Python_EDA_Book4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Model Development</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>In this section, we will develop several models that will predict the price of the car using the variables or features. This is just an estimate but should give us an objective idea of how much the car should cost.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some questions we want to ask in this module\n",
    "<ul>\n",
    "    <li>do I know if the dealer is offering fair value for my trade-in?</li>\n",
    "    <li>do I know if I put a fair value on my car?</li>\n",
    "</ul>\n",
    "<p>Data Analytics, we often use <b>Model Development</b> to help us predict future observations from the data we have.</p>\n",
    "\n",
    "<p>A Model will help us understand the exact relationship between different variables and how these variables are used to predict the result.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "load data and store in dataframe df:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>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>...</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>...</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>...</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>...</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>...</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>...</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",
       "<p>5 rows × 32 columns</p>\n",
       "</div>"
      ],
      "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  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \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  \n",
       "\n",
       "[5 rows x 32 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('automobileEDA.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>1. Linear Regression and Multiple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Linear Regression</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>One example of a Data  Model that we will be using is</p>\n",
    "<b>Simple Linear Regression</b>.\n",
    "\n",
    "<br>\n",
    "<p>Simple Linear Regression is a method to help us understand the relationship between two variables:</p>\n",
    "<ul>\n",
    "    <li>The predictor/independent variable (X)</li>\n",
    "    <li>The response/dependent variable (that we want to predict)(Y)</li>\n",
    "</ul>\n",
    "\n",
    "<p>The result of Linear Regression is a <b>linear function</b> that predicts the response (dependent) variable as a function of the predictor (independent) variable.</p>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    " Y: Response \\ Variable\\\\\n",
    " X: Predictor \\ Variables\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " <b>Linear function:</b>\n",
    "$$\n",
    "Yhat = a + b  X\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li>a refers to the <b>intercept</b> of the regression line0, in other words: the value of Y when X is 0</li>\n",
    "    <li>b refers to the <b>slope</b> of the regression line, in other words: the value with which Y changes when X increases by 1 unit</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Lets load the modules for linear regression</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Create the linear regression object</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>How could Highway-mpg help us predict car price?</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this example, we want to look at how highway-mpg can help us predict car price.\n",
    "Using simple linear regression, we will create a linear function with \"highway-mpg\" as the predictor variable and the \"price\" as the response variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "X = df[['highway-mpg']]\n",
    "Y = df['price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     highway-mpg\n",
      "0             27\n",
      "1             27\n",
      "2             26\n",
      "3             30\n",
      "4             22\n",
      "..           ...\n",
      "196           28\n",
      "197           25\n",
      "198           23\n",
      "199           27\n",
      "200           25\n",
      "\n",
      "[201 rows x 1 columns]\n"
     ]
    }
   ],
   "source": [
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the linear model using highway-mpg."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X,Y)\n",
    "#We passed the Highway mpg and Price as inputs to the Linear regression Fit method/module"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can output a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
       "       20345.17153508])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Yhat=lm.predict(X)\n",
    "Yhat[0:5]   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>What is the value of the intercept (a)?</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38423.305858157415"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>What is the value of the Slope (b)?</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-821.73337832])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What is the final estimated linear model we get?</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw above, we should get a final linear model with the structure:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b  X\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plugging in the actual values we get:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>price</b> = 38423.31 - 821.73 x  <b>highway-mpg</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm1 = LinearRegression()\n",
    "lm1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A=df[['engine-size']]\n",
    "B=df[['price']]\n",
    "lm1.fit(A,B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Slope</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[166.86001569]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm1.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Intercept</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-7963.33890628])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm1.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# You can type you answer here\n",
    "Yhat = 38423.31-821.733*X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Multiple Linear Regression</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>What if we want to predict car price using more than one variable?</p>\n",
    "\n",
    "<p>If we want to use more variables in our model to predict car price, we can use <b>Multiple Linear Regression</b>.\n",
    "Multiple Linear Regression is very similar to Simple Linear Regression, but this method is used to explain the relationship between one continuous response (dependent) variable and <b>two or more</b> predictor (independent) variables.\n",
    "Most of the real-world regression models involve multiple predictors. We will illustrate the structure by using four predictor variables, but these results can generalize to any integer:</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Y: Response \\ Variable\\\\\n",
    "X_1 :Predictor\\ Variable \\ 1\\\\\n",
    "X_2: Predictor\\ Variable \\ 2\\\\\n",
    "X_3: Predictor\\ Variable \\ 3\\\\\n",
    "X_4: Predictor\\ Variable \\ 4\\\\\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "a: intercept\\\\\n",
    "b_1 :coefficients \\ of\\ Variable \\ 1\\\\\n",
    "b_2: coefficients \\ of\\ Variable \\ 2\\\\\n",
    "b_3: coefficients \\ of\\ Variable \\ 3\\\\\n",
    "b_4: coefficients \\ of\\ Variable \\ 4\\\\\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equation is given by"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From the previous section  we know that other good predictors of price could be:</p>\n",
    "<ul>\n",
    "    <li>Horsepower</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Highway-mpg</li>\n",
    "</ul>\n",
    "Let's develop a model using these variables as the predictor variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the linear model using the four above-mentioned variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(Z, df['price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the value of the intercept(a)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-15811.863767729246"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the values of the coefficients (b1, b2, b3, b4)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([53.53022809,  4.70805253, 81.51280006, 36.1593925 ])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " What is the final estimated linear model that we get?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw above, we should get a final linear function with the structure:\n",
    "\n",
    "$$\n",
    "Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
    "$$\n",
    "\n",
    "What is the linear function we get in this example?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Price</b> = -15678.742628061467 + 52.65851272 x <b>horsepower</b> + 4.69878948 x <b>curb-weight</b> + 81.95906216 x <b>engine-size</b> + 33.58258185 x <b>highway-mpg</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm2 = LinearRegression()\n",
    "G=df[['normalized-losses', 'highway-mpg']]\n",
    "lm2.fit(G, df['price'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   1.49789586, -820.45434016])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm2.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>2)  Model Evaluation using Visualization</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've developed some models, how do we evaluate our models and how do we choose the best one? One way to do this is by using visualization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "import the visualization package: seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the visualization package: seaborn\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Regression Plot</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When it comes to simple linear regression, an excellent way to visualize the fit of our model is by using <b>regression plots</b>.</p>\n",
    "\n",
    "<p>This plot will show a combination of a scattered data points (a <b>scatter plot</b>), as well as the fitted <b>linear regression</b> line going through the data. This will give us a reasonable estimate of the relationship between the two variables, the strength of the correlation, as well as the direction (positive or negative correlation).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's visualize Horsepower as potential predictor variable of price:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 48282.67104104428)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see from this plot that price is negatively correlated to highway-mpg, since the regression slope is negative.\n",
    "One thing to keep in mind when looking at a regression plot is to pay attention to how scattered the data points are around the regression line. This will give you a good indication of the variance of the data, and whether a linear model would be the best fit or not. If the data is too far off from the line, this linear model might not be the best model for this data. Let's compare this plot to the regression plot of \"peak-rpm\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 47422.919330307624)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing the regression plot of \"peak-rpm\" and \"highway-mpg\" we see that the points for \"highway-mpg\" are much closer to the generated line and on the average decrease. The points for \"peak-rpm\" have more spread around the predicted line, and it is much harder to determine if the points are decreasing or increasing as the \"highway-mpg\" increases.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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>peak-rpm</th>\n",
       "      <th>highway-mpg</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>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>highway-mpg</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             peak-rpm  highway-mpg     price\n",
       "peak-rpm     1.000000    -0.058598 -0.101616\n",
       "highway-mpg -0.058598     1.000000 -0.704692\n",
       "price       -0.101616    -0.704692  1.000000"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','highway-mpg','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Residual Plot</h3>\n",
    "\n",
    "<p>A good way to visualize the variance of the data is to use a residual plot.</p>\n",
    "\n",
    "<p>What is a <b>residual</b>?</p>\n",
    "\n",
    "<p>The difference between the observed value (y) and the predicted value (Yhat) is called the residual (e). When we look at a regression plot, the residual is the distance from the data point to the fitted regression line.</p>\n",
    "\n",
    "<p>So what is a <b>residual plot</b>?</p>\n",
    "\n",
    "<p>A residual plot is a graph that shows the residuals on the vertical y-axis and the independent variable on the horizontal x-axis.</p>\n",
    "\n",
    "<p>What do we pay attention to when looking at a residual plot?</p>\n",
    "\n",
    "<p>We look at the spread of the residuals:</p>\n",
    "\n",
    "<p>- If the points in a residual plot are <b>randomly spread out around the x-axis</b>, then a <b>linear model is appropriate</b> for the data. Why is that? Randomly spread out residuals means that the variance is constant, and thus the linear model is a good fit for this data.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.residplot(df['highway-mpg'], df['price'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>What is this plot telling us?</i>\n",
    "\n",
    "<p>We can see from this residual plot that the residuals are not randomly spread around the x-axis, which leads us to believe that maybe a non-linear model is more appropriate for this data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>How do we visualize a model for Multiple Linear Regression? This gets a bit more complicated because you can't visualize it with regression or residual plot.</p>\n",
    "\n",
    "<p>One way to look at the fit of the model is by looking at the <b>distribution plot</b>: We can look at the distribution of the fitted values that result from the model and compare it to the distribution of the actual values.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First lets make a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Y_hat = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(width, height))\n",
    "\n",
    "\n",
    "ax1 = sns.distplot(df['price'], hist=False, color=\"r\", label=\"Actual Value\")\n",
    "sns.distplot(Yhat, hist=False, color=\"b\", label=\"Fitted Values\" , ax=ax1)\n",
    "\n",
    "\n",
    "plt.title('Actual vs Fitted Values for Price')\n",
    "plt.xlabel('Price (in dollars)')\n",
    "plt.ylabel('Proportion of Cars')\n",
    "\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see that the fitted values are reasonably close to the actual values, since the two distributions overlap a bit. However, there is definitely some room for improvement.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 3: Polynomial Regression and Pipelines</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Polynomial regression</b> is a particular case of the general linear regression model or multiple linear regression models.</p> \n",
    "<p>We get non-linear relationships by squaring or setting higher-order terms of the predictor variables.</p>\n",
    "\n",
    "<p>There are different orders of polynomial regression:</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><b>Quadratic - 2nd order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X^2 +b_2 X^2 \n",
    "$$\n",
    "\n",
    "\n",
    "<center><b>Cubic - 3rd order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X^2 +b_2 X^2 +b_3 X^3\\\\\n",
    "$$\n",
    "\n",
    "\n",
    "<center><b>Higher order</b>:</center>\n",
    "$$\n",
    "Y = a + b_1 X^2 +b_2 X^2 +b_3 X^3 ....\\\\\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We saw earlier that a linear model did not provide the best fit while using highway-mpg as the predictor variable. Let's see if we can try fitting a polynomial model to the data instead.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We will use the following function to plot the data:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "def PlotPolly(model, independent_variable, dependent_variabble, Name):\n",
    "    x_new = np.linspace(15, 55, 100)\n",
    "    y_new = model(x_new)\n",
    "\n",
    "    plt.plot(independent_variable, dependent_variabble, '.', x_new, y_new, '-')\n",
    "    plt.title('Polynomial Fit with Matplotlib for Price ~ Length')\n",
    "    ax = plt.gca()\n",
    "    ax.set_facecolor((0.898, 0.898, 0.898))\n",
    "    fig = plt.gcf()\n",
    "    plt.xlabel(Name)\n",
    "    plt.ylabel('Price of Cars')\n",
    "\n",
    "    plt.show()\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "lets get the variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "x = df['highway-mpg']\n",
    "y = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's fit the polynomial using the function <b>polyfit</b>, then use the function <b>poly1d</b> to display the polynomial function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            8            7          6         5         4             3\n",
      "-9.519e-06 x + 0.002642 x - 0.3139 x + 20.82 x - 841.1 x + 2.117e+04 x\n",
      "              2\n",
      " - 3.235e+05 x + 2.735e+06 x - 9.728e+06\n"
     ]
    }
   ],
   "source": [
    "# Here we use a polynomial of the 3rd order (cubic) \n",
    "f = np.polyfit(x, y, 8)\n",
    "#print(f)\n",
    "p = np.poly1d(f)\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's plot the function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "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": [
    "PlotPolly(p, x, y, 'highway-mpg') #3rd degree Polynomial regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "PlotPolly(p, x, y, 'highway-mpg') #5th Degree polynomial Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.polyfit(x, y, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can already see from plotting that this polynomial model performs better than the linear model. This is because the generated polynomial function  \"hits\" more of the data points.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "t1 = np.polyfit(x, y, 11)\n",
    "r = np.poly1d(t1)\n",
    "PlotPolly(r,x,y, 'Length')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The analytical expression for Multivariate Polynomial function gets complicated. For example, the expression for a second-order (degree=2)polynomial with two variables is given by:</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b_1 X_1 +b_2 X_2 +b_3 X_1 X_2+b_4 X_1^2+b_5 X_2^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can perform a polynomial transform on multiple features. First, we import the module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a <b>PolynomialFeatures</b> object of degree 2: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=2, include_bias=True, interaction_only=False,\n",
       "                   order='C')"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_pr=pr.fit_transform(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The original data is of 201 samples and 4 features "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 4)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "after the transformation, there 201 samples and 15 features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 15)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z_pr.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.0000e+00, 1.1100e+02, 2.5480e+03, ..., 1.6900e+04, 3.5100e+03,\n",
       "        7.2900e+02],\n",
       "       [1.0000e+00, 1.1100e+02, 2.5480e+03, ..., 1.6900e+04, 3.5100e+03,\n",
       "        7.2900e+02],\n",
       "       [1.0000e+00, 1.5400e+02, 2.8230e+03, ..., 2.3104e+04, 3.9520e+03,\n",
       "        6.7600e+02],\n",
       "       ...,\n",
       "       [1.0000e+00, 1.3400e+02, 3.0120e+03, ..., 2.9929e+04, 3.9790e+03,\n",
       "        5.2900e+02],\n",
       "       [1.0000e+00, 1.0600e+02, 3.2170e+03, ..., 2.1025e+04, 3.9150e+03,\n",
       "        7.2900e+02],\n",
       "       [1.0000e+00, 1.1400e+02, 3.0620e+03, ..., 1.9881e+04, 3.5250e+03,\n",
       "        6.2500e+02]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z_pr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Pipeline</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Data Pipelines simplify the steps of processing the data. We use the module <b>Pipeline</b> to create a pipeline. We also use <b>StandardScaler</b> as a step in our pipeline.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create the pipeline, by creating a list of tuples including the name of the model or estimator and its corresponding constructor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we input the list as an argument to the pipeline constructor "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('polynomial',\n",
       "                 PolynomialFeatures(degree=2, include_bias=False,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('model',\n",
       "                 LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "                                  normalize=False))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe=Pipeline(Input)\n",
    "pipe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can normalize the data,  perform a transform and fit the model simultaneously. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('polynomial',\n",
       "                 PolynomialFeatures(degree=2, include_bias=False,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('model',\n",
       "                 LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "                                  normalize=False))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe.fit(Z,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Similarly,  we can normalize the data, perform a transform and produce a prediction  simultaneously"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13102.93329646, 13102.93329646, 18226.43450275, 10391.09183955])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13699.07700462, 13699.07700462, 19052.71346719, 10620.61524404,\n",
       "       15520.90025344, 13869.27463809, 15455.88834114, 15973.77411958,\n",
       "       17612.7829335 , 10722.47987021])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
    "\n",
    "pipe=Pipeline(Input)\n",
    "\n",
    "pipe.fit(Z,y)\n",
    "\n",
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 4: Measures for In-Sample Evaluation</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When evaluating our models, not only do we want to visualize the results, but we also want a quantitative measure to determine how accurate the model is.</p>\n",
    "\n",
    "<p>Two very important measures that are often used in Statistics to determine the accuracy of a model are:</p>\n",
    "<ul>\n",
    "    <li><b>R^2 / R-squared</b></li>\n",
    "    <li><b>Mean Squared Error (MSE)</b></li>\n",
    "</ul>\n",
    "    \n",
    "<b>R-squared</b>\n",
    "\n",
    "<p>R squared, also known as the coefficient of determination, is a measure to indicate how close the data is to the fitted regression line.</p>\n",
    "    \n",
    "<p>The value of the R-squared is the percentage of variation of the response variable (y) that is explained by a linear model.</p>\n",
    "\n",
    "\n",
    "\n",
    "<b>Mean Squared Error (MSE)</b>\n",
    "\n",
    "<p>The Mean Squared Error measures the average of the squares of errors, that is, the difference between actual value (y) and the estimated value (ŷ).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 1: Simple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.4965911884339176\n"
     ]
    }
   ],
   "source": [
    "#highway_mpg_fit\n",
    "lm.fit(X, Y)\n",
    "# Find the R^2\n",
    "print('The R-square is: ', lm.score(X, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 49.659% of the variation of the price is explained by this simple linear model \"horsepower_fit\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The output of the first four predicted value is:  [16236.50464347 16236.50464347 17058.23802179 13771.3045085 ]\n"
     ]
    }
   ],
   "source": [
    "Yhat=lm.predict(X)\n",
    "print('The output of the first four predicted value is: ', Yhat[0:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "lets import the function <b>mean_squared_error</b> from the module <b>metrics</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we compare the predicted results with the actual results "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value is:  31635042.944639888\n"
     ]
    }
   ],
   "source": [
    "mse = mean_squared_error(df['price'], Yhat)\n",
    "print('The mean square error of price and predicted value is: ', mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 2: Multiple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.8093732522175299\n"
     ]
    }
   ],
   "source": [
    "# fit the model \n",
    "lm.fit(Z, df['price'])\n",
    "# Find the R^2\n",
    "print('The R-square is: ', lm.score(Z, df['price']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 80.896 % of the variation of price is explained by this multiple linear regression \"multi_fit\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we produce a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Y_predict_multifit = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we compare the predicted results with the actual results "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value using multifit is:  11979300.349818882\n"
     ]
    }
   ],
   "source": [
    "print('The mean square error of price and predicted value using multifit is: ', \\\n",
    "      mean_squared_error(df['price'], Y_predict_multifit))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 3: Polynomial Fit</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let’s import the function <b>r2_score</b> from the module <b>metrics</b> as we are using a different function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We apply the function to get the value of r^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square value is:  0.6874502198798907\n"
     ]
    }
   ],
   "source": [
    "r_squared = r2_score(y, p(x))\n",
    "print('The R-square value is: ', r_squared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 67.419 % of the variation of price is explained by this polynomial fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>MSE</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate the MSE:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19641145.50493814"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(df['price'], p(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 5: Prediction and Decision Making</h2>\n",
    "<h3>Prediction</h3>\n",
    "\n",
    "<p>In the previous section, we trained the model using the method <b>fit</b>. Now we will use the method <b>predict</b> to produce a prediction. Lets import <b>pyplot</b> for plotting; we will also be using some functions from numpy.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a new input "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "new_input=np.arange(1, 100, 1).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Fit the model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X, Y) #Where X is the Highway MPG and Y is Price, which is the target variable.\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce a prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([37601.57247984, 36779.83910151, 35958.10572319, 35136.37234487,\n",
       "       34314.63896655])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat=lm.predict(new_input)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can plot the data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "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": [
    "plt.plot(new_input, yhat)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Decision Making: Determining a Good Model Fit</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now that we have visualized the different models, and generated the R-squared and MSE values for the fits, how do we determine a good model fit?\n",
    "<ul>\n",
    "    <li><i>What is a good R-squared value?</i></li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>When comparing models, <b>the model with the higher R-squared value is a better fit</b> for the data.\n",
    "<ul>\n",
    "    <li><i>What is a good MSE?</i></li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>When comparing models, <b>the model with the smallest MSE value is a better fit</b> for the data.</p>\n",
    "\n",
    "\n",
    "<h4>Let's take a look at the values for the different models.</h4>\n",
    "<p>Simple Linear Regression: Using Highway-mpg as a Predictor Variable of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.49659118843391759</li>\n",
    "    <li>MSE: 3.16 x10^7</li>\n",
    "</ul>\n",
    "</p>\n",
    "    \n",
    "<p>Multiple Linear Regression: Using Horsepower, Curb-weight, Engine-size, and Highway-mpg as Predictor Variables of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.80896354913783497</li>\n",
    "    <li>MSE: 1.2 x10^7</li>\n",
    "</ul>\n",
    "</p>\n",
    "    \n",
    "<p>Polynomial Fit: Using Highway-mpg as a Predictor Variable of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.6741946663906514</li>\n",
    "    <li>MSE: 2.05 x 10^7</li>\n",
    "</ul>\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Regression model (SLR) vs Multiple Linear Regression model (MLR)</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Usually, the more variables you have, the better your model is at predicting, but this is not always true. Sometimes you may not have enough data, you may run into numerical problems, or many of the variables may not be useful and or even act as noise. As a result, you should always check the MSE and R^2.</p>\n",
    "\n",
    "<p>So to be able to compare the results of the MLR vs SLR models, we look at a combination of both the R-squared and MSE to make the best conclusion about the fit of the model.\n",
    "<ul>\n",
    "    <li><b>MSE</b>The MSE of SLR is  3.16x10^7  while MLR has an MSE of 1.2 x10^7.  The MSE of MLR is much smaller.</li>\n",
    "    <li><b>R-squared</b>: In this case, we can also see that there is a big difference between the R-squared of the SLR and the R-squared of the MLR. The R-squared for the SLR (~0.497) is very small compared to the R-squared for the MLR (~0.809).</li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "This R-squared in combination with the MSE show that MLR seems like the better model fit in this case, compared to SLR."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Model (SLR) vs Polynomial Fit</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li><b>MSE</b>: We can see that Polynomial Fit brought down the MSE, since this MSE is smaller than the one from the SLR.</li> \n",
    "    <li><b>R-squared</b>: The R-squared for the Polyfit is larger than the R-squared for the SLR, so the Polynomial Fit also brought up the R-squared quite a bit.</li>\n",
    "</ul>\n",
    "<p>Since the Polynomial Fit resulted in a lower MSE and a higher R-squared, we can conclude that this was a better fit model than the simple linear regression for predicting Price with Highway-mpg as a predictor variable.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression (MLR) vs Polynomial Fit</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li><b>MSE</b>: The MSE for the MLR is smaller than the MSE for the Polynomial Fit.</li>\n",
    "    <li><b>R-squared</b>: The R-squared for the MLR is also much larger than for the Polynomial Fit.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Conclusion:</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing these three models, we conclude that <b>the MLR model is the best model</b> to be able to predict price from our dataset. This result makes sense, since we have 27 variables in total, and we know that more than one of those variables are potential predictors of the final car price.</p>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}