18. Accuracy of Linear Refression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Accuracy of Linear Refression\n",
    "\n",
    "$MSE = \\frac {1}{n} \\sum _{i=1} ^n(y_{test(i)} - \\hat y_{test(i)})^2$ \n",
    " \n",
    " $RMSE = \\sqrt {MSE_{test}} = \\sqrt {\\frac {1}{n} \\sum _{i=1} ^n(y_{test(i)} - \\hat y_{test(i)})^2}$\n",
    " \n",
    " $MAE = \\frac {1}{n} \\sum _{i=1} ^n|y_{test(i)} - \\hat y_{test(i)}|$\n",
    " \n",
    " $R^2 = 1 - \\frac {SS_{residual}}{SS_{total}} = 1- \\frac {\\sum (\\hat y_i - y_i)^2}{\\sum (\\overline y - y_i)^2} = 1- \\frac {(\\sum (\\hat y_i - y_i)^2)/m}{(\\sum (\\overline y - y_i)^2)/m} = 1 - \\frac{MSE(\\hat y, y)}{Var(y)} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Boston House Price Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "boston = datasets.load_boston()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _boston_dataset:\n",
      "\n",
      "Boston house prices dataset\n",
      "---------------------------\n",
      "\n",
      "**Data Set Characteristics:**  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\n",
      "\n",
      "    :Attribute Information (in order):\n",
      "        - CRIM     per capita crime rate by town\n",
      "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
      "        - INDUS    proportion of non-retail business acres per town\n",
      "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
      "        - NOX      nitric oxides concentration (parts per 10 million)\n",
      "        - RM       average number of rooms per dwelling\n",
      "        - AGE      proportion of owner-occupied units built prior to 1940\n",
      "        - DIS      weighted distances to five Boston employment centres\n",
      "        - RAD      index of accessibility to radial highways\n",
      "        - TAX      full-value property-tax rate per $10,000\n",
      "        - PTRATIO  pupil-teacher ratio by town\n",
      "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
      "        - LSTAT    % lower status of the population\n",
      "        - MEDV     Median value of owner-occupied homes in $1000's\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
      "\n",
      "This is a copy of UCI ML housing dataset.\n",
      "https://archive.ics.uci.edu/ml/machine-learning-databases/housing/\n",
      "\n",
      "\n",
      "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
      "\n",
      "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
      "prices and the demand for clean air', J. Environ. Economics & Management,\n",
      "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
      "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
      "pages 244-261 of the latter.\n",
      "\n",
      "The Boston house-price data has been used in many machine learning papers that address regression\n",
      "problems.   \n",
      "     \n",
      ".. topic:: References\n",
      "\n",
      "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
      "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(boston.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD',\n",
       "       'TAX', 'PTRATIO', 'B', 'LSTAT'], dtype='<U7')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.feature_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = boston.data[:, 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506,)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = boston.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506,)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = x[y < 50.0]\n",
    "y = y[y < 50.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": [
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size = 0.2, random_state = 666)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(392,)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(98,)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from playML.SimpleLinearRegression import SimpleLinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg = SimpleLinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SimpleLinearRegression()"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.8608543562689555"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.a_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-27.459342806705543"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.b_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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": [
    "plt.scatter(x_train, y_train)\n",
    "plt.plot(x_train, reg.predict(x_train), color = 'red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_predict = reg.predict(x_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.156602134387438"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse_test = np.sum((y_predict - y_test) ** 2) / len(y_predict)\n",
    "mse_test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.914936635846635"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import sqrt\n",
    "\n",
    "rmse_test = sqrt(np.sum((y_predict - y_test) ** 2) / len(y_predict))\n",
    "rmse_test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MAE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.543097440946387"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mae_test = np.sum(np.absolute(y_predict - y_test) / len(y_predict))\n",
    "mae_test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MSE & RMSE & MAE Packaging"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from playML.metrics import mean_squared_error\n",
    "from playML.metrics import root_mean_squared_error\n",
    "from playML.metrics import mean_absolute_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.156602134387438"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(y_test, y_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.914936635846635"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "root_mean_squared_error(y_test, y_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.543097440946387"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_error(y_test, y_predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scikit-learning MSE & MAE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import mean_absolute_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.156602134387438"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(y_test, y_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5430974409463873"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_error(y_test, y_predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## R Squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6129316803937322"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - mean_squared_error(y_test, y_predict) / np.var(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "from playML.metrics import r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6129316803937322"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y_test, y_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6129316803937324"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "r2_score(y_test, y_predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "packaging R Squared in SimpleLinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6129316803937322"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.score(x_test, y_test)"
   ]
  }
 ],
 "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}