <td>-0.169030</td>\n",
       "      <td>0.169030</td>\n",
       "      <td>-0.251159</td>\n",
       "      <td>0.251159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>peak-rpm</td>\n",
       "      <td>-0.195662</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.063561</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107884</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.017694</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>0.190057</td>\n",
       "      <td>-0.190057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>city-mpg</td>\n",
       "      <td>0.027956</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.033956</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822192</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.909024</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>0.189237</td>\n",
       "      <td>-0.189237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>highway-mpg</td>\n",
       "      <td>0.020344</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.034636</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804579</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.951100</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>0.241851</td>\n",
       "      <td>-0.241851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\n",
       "      <td>-0.118214</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082269</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809607</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.801118</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>-0.179578</td>\n",
       "      <td>0.179578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>highway-L/100km</td>\n",
       "      <td>-0.078346</td>\n",
       "      <td>-0.029807</td>\n",
       "      <td>0.181189</td>\n",
       "      <td>0.577576</td>\n",
       "      <td>0.707108</td>\n",
       "      <td>0.736728</td>\n",
       "      <td>0.084301</td>\n",
       "      <td>0.836921</td>\n",
       "      <td>0.783465</td>\n",
       "      <td>0.559112</td>\n",
       "      <td>0.047089</td>\n",
       "      <td>-0.223361</td>\n",
       "      <td>0.840627</td>\n",
       "      <td>0.017694</td>\n",
       "      <td>-0.909024</td>\n",
       "      <td>-0.951100</td>\n",
       "      <td>0.801118</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.958306</td>\n",
       "      <td>-0.158091</td>\n",
       "      <td>0.158091</td>\n",
       "      <td>-0.210720</td>\n",
       "      <td>0.210720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>city-L/100km</td>\n",
       "      <td>-0.099157</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.036133</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889482</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.958306</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-0.157578</td>\n",
       "      <td>0.157578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>diesel</td>\n",
       "      <td>0.121454</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241064</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169030</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.158091</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-0.408228</td>\n",
       "      <td>0.408228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>gas</td>\n",
       "      <td>-0.121454</td>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241064</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169030</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.158091</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.408228</td>\n",
       "      <td>-0.408228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>-0.082739</td>\n",
       "      <td>0.054615</td>\n",
       "      <td>0.006911</td>\n",
       "      <td>-0.256889</td>\n",
       "      <td>-0.230085</td>\n",
       "      <td>-0.305732</td>\n",
       "      <td>-0.090336</td>\n",
       "      <td>-0.321955</td>\n",
       "      <td>-0.110040</td>\n",
       "      <td>-0.227816</td>\n",
       "      <td>-0.218233</td>\n",
       "      <td>-0.307522</td>\n",
       "      <td>-0.251159</td>\n",
       "      <td>0.190057</td>\n",
       "      <td>0.189237</td>\n",
       "      <td>0.241851</td>\n",
       "      <td>-0.179578</td>\n",
       "      <td>-0.210720</td>\n",
       "      <td>-0.157578</td>\n",
       "      <td>-0.408228</td>\n",
       "      <td>0.408228</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>turbo</td>\n",
       "      <td>0.082739</td>\n",
       "      <td>-0.054615</td>\n",
       "      <td>-0.006911</td>\n",
       "      <td>0.256889</td>\n",
       "      <td>0.230085</td>\n",
       "      <td>0.305732</td>\n",
       "      <td>0.090336</td>\n",
       "      <td>0.321955</td>\n",
       "      <td>0.110040</td>\n",
       "      <td>0.227816</td>\n",
       "      <td>0.218233</td>\n",
       "      <td>0.307522</td>\n",
       "      <td>0.251159</td>\n",
       "      <td>-0.190057</td>\n",
       "      <td>-0.189237</td>\n",
       "      <td>-0.241851</td>\n",
       "      <td>0.179578</td>\n",
       "      <td>0.210720</td>\n",
       "      <td>0.157578</td>\n",
       "      <td>0.408228</td>\n",
       "      <td>-0.408228</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Unnamed: 0  symboling  normalized-losses  wheel-base  \\\n",
       "Unnamed: 0           1.000000  -0.162764          -0.241092    0.125517   \n",
       "symboling           -0.162764   1.000000           0.466264   -0.535987   \n",
       "normalized-losses   -0.241092   0.466264           1.000000   -0.056661   \n",
       "wheel-base           0.125517  -0.535987          -0.056661    1.000000   \n",
       "length               0.161848  -0.365404           0.019424    0.876024   \n",
       "width                0.043976  -0.242423           0.086802    0.814507   \n",
       "height               0.252015  -0.550160          -0.373737    0.590742   \n",
       "curb-weight          0.064820  -0.233118           0.099404    0.782097   \n",
       "engine-size         -0.047764  -0.110581           0.112360    0.572027   \n",
       "bore                 0.244734  -0.140019          -0.029862    0.493244   \n",
       "stroke              -0.162490  -0.008153           0.055045    0.158018   \n",
       "compression-ratio    0.144301  -0.182196          -0.114713    0.250313   \n",
       "horsepower          -0.022505   0.075810           0.217300    0.371178   \n",
       "peak-rpm            -0.195662   0.279740           0.239543   -0.360305   \n",
       "city-mpg             0.027956  -0.035527          -0.225016   -0.470606   \n",
       "highway-mpg          0.020344   0.036233          -0.181877   -0.543304   \n",
       "price               -0.118214  -0.082391           0.133999    0.584642   \n",
       "highway-L/100km     -0.078346  -0.029807           0.181189    0.577576   \n",
       "city-L/100km        -0.099157   0.066171           0.238567    0.476153   \n",
       "diesel               0.121454  -0.196735          -0.101546    0.307237   \n",
       "gas                 -0.121454   0.196735           0.101546   -0.307237   \n",
       "std                 -0.082739   0.054615           0.006911   -0.256889   \n",
       "turbo                0.082739  -0.054615          -0.006911    0.256889   \n",
       "\n",
       "                     length     width    height  curb-weight  engine-size  \\\n",
       "Unnamed: 0         0.161848  0.043976  0.252015     0.064820    -0.047764   \n",
       "symboling         -0.365404 -0.242423 -0.550160    -0.233118    -0.110581   \n",
       "normalized-losses  0.019424  0.086802 -0.373737     0.099404     0.112360   \n",
       "wheel-base         0.876024  0.814507  0.590742     0.782097     0.572027   \n",
       "length             1.000000  0.857170  0.492063     0.880665     0.685025   \n",
       "width              0.857170  1.000000  0.306002     0.866201     0.729436   \n",
       "height             0.492063  0.306002  1.000000     0.307581     0.074694   \n",
       "curb-weight        0.880665  0.866201  0.307581     1.000000     0.849072   \n",
       "engine-size        0.685025  0.729436  0.074694     0.849072     1.000000   \n",
       "bore               0.608971  0.544885  0.180449     0.644060     0.572609   \n",
       "stroke             0.123952  0.188822 -0.060663     0.167438     0.205928   \n",
       "compression-ratio  0.159733  0.189867  0.259737     0.156433     0.028889   \n",
       "horsepower         0.579795  0.615056 -0.087001     0.757981     0.822668   \n",
       "peak-rpm          -0.285970 -0.245800 -0.309974    -0.279361    -0.256733   \n",
       "city-mpg          -0.665192 -0.633531 -0.049800    -0.749543    -0.650546   \n",
       "highway-mpg       -0.698142 -0.680635 -0.104812    -0.794889    -0.679571   \n",
       "price              0.690628  0.751265  0.135486     0.834415     0.872335   \n",
       "highway-L/100km    0.707108  0.736728  0.084301     0.836921     0.783465   \n",
       "city-L/100km       0.657373  0.673363  0.003811     0.785353     0.745059   \n",
       "diesel             0.211187  0.244356  0.281578     0.221046     0.070779   \n",
       "gas               -0.211187 -0.244356 -0.281578    -0.221046    -0.070779   \n",
       "std               -0.230085 -0.305732 -0.090336    -0.321955    -0.110040   \n",
       "turbo              0.230085  0.305732  0.090336     0.321955     0.110040   \n",
       "\n",
       "                       bore    stroke  compression-ratio  horsepower  \\\n",
       "Unnamed: 0         0.244734 -0.162490           0.144301   -0.022505   \n",
       "symboling         -0.140019 -0.008153          -0.182196    0.075810   \n",
       "normalized-losses -0.029862  0.055045          -0.114713    0.217300   \n",
       "wheel-base         0.493244  0.158018           0.250313    0.371178   \n",
       "length             0.608971  0.123952           0.159733    0.579795   \n",
       "width              0.544885  0.188822           0.189867    0.615056   \n",
       "height             0.180449 -0.060663           0.259737   -0.087001   \n",
       "curb-weight        0.644060  0.167438           0.156433    0.757981   \n",
       "engine-size        0.572609  0.205928           0.028889    0.822668   \n",
       "bore               1.000000 -0.055390           0.001263    0.566903   \n",
       "stroke            -0.055390  1.000000           0.187871    0.098128   \n",
       "compression-ratio  0.001263  0.187871           1.000000   -0.214489   \n",
       "horsepower         0.566903  0.098128          -0.214489    1.000000   \n",
       "peak-rpm          -0.267392 -0.063561          -0.435780    0.107884   \n",
       "city-mpg          -0.582027 -0.033956           0.331425   -0.822192   \n",
       "highway-mpg       -0.591309 -0.034636           0.268465   -0.804579   \n",
       "price              0.543155  0.082269           0.071107    0.809607   \n",
       "highway-L/100km    0.559112  0.047089          -0.223361    0.840627   \n",
       "city-L/100km       0.554610  0.036133          -0.299372    0.889482   \n",
       "diesel             0.054458  0.241064           0.985231   -0.169030   \n",
       "gas               -0.054458 -0.241064          -0.985231    0.169030   \n",
       "std               -0.227816 -0.218233          -0.307522   -0.251159   \n",
       "turbo              0.227816  0.218233           0.307522    0.251159   \n",
       "\n",
       "                   peak-rpm  city-mpg  highway-mpg     price  highway-L/100km  \\\n",
       "Unnamed: 0        -0.195662  0.027956     0.020344 -0.118214        -0.078346   \n",
       "symboling          0.279740 -0.035527     0.036233 -0.082391        -0.029807   \n",
       "normalized-losses  0.239543 -0.225016    -0.181877  0.133999         0.181189   \n",
       "wheel-base        -0.360305 -0.470606    -0.543304  0.584642         0.577576   \n",
       "length            -0.285970 -0.665192    -0.698142  0.690628         0.707108   \n",
       "width             -0.245800 -0.633531    -0.680635  0.751265         0.736728   \n",
       "height            -0.309974 -0.049800    -0.104812  0.135486         0.084301   \n",
       "curb-weight       -0.279361 -0.749543    -0.794889  0.834415         0.836921   \n",
       "engine-size       -0.256733 -0.650546    -0.679571  0.872335         0.783465   \n",
       "bore              -0.267392 -0.582027    -0.591309  0.543155         0.559112   \n",
       "stroke            -0.063561 -0.033956    -0.034636  0.082269         0.047089   \n",
       "compression-ratio -0.435780  0.331425     0.268465  0.071107        -0.223361   \n",
       "horsepower         0.107884 -0.822192    -0.804579  0.809607         0.840627   \n",
       "peak-rpm           1.000000 -0.115413    -0.058598 -0.101616         0.017694   \n",
       "city-mpg          -0.115413  1.000000     0.972044 -0.686571        -0.909024   \n",
       "highway-mpg       -0.058598  0.972044     1.000000 -0.704692        -0.951100   \n",
       "price             -0.101616 -0.686571    -0.704692  1.000000         0.801118   \n",
       "highway-L/100km    0.017694 -0.909024    -0.951100  0.801118         1.000000   \n",
       "city-L/100km       0.115830 -0.949713    -0.930028  0.789898         0.958306   \n",
       "diesel            -0.475812  0.265676     0.198690  0.110326        -0.158091   \n",
       "gas                0.475812 -0.265676    -0.198690 -0.110326         0.158091   \n",
       "std                0.190057  0.189237     0.241851 -0.179578        -0.210720   \n",
       "turbo             -0.190057 -0.189237    -0.241851  0.179578         0.210720   \n",
       "\n",
       "                   city-L/100km    diesel       gas       std     turbo  \n",
       "Unnamed: 0            -0.099157  0.121454 -0.121454 -0.082739  0.082739  \n",
       "symboling              0.066171 -0.196735  0.196735  0.054615 -0.054615  \n",
       "normalized-losses      0.238567 -0.101546  0.101546  0.006911 -0.006911  \n",
       "wheel-base             0.476153  0.307237 -0.307237 -0.256889  0.256889  \n",
       "length                 0.657373  0.211187 -0.211187 -0.230085  0.230085  \n",
       "width                  0.673363  0.244356 -0.244356 -0.305732  0.305732  \n",
       "height                 0.003811  0.281578 -0.281578 -0.090336  0.090336  \n",
       "curb-weight            0.785353  0.221046 -0.221046 -0.321955  0.321955  \n",
       "engine-size            0.745059  0.070779 -0.070779 -0.110040  0.110040  \n",
       "bore                   0.554610  0.054458 -0.054458 -0.227816  0.227816  \n",
       "stroke                 0.036133  0.241064 -0.241064 -0.218233  0.218233  \n",
       "compression-ratio     -0.299372  0.985231 -0.985231 -0.307522  0.307522  \n",
       "horsepower             0.889482 -0.169030  0.169030 -0.251159  0.251159  \n",
       "peak-rpm               0.115830 -0.475812  0.475812  0.190057 -0.190057  \n",
       "city-mpg              -0.949713  0.265676 -0.265676  0.189237 -0.189237  \n",
       "highway-mpg           -0.930028  0.198690 -0.198690  0.241851 -0.241851  \n",
       "price                  0.789898  0.110326 -0.110326 -0.179578  0.179578  \n",
       "highway-L/100km        0.958306 -0.158091  0.158091 -0.210720  0.210720  \n",
       "city-L/100km           1.000000 -0.241282  0.241282 -0.157578  0.157578  \n",
       "diesel                -0.241282  1.000000 -1.000000 -0.408228  0.408228  \n",
       "gas                    0.241282 -1.000000  1.000000  0.408228 -0.408228  \n",
       "std                   -0.157578 -0.408228  0.408228  1.000000 -1.000000  \n",
       "turbo                  0.157578  0.408228 -0.408228 -1.000000  1.000000  "
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " sometimes we would like to know the significant of the correlation estimate. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>P-value</b>: \n",
    "<p>What is this P-value? The P-value is the probability value that the correlation between these two variables is statistically significant. Normally, we choose a significance level of 0.05, which means that we are 95% confident that the correlation between the variables is significant.</p>\n",
    "\n",
    "By convention, when the\n",
    "<ul>\n",
    "    <li>p-value is $<$ 0.001: we say there is strong evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.05: there is moderate evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.1: there is weak evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $>$ 0.1: there is no evidence that the correlation is significant.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain this information using  \"stats\" module in the \"scipy\"  library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Wheel-base vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'wheel-base' and 'price'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.584641822265508\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['wheel-base'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef)  \n",
    "print (round(p_value, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between wheel-base and price is statistically significant, although the linear relationship isn't extremely strong (~0.585)</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Horsepower vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'horsepower' and 'price'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8096068016571054  with a P-value of P =  6.273536270650504e-48\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['horsepower'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between horsepower and price is statistically significant, and the linear relationship is quite strong (~0.809, close to 1)</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Length vs Price</h3>\n",
    "\n",
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'length' and 'price'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.6906283804483639  with a P-value of P =  8.016477466159328e-30\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['length'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between length and price is statistically significant, and the linear relationship is moderately strong (~0.691).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Width vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'width' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522675  with a P-value of P = 9.200335510481123e-38\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['width'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "\n",
    "Since the p-value is < 0.001, the correlation between width and price is statistically significant, and the linear relationship is quite strong (~0.751)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curb-weight vs Price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'curb-weight' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702844  with a P-value of P =  2.189577238893878e-53\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['curb-weight'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between curb-weight and price is statistically significant, and the linear relationship is quite strong (~0.834).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Engine-size vs Price</h3>\n",
    "\n",
    "Let's calculate the Pearson Correlation Coefficient and P-value of 'engine-size' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['engine-size'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between engine-size and price is statistically significant, and the linear relationship is very strong (~0.872).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Bore vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'bore' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5431553832626602  with a P-value of P =   8.049189483935489e-17\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['bore'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =  \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between bore and price is statistically significant, but the linear relationship is only moderate (~0.521).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can relate the process for each 'City-mpg'  and 'Highway-mpg':"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>City-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6865710067844678  with a P-value of P =  2.321132065567641e-29\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['city-mpg'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between city-mpg and price is statistically significant, and the coefficient of ~ -0.687 shows that the relationship is negative and moderately strong.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Highway-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.704692265058953  with a P-value of P =  1.7495471144476358e-31\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['highway-mpg'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "Since the p-value is < 0.001, the correlation between highway-mpg and price is statistically significant, and the coefficient of ~ -0.705 shows that the relationship is negative and moderately strong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"anova\">6. ANOVA</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>ANOVA: Analysis of Variance</h3>\n",
    "<p>The Analysis of Variance  (ANOVA) is a statistical method used to test whether there are significant differences between the means of two or more groups. ANOVA returns two parameters:</p>\n",
    "\n",
    "<p><b>F-test score</b>: ANOVA assumes the means of all groups are the same, calculates how much the actual means deviate from the assumption, and reports it as the F-test score. A larger score means there is a larger difference between the means.</p>\n",
    "\n",
    "<p><b>P-value</b>:  P-value tells how statistically significant is our calculated score value.</p>\n",
    "\n",
    "<p>If our price variable is strongly correlated with the variable we are analyzing, expect ANOVA to return a sizeable F-test score and a small p-value.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Drive Wheels</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Since ANOVA analyzes the difference between different groups of the same variable, the groupby function will come in handy. Because the ANOVA algorithm averages the data automatically, we do not need to take the average before hand.</p>\n",
    "\n",
    "<p>Let's see if different types 'drive-wheels' impact  'price', we group the data.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>16500.0</td>\n",
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       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15250.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>17710.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>18920.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>23875.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16430.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16925.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>20970.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21105.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>24565.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>14</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>30760.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>15</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>41315.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>36880.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>17</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5151.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>18</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>19</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6575.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>20</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5572.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>21</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6377.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>22</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7957.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>23</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6229.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>24</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6692.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7609.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>26</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8558.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>27</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>8921.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>28</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>12964.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>29</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6479.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>30</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6855.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>31</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5399.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>32</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6529.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>33</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7129.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>34</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>35</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>7295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>36</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7895.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>37</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9095.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>38</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>39</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>10295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>40</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12945.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>41</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>10345.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>42</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6785.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>43</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>11048.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>44</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>32250.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>45</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>35550.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>46</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>36000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>47</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5195.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>48</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6095.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>49</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6795.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6695.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>51</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7395.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>52</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>10945.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>53</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>11845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>54</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>13645.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>55</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>15645.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>56</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>57</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>58</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>10595.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>59</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>10245.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>60</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>10795.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>61</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>11245.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>62</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>18280.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>63</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>18344.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>64</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>25552.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>65</td>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>28248.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>66</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>28176.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>67</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>31600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>68</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>34184.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>69</td>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>35056.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>70</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>40960.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>71</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>45400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>72</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16503.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>73</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5389.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>74</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6189.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>75</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6669.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>76</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7689.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>77</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9959.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>78</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8499.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>79</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>12629.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>80</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>14869.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>81</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>14489.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>82</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6989.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>83</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8189.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>84</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9279.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>85</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9279.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>86</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>5499.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>87</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7099.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>88</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6649.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>89</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6849.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>90</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>7349.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>91</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7299.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>92</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7799.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>93</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7499.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>94</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>7999.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>95</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>8249.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>96</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8949.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>97</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9549.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>98</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13499.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>99</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>14399.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>100</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13499.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>101</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>17199.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>102</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>19699.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>103</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>18399.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>104</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>11900.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>105</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13200.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>106</td>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>12440.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>107</td>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>13860.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>108</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15580.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>109</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16900.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>110</td>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16695.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>111</td>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>17075.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>112</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16630.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>113</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>17950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>114</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>18150.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>115</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5572.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>116</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7957.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>117</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6229.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>118</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6692.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>119</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7609.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>120</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>8921.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>121</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>12764.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>122</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>22018.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>123</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>32528.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>124</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>34028.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>125</td>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>37028.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>126</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>127</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9895.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>128</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>11850.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>129</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12170.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>130</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>15040.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>131</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15510.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>132</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>18150.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>133</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>18620.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>134</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5118.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>135</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7053.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>136</td>\n",
       "      <td>4wd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7603.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>137</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7126.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>138</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7775.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>139</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9960.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>140</td>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9233.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>141</td>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>11259.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>142</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>7463.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>143</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>10198.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>144</td>\n",
       "      <td>4wd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>8013.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>145</td>\n",
       "      <td>4wd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>11694.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>146</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5348.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>147</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6338.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>148</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6488.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>149</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>6918.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>150</td>\n",
       "      <td>4wd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>7898.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>151</td>\n",
       "      <td>4wd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>8778.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>152</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6938.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>153</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7198.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>154</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7898.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>155</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7788.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>156</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7738.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>157</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8358.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>158</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9258.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>159</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8058.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>160</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8238.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>161</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9298.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>162</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9538.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>163</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>8449.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>164</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>9639.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>165</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9989.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>166</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>11199.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>167</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>11549.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>168</td>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>17669.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>169</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8948.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>170</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>10698.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>171</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9988.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>172</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>10898.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>173</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>11248.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>174</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16558.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>175</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>15998.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>176</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15690.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>177</td>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>15750.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>178</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7775.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>179</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7975.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>180</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7995.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>181</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8195.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>182</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>183</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>184</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9995.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>185</td>\n",
       "      <td>fwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>186</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9980.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>187</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>188</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>189</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>12290.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>190</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12940.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>191</td>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>13415.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>192</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15985.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>193</td>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16515.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>194</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>18420.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>195</td>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>18950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>196</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>197</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>19045.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>198</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21485.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>199</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>22470.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>200</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>22625.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    drive-wheels   body-style    price\n",
       "0            rwd  convertible  13495.0\n",
       "1            rwd  convertible  16500.0\n",
       "2            rwd    hatchback  16500.0\n",
       "3            fwd        sedan  13950.0\n",
       "4            4wd        sedan  17450.0\n",
       "5            fwd        sedan  15250.0\n",
       "6            fwd        sedan  17710.0\n",
       "7            fwd        wagon  18920.0\n",
       "8            fwd        sedan  23875.0\n",
       "9            rwd        sedan  16430.0\n",
       "10           rwd        sedan  16925.0\n",
       "11           rwd        sedan  20970.0\n",
       "12           rwd        sedan  21105.0\n",
       "13           rwd        sedan  24565.0\n",
       "14           rwd        sedan  30760.0\n",
       "15           rwd        sedan  41315.0\n",
       "16           rwd        sedan  36880.0\n",
       "17           fwd    hatchback   5151.0\n",
       "18           fwd    hatchback   6295.0\n",
       "19           fwd        sedan   6575.0\n",
       "20           fwd    hatchback   5572.0\n",
       "21           fwd    hatchback   6377.0\n",
       "22           fwd    hatchback   7957.0\n",
       "23           fwd    hatchback   6229.0\n",
       "24           fwd        sedan   6692.0\n",
       "25           fwd        sedan   7609.0\n",
       "26           fwd        sedan   8558.0\n",
       "27           fwd        wagon   8921.0\n",
       "28           fwd    hatchback  12964.0\n",
       "29           fwd    hatchback   6479.0\n",
       "30           fwd    hatchback   6855.0\n",
       "31           fwd    hatchback   5399.0\n",
       "32           fwd    hatchback   6529.0\n",
       "33           fwd    hatchback   7129.0\n",
       "34           fwd        sedan   7295.0\n",
       "35           fwd        wagon   7295.0\n",
       "36           fwd    hatchback   7895.0\n",
       "37           fwd    hatchback   9095.0\n",
       "38           fwd        sedan   8845.0\n",
       "39           fwd        sedan  10295.0\n",
       "40           fwd        sedan  12945.0\n",
       "41           fwd        sedan  10345.0\n",
       "42           rwd        sedan   6785.0\n",
       "43           rwd    hatchback  11048.0\n",
       "44           rwd        sedan  32250.0\n",
       "45           rwd        sedan  35550.0\n",
       "46           rwd        sedan  36000.0\n",
       "47           fwd    hatchback   5195.0\n",
       "48           fwd    hatchback   6095.0\n",
       "49           fwd    hatchback   6795.0\n",
       "50           fwd        sedan   6695.0\n",
       "51           fwd        sedan   7395.0\n",
       "52           rwd    hatchback  10945.0\n",
       "53           rwd    hatchback  11845.0\n",
       "54           rwd    hatchback  13645.0\n",
       "55           rwd    hatchback  15645.0\n",
       "56           fwd    hatchback   8845.0\n",
       "57           fwd        sedan   8495.0\n",
       "58           fwd    hatchback  10595.0\n",
       "59           fwd        sedan  10245.0\n",
       "60           fwd        sedan  10795.0\n",
       "61           fwd    hatchback  11245.0\n",
       "62           rwd        sedan  18280.0\n",
       "63           rwd        sedan  18344.0\n",
       "64           rwd        sedan  25552.0\n",
       "65           rwd        wagon  28248.0\n",
       "66           rwd      hardtop  28176.0\n",
       "67           rwd        sedan  31600.0\n",
       "68           rwd        sedan  34184.0\n",
       "69           rwd  convertible  35056.0\n",
       "70           rwd        sedan  40960.0\n",
       "71           rwd      hardtop  45400.0\n",
       "72           rwd    hatchback  16503.0\n",
       "73           fwd    hatchback   5389.0\n",
       "74           fwd    hatchback   6189.0\n",
       "75           fwd    hatchback   6669.0\n",
       "76           fwd    hatchback   7689.0\n",
       "77           fwd    hatchback   9959.0\n",
       "78           fwd    hatchback   8499.0\n",
       "79           fwd    hatchback  12629.0\n",
       "80           fwd    hatchback  14869.0\n",
       "81           fwd    hatchback  14489.0\n",
       "82           fwd        sedan   6989.0\n",
       "83           fwd        sedan   8189.0\n",
       "84           fwd        sedan   9279.0\n",
       "85           fwd        sedan   9279.0\n",
       "86           fwd        sedan   5499.0\n",
       "87           fwd        sedan   7099.0\n",
       "88           fwd        sedan   6649.0\n",
       "89           fwd        sedan   6849.0\n",
       "90           fwd        wagon   7349.0\n",
       "91           fwd        sedan   7299.0\n",
       "92           fwd    hatchback   7799.0\n",
       "93           fwd        sedan   7499.0\n",
       "94           fwd        wagon   7999.0\n",
       "95           fwd      hardtop   8249.0\n",
       "96           fwd    hatchback   8949.0\n",
       "97           fwd        sedan   9549.0\n",
       "98           fwd        sedan  13499.0\n",
       "99           fwd        wagon  14399.0\n",
       "100          fwd        sedan  13499.0\n",
       "101          rwd    hatchback  17199.0\n",
       "102          rwd    hatchback  19699.0\n",
       "103          rwd    hatchback  18399.0\n",
       "104          rwd        sedan  11900.0\n",
       "105          rwd        sedan  13200.0\n",
       "106          rwd        wagon  12440.0\n",
       "107          rwd        wagon  13860.0\n",
       "108          rwd        sedan  15580.0\n",
       "109          rwd        sedan  16900.0\n",
       "110          rwd        wagon  16695.0\n",
       "111          rwd        wagon  17075.0\n",
       "112          rwd        sedan  16630.0\n",
       "113          rwd        sedan  17950.0\n",
       "114          rwd        sedan  18150.0\n",
       "115          fwd    hatchback   5572.0\n",
       "116          fwd    hatchback   7957.0\n",
       "117          fwd    hatchback   6229.0\n",
       "118          fwd        sedan   6692.0\n",
       "119          fwd        sedan   7609.0\n",
       "120          fwd        wagon   8921.0\n",
       "121          rwd    hatchback  12764.0\n",
       "122          rwd    hatchback  22018.0\n",
       "123          rwd      hardtop  32528.0\n",
       "124          rwd      hardtop  34028.0\n",
       "125          rwd  convertible  37028.0\n",
       "126          fwd        wagon   9295.0\n",
       "127          fwd    hatchback   9895.0\n",
       "128          fwd    hatchback  11850.0\n",
       "129          fwd        sedan  12170.0\n",
       "130          fwd    hatchback  15040.0\n",
       "131          fwd        sedan  15510.0\n",
       "132          fwd    hatchback  18150.0\n",
       "133          fwd        sedan  18620.0\n",
       "134          fwd    hatchback   5118.0\n",
       "135          fwd    hatchback   7053.0\n",
       "136          4wd    hatchback   7603.0\n",
       "137          fwd        sedan   7126.0\n",
       "138          fwd        sedan   7775.0\n",
       "139          fwd        sedan   9960.0\n",
       "140          4wd        sedan   9233.0\n",
       "141          4wd        sedan  11259.0\n",
       "142          fwd        wagon   7463.0\n",
       "143          fwd        wagon  10198.0\n",
       "144          4wd        wagon   8013.0\n",
       "145          4wd        wagon  11694.0\n",
       "146          fwd    hatchback   5348.0\n",
       "147          fwd    hatchback   6338.0\n",
       "148          fwd    hatchback   6488.0\n",
       "149          fwd        wagon   6918.0\n",
       "150          4wd        wagon   7898.0\n",
       "151          4wd        wagon   8778.0\n",
       "152          fwd        sedan   6938.0\n",
       "153          fwd    hatchback   7198.0\n",
       "154          fwd        sedan   7898.0\n",
       "155          fwd    hatchback   7788.0\n",
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       "172          fwd        sedan  10898.0\n",
       "173          fwd    hatchback  11248.0\n",
       "174          rwd    hatchback  16558.0\n",
       "175          rwd    hatchback  15998.0\n",
       "176          rwd        sedan  15690.0\n",
       "177          rwd        wagon  15750.0\n",
       "178          fwd        sedan   7775.0\n",
       "179          fwd        sedan   7975.0\n",
       "180          fwd        sedan   7995.0\n",
       "181          fwd        sedan   8195.0\n",
       "182          fwd        sedan   8495.0\n",
       "183          fwd        sedan   9495.0\n",
       "184          fwd        sedan   9995.0\n",
       "185          fwd  convertible  11595.0\n",
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       "189          fwd        wagon  12290.0\n",
       "190          rwd        sedan  12940.0\n",
       "191          rwd        wagon  13415.0\n",
       "192          rwd        sedan  15985.0\n",
       "193          rwd        wagon  16515.0\n",
       "194          rwd        sedan  18420.0\n",
       "195          rwd        wagon  18950.0\n",
       "196          rwd        sedan  16845.0\n",
       "197          rwd        sedan  19045.0\n",
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       "199          rwd        sedan  22470.0\n",
       "200          rwd        sedan  22625.0"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_gptest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see if different types 'drive-wheels' impact  'price', we group the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
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       "      <td>rwd</td>\n",
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       "      <td>10595.0</td>\n",
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       "      <td>fwd</td>\n",
       "      <td>10245.0</td>\n",
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       "      <td>fwd</td>\n",
       "      <td>10795.0</td>\n",
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       "      <td>fwd</td>\n",
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       "      <td>rwd</td>\n",
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       "      <td>rwd</td>\n",
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       "      <td>fwd</td>\n",
       "      <td>9959.0</td>\n",
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       "      <td>fwd</td>\n",
       "      <td>8499.0</td>\n",
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       "      <td>79</td>\n",
       "      <td>fwd</td>\n",
       "      <td>12629.0</td>\n",
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       "      <td>80</td>\n",
       "      <td>fwd</td>\n",
       "      <td>14869.0</td>\n",
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       "    <tr>\n",
       "      <td>81</td>\n",
       "      <td>fwd</td>\n",
       "      <td>14489.0</td>\n",
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       "    <tr>\n",
       "      <td>82</td>\n",
       "      <td>fwd</td>\n",
       "      <td>6989.0</td>\n",
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       "    <tr>\n",
       "      <td>83</td>\n",
       "      <td>fwd</td>\n",
       "      <td>8189.0</td>\n",
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       "    <tr>\n",
       "      <td>84</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9279.0</td>\n",
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       "      <td>fwd</td>\n",
       "      <td>9279.0</td>\n",
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       "    <tr>\n",
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       "      <td>fwd</td>\n",
       "      <td>5499.0</td>\n",
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       "      <td>87</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7099.0</td>\n",
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       "    <tr>\n",
       "      <td>88</td>\n",
       "      <td>fwd</td>\n",
       "      <td>6649.0</td>\n",
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       "    <tr>\n",
       "      <td>89</td>\n",
       "      <td>fwd</td>\n",
       "      <td>6849.0</td>\n",
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       "    <tr>\n",
       "      <td>90</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7349.0</td>\n",
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       "    <tr>\n",
       "      <td>91</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7299.0</td>\n",
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       "    <tr>\n",
       "      <td>92</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7799.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>93</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7499.0</td>\n",
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       "    <tr>\n",
       "      <td>94</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7999.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>95</td>\n",
       "      <td>fwd</td>\n",
       "      <td>8249.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>96</td>\n",
       "      <td>fwd</td>\n",
       "      <td>8949.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>97</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9549.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>98</td>\n",
       "      <td>fwd</td>\n",
       "      <td>13499.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>99</td>\n",
       "      <td>fwd</td>\n",
       "      <td>14399.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>100</td>\n",
       "      <td>fwd</td>\n",
       "      <td>13499.0</td>\n",
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       "    <tr>\n",
       "      <td>101</td>\n",
       "      <td>rwd</td>\n",
       "      <td>17199.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>102</td>\n",
       "      <td>rwd</td>\n",
       "      <td>19699.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>103</td>\n",
       "      <td>rwd</td>\n",
       "      <td>18399.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>104</td>\n",
       "      <td>rwd</td>\n",
       "      <td>11900.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>105</td>\n",
       "      <td>rwd</td>\n",
       "      <td>13200.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>106</td>\n",
       "      <td>rwd</td>\n",
       "      <td>12440.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>107</td>\n",
       "      <td>rwd</td>\n",
       "      <td>13860.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>108</td>\n",
       "      <td>rwd</td>\n",
       "      <td>15580.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>109</td>\n",
       "      <td>rwd</td>\n",
       "      <td>16900.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>110</td>\n",
       "      <td>rwd</td>\n",
       "      <td>16695.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>111</td>\n",
       "      <td>rwd</td>\n",
       "      <td>17075.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>112</td>\n",
       "      <td>rwd</td>\n",
       "      <td>16630.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>113</td>\n",
       "      <td>rwd</td>\n",
       "      <td>17950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>114</td>\n",
       "      <td>rwd</td>\n",
       "      <td>18150.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>115</td>\n",
       "      <td>fwd</td>\n",
       "      <td>5572.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>116</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7957.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>117</td>\n",
       "      <td>fwd</td>\n",
       "      <td>6229.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>118</td>\n",
       "      <td>fwd</td>\n",
       "      <td>6692.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>119</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7609.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>120</td>\n",
       "      <td>fwd</td>\n",
       "      <td>8921.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>121</td>\n",
       "      <td>rwd</td>\n",
       "      <td>12764.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>122</td>\n",
       "      <td>rwd</td>\n",
       "      <td>22018.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>123</td>\n",
       "      <td>rwd</td>\n",
       "      <td>32528.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>124</td>\n",
       "      <td>rwd</td>\n",
       "      <td>34028.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>125</td>\n",
       "      <td>rwd</td>\n",
       "      <td>37028.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>126</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>127</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9895.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>128</td>\n",
       "      <td>fwd</td>\n",
       "      <td>11850.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>129</td>\n",
       "      <td>fwd</td>\n",
       "      <td>12170.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>130</td>\n",
       "      <td>fwd</td>\n",
       "      <td>15040.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>131</td>\n",
       "      <td>fwd</td>\n",
       "      <td>15510.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>132</td>\n",
       "      <td>fwd</td>\n",
       "      <td>18150.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>133</td>\n",
       "      <td>fwd</td>\n",
       "      <td>18620.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>134</td>\n",
       "      <td>fwd</td>\n",
       "      <td>5118.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>135</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7053.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>136</td>\n",
       "      <td>4wd</td>\n",
       "      <td>7603.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>137</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7126.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>138</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7775.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>139</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9960.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>140</td>\n",
       "      <td>4wd</td>\n",
       "      <td>9233.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>141</td>\n",
       "      <td>4wd</td>\n",
       "      <td>11259.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>142</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7463.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>143</td>\n",
       "      <td>fwd</td>\n",
       "      <td>10198.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>144</td>\n",
       "      <td>4wd</td>\n",
       "      <td>8013.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>145</td>\n",
       "      <td>4wd</td>\n",
       "      <td>11694.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>146</td>\n",
       "      <td>fwd</td>\n",
       "      <td>5348.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>147</td>\n",
       "      <td>fwd</td>\n",
       "      <td>6338.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>148</td>\n",
       "      <td>fwd</td>\n",
       "      <td>6488.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>149</td>\n",
       "      <td>fwd</td>\n",
       "      <td>6918.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>150</td>\n",
       "      <td>4wd</td>\n",
       "      <td>7898.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>151</td>\n",
       "      <td>4wd</td>\n",
       "      <td>8778.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>152</td>\n",
       "      <td>fwd</td>\n",
       "      <td>6938.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>153</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7198.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>154</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7898.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>155</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7788.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>156</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7738.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>157</td>\n",
       "      <td>fwd</td>\n",
       "      <td>8358.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>158</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9258.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>159</td>\n",
       "      <td>rwd</td>\n",
       "      <td>8058.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>160</td>\n",
       "      <td>rwd</td>\n",
       "      <td>8238.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>161</td>\n",
       "      <td>rwd</td>\n",
       "      <td>9298.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>162</td>\n",
       "      <td>rwd</td>\n",
       "      <td>9538.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>163</td>\n",
       "      <td>rwd</td>\n",
       "      <td>8449.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>164</td>\n",
       "      <td>rwd</td>\n",
       "      <td>9639.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>165</td>\n",
       "      <td>rwd</td>\n",
       "      <td>9989.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>166</td>\n",
       "      <td>rwd</td>\n",
       "      <td>11199.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>167</td>\n",
       "      <td>rwd</td>\n",
       "      <td>11549.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>168</td>\n",
       "      <td>rwd</td>\n",
       "      <td>17669.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>169</td>\n",
       "      <td>fwd</td>\n",
       "      <td>8948.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>170</td>\n",
       "      <td>fwd</td>\n",
       "      <td>10698.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>171</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9988.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>172</td>\n",
       "      <td>fwd</td>\n",
       "      <td>10898.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>173</td>\n",
       "      <td>fwd</td>\n",
       "      <td>11248.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>174</td>\n",
       "      <td>rwd</td>\n",
       "      <td>16558.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>175</td>\n",
       "      <td>rwd</td>\n",
       "      <td>15998.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>176</td>\n",
       "      <td>rwd</td>\n",
       "      <td>15690.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>177</td>\n",
       "      <td>rwd</td>\n",
       "      <td>15750.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>178</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7775.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>179</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7975.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>180</td>\n",
       "      <td>fwd</td>\n",
       "      <td>7995.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>181</td>\n",
       "      <td>fwd</td>\n",
       "      <td>8195.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>182</td>\n",
       "      <td>fwd</td>\n",
       "      <td>8495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>183</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>184</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9995.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>185</td>\n",
       "      <td>fwd</td>\n",
       "      <td>11595.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>186</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9980.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>187</td>\n",
       "      <td>fwd</td>\n",
       "      <td>13295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>188</td>\n",
       "      <td>fwd</td>\n",
       "      <td>13845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>189</td>\n",
       "      <td>fwd</td>\n",
       "      <td>12290.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>190</td>\n",
       "      <td>rwd</td>\n",
       "      <td>12940.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>191</td>\n",
       "      <td>rwd</td>\n",
       "      <td>13415.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>192</td>\n",
       "      <td>rwd</td>\n",
       "      <td>15985.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>193</td>\n",
       "      <td>rwd</td>\n",
       "      <td>16515.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>194</td>\n",
       "      <td>rwd</td>\n",
       "      <td>18420.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>195</td>\n",
       "      <td>rwd</td>\n",
       "      <td>18950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>196</td>\n",
       "      <td>rwd</td>\n",
       "      <td>16845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>197</td>\n",
       "      <td>rwd</td>\n",
       "      <td>19045.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>198</td>\n",
       "      <td>rwd</td>\n",
       "      <td>21485.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>199</td>\n",
       "      <td>rwd</td>\n",
       "      <td>22470.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>200</td>\n",
       "      <td>rwd</td>\n",
       "      <td>22625.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    drive-wheels    price\n",
       "0            rwd  13495.0\n",
       "1            rwd  16500.0\n",
       "2            rwd  16500.0\n",
       "3            fwd  13950.0\n",
       "4            4wd  17450.0\n",
       "5            fwd  15250.0\n",
       "6            fwd  17710.0\n",
       "7            fwd  18920.0\n",
       "8            fwd  23875.0\n",
       "9            rwd  16430.0\n",
       "10           rwd  16925.0\n",
       "11           rwd  20970.0\n",
       "12           rwd  21105.0\n",
       "13           rwd  24565.0\n",
       "14           rwd  30760.0\n",
       "15           rwd  41315.0\n",
       "16           rwd  36880.0\n",
       "17           fwd   5151.0\n",
       "18           fwd   6295.0\n",
       "19           fwd   6575.0\n",
       "20           fwd   5572.0\n",
       "21           fwd   6377.0\n",
       "22           fwd   7957.0\n",
       "23           fwd   6229.0\n",
       "24           fwd   6692.0\n",
       "25           fwd   7609.0\n",
       "26           fwd   8558.0\n",
       "27           fwd   8921.0\n",
       "28           fwd  12964.0\n",
       "29           fwd   6479.0\n",
       "30           fwd   6855.0\n",
       "31           fwd   5399.0\n",
       "32           fwd   6529.0\n",
       "33           fwd   7129.0\n",
       "34           fwd   7295.0\n",
       "35           fwd   7295.0\n",
       "36           fwd   7895.0\n",
       "37           fwd   9095.0\n",
       "38           fwd   8845.0\n",
       "39           fwd  10295.0\n",
       "40           fwd  12945.0\n",
       "41           fwd  10345.0\n",
       "42           rwd   6785.0\n",
       "43           rwd  11048.0\n",
       "44           rwd  32250.0\n",
       "45           rwd  35550.0\n",
       "46           rwd  36000.0\n",
       "47           fwd   5195.0\n",
       "48           fwd   6095.0\n",
       "49           fwd   6795.0\n",
       "50           fwd   6695.0\n",
       "51           fwd   7395.0\n",
       "52           rwd  10945.0\n",
       "53           rwd  11845.0\n",
       "54           rwd  13645.0\n",
       "55           rwd  15645.0\n",
       "56           fwd   8845.0\n",
       "57           fwd   8495.0\n",
       "58           fwd  10595.0\n",
       "59           fwd  10245.0\n",
       "60           fwd  10795.0\n",
       "61           fwd  11245.0\n",
       "62           rwd  18280.0\n",
       "63           rwd  18344.0\n",
       "64           rwd  25552.0\n",
       "65           rwd  28248.0\n",
       "66           rwd  28176.0\n",
       "67           rwd  31600.0\n",
       "68           rwd  34184.0\n",
       "69           rwd  35056.0\n",
       "70           rwd  40960.0\n",
       "71           rwd  45400.0\n",
       "72           rwd  16503.0\n",
       "73           fwd   5389.0\n",
       "74           fwd   6189.0\n",
       "75           fwd   6669.0\n",
       "76           fwd   7689.0\n",
       "77           fwd   9959.0\n",
       "78           fwd   8499.0\n",
       "79           fwd  12629.0\n",
       "80           fwd  14869.0\n",
       "81           fwd  14489.0\n",
       "82           fwd   6989.0\n",
       "83           fwd   8189.0\n",
       "84           fwd   9279.0\n",
       "85           fwd   9279.0\n",
       "86           fwd   5499.0\n",
       "87           fwd   7099.0\n",
       "88           fwd   6649.0\n",
       "89           fwd   6849.0\n",
       "90           fwd   7349.0\n",
       "91           fwd   7299.0\n",
       "92           fwd   7799.0\n",
       "93           fwd   7499.0\n",
       "94           fwd   7999.0\n",
       "95           fwd   8249.0\n",
       "96           fwd   8949.0\n",
       "97           fwd   9549.0\n",
       "98           fwd  13499.0\n",
       "99           fwd  14399.0\n",
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       "200          rwd  22625.0"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2=df_gptest[['drive-wheels', 'price']].groupby(['drive-wheels'])\n",
    "grouped_test2.head(300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 2)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_gptest[['drive-wheels', 'price']].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain the values of the method group using the method \"get_group\".  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4      17450.0\n",
       "136     7603.0\n",
       "140     9233.0\n",
       "141    11259.0\n",
       "144     8013.0\n",
       "145    11694.0\n",
       "150     7898.0\n",
       "151     8778.0\n",
       "Name: price, dtype: float64"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=grouped_test2.get_group('4wd')['price']\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can use the function 'f_oneway' in the module 'stats'  to obtain the <b>F-test score</b> and <b>P-value</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 67.95406500780399 , P = 3.3945443577151245e-23\n"
     ]
    }
   ],
   "source": [
    "# ANOVA\n",
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'], grouped_test2.get_group('4wd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a great result, with a large F test score showing a strong correlation and a P value of almost 0 implying almost certain statistical significance. But does this mean all three tested groups are all this highly correlated? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Separately: fwd and rwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 130.5533160959111 , P = 2.2355306355677845e-23\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine the other groups "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4wd and rwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 8.580681368924756 , P = 0.004411492211225333\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('rwd')['price'])  \n",
    "   \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>4wd and fwd</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 0.665465750252303 , P = 0.41620116697845666\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('fwd')['price'])  \n",
    " \n",
    "print(\"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Conclusion: Important Variables</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We now have a better idea of what our data looks like and which variables are important to take into account when predicting the car price. We have narrowed it down to the following variables:</p>\n",
    "\n",
    "Continuous numerical variables:\n",
    "<ul>\n",
    "    <li>Length</li>\n",
    "    <li>Width</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Horsepower</li>\n",
    "    <li>City-mpg</li>\n",
    "    <li>Highway-mpg</li>\n",
    "    <li>Wheel-base</li>\n",
    "    <li>Bore</li>\n",
    "</ul>\n",
    "    \n",
    "Categorical variables:\n",
    "<ul>\n",
    "    <li>Drive-wheels</li>\n",
    "</ul>\n",
    "\n",
    "<p>As we now move into building machine learning models to automate our analysis, feeding the model with variables that meaningfully affect our target variable will improve our model's prediction performance.</p>"
   ]
  }
 ],
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