Sesi 11.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "05b723f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "212be26a",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([5,15,25,35,45,55]).reshape((-1,1))\n",
    "y = np.array([5,20,14,32,22,38])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7bca4747",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5],\n",
       "       [15],\n",
       "       [25],\n",
       "       [35],\n",
       "       [45],\n",
       "       [55]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1fd87c5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5, 20, 14, 32, 22, 38])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1f7be51e",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8a18245d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c2f132d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LinearRegression().fit(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7e973149",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2:  0.715875613747954\n"
     ]
    }
   ],
   "source": [
    "r_sq = model.score(x,y)\n",
    "print(\"R^2: \",r_sq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "436a250c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.633333333333329"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "acdb5c8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.54])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9efdbdcd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.33333333, 13.73333333, 19.13333333, 24.53333333, 29.93333333,\n",
       "       35.33333333])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = model.predict(x)\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3fe90493",
   "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,alpha=0.5)\n",
    "plt.plot(x,y_pred)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58dc6931",
   "metadata": {},
   "source": [
    "y = b0 + b1x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9a505089",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8.33333333],\n",
       "       [13.73333333],\n",
       "       [19.13333333],\n",
       "       [24.53333333],\n",
       "       [29.93333333],\n",
       "       [35.33333333]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = model.intercept_ + (model.coef_ * x)\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "dc30f7be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [1],\n",
       "       [2],\n",
       "       [3],\n",
       "       [4]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_new = np.arange(5).reshape((-1,1))\n",
    "x_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "26337319",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.63333333, 6.17333333, 6.71333333, 7.25333333, 7.79333333])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_new = model.predict(x_new)\n",
    "y_new"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15c6b9af",
   "metadata": {},
   "source": [
    "# Multiple Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5c12b87b",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [[0,1],[5,1],[15,2],[25,5],[35,11],[45,15],[55,34],[60,35]]\n",
    "\n",
    "y = [4,5,20,14,32,22,38,43]\n",
    "\n",
    "x,y = np.array(x),np.array(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "95a8aafa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1],\n",
       "       [ 5,  1],\n",
       "       [15,  2],\n",
       "       [25,  5],\n",
       "       [35, 11],\n",
       "       [45, 15],\n",
       "       [55, 34],\n",
       "       [60, 35]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "4de32276",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4,  5, 20, 14, 32, 22, 38, 43])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "bb033b5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LinearRegression().fit(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b1965b6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8615939258756775"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_sq = model.score(x,y)\n",
    "r_sq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6797419e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.52257927519819"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "801333f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.44706965, 0.25502548])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "fd4c36d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.77760476,  8.012953  , 12.73867497, 17.9744479 , 23.97529728,\n",
       "       29.4660957 , 38.78227633, 41.27265006])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = model.predict(x)\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b0473505",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_new = np.arange(10).reshape((-1,2))\n",
    "y_new = model.predict(x_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "19ff02bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1],\n",
       "       [2, 3],\n",
       "       [4, 5],\n",
       "       [6, 7],\n",
       "       [8, 9]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0e767b84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.77760476,  7.18179502,  8.58598528,  9.99017554, 11.3943658 ])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_new"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b65ef937",
   "metadata": {},
   "source": [
    "# Polynomial Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "66b16924",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "6015f233",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([5,15,25,35,45,55]).reshape((-1,1))\n",
    "y = np.array([15,11,2,8,25,32])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "9cdc59bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5],\n",
       "       [15],\n",
       "       [25],\n",
       "       [35],\n",
       "       [45],\n",
       "       [55]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "2acad951",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15, 11,  2,  8, 25, 32])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c15f2198",
   "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",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "98018a4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(include_bias=False)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transformer = PolynomialFeatures(degree=2,include_bias=False)\n",
    "transformer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "73845ce7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(include_bias=False)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transformer.fit(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "a3b297ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   5.,   25.],\n",
       "       [  15.,  225.],\n",
       "       [  25.,  625.],\n",
       "       [  35., 1225.],\n",
       "       [  45., 2025.],\n",
       "       [  55., 3025.]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_ = transformer.transform(x)\n",
    "x_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "c4bc8a7b",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LinearRegression().fit(x_,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "1abc5c7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8908516262498564"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_sq = model.score(x_,y)\n",
    "r_sq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "1d79bcd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21.372321428571425"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "432d3bd2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.32357143,  0.02839286])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "c284e8c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15.46428571,  7.90714286,  6.02857143,  9.82857143, 19.30714286,\n",
       "       34.46428571])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = model.predict(x_)\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "4bbe4073",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [[0,1],[5,1],[15,2],[25,5],[35,11],[45,15],[55,34],[60,35]]\n",
    "\n",
    "y = [4,5,20,14,32,22,38,43]\n",
    "\n",
    "x,y = np.array(x),np.array(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "d16df8e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.000e+00, 1.000e+00, 0.000e+00, 0.000e+00, 1.000e+00],\n",
       "       [5.000e+00, 1.000e+00, 2.500e+01, 5.000e+00, 1.000e+00],\n",
       "       [1.500e+01, 2.000e+00, 2.250e+02, 3.000e+01, 4.000e+00],\n",
       "       [2.500e+01, 5.000e+00, 6.250e+02, 1.250e+02, 2.500e+01],\n",
       "       [3.500e+01, 1.100e+01, 1.225e+03, 3.850e+02, 1.210e+02],\n",
       "       [4.500e+01, 1.500e+01, 2.025e+03, 6.750e+02, 2.250e+02],\n",
       "       [5.500e+01, 3.400e+01, 3.025e+03, 1.870e+03, 1.156e+03],\n",
       "       [6.000e+01, 3.500e+01, 3.600e+03, 2.100e+03, 1.225e+03]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_ = PolynomialFeatures(degree=2,include_bias=False).fit_transform(x)\n",
    "x_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "857c83bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9453701449127822\n"
     ]
    }
   ],
   "source": [
    "model = LinearRegression().fit(x_,y)\n",
    "\n",
    "r_sq = model.score(x_,y)\n",
    "print(r_sq)\n",
    "\n",
    "intercept = model.intercept_\n",
    "\n",
    "coefficients = model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "773859b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8430556452395734"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "15fba32a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.44828275,  0.16160353, -0.15259677,  0.47928683, -0.4641851 ])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefficients"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ec46d99",
   "metadata": {},
   "source": [
    "# Advanced Linear Regression with Statmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "0638cca1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "81a44cf7",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [[0,1],[5,1],[15,2],[25,5],[35,11],[45,15],[55,34],[60,35]]\n",
    "\n",
    "y = [4,5,20,14,32,22,38,43]\n",
    "\n",
    "x,y = np.array(x),np.array(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "49940369",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  1.],\n",
       "       [ 1.,  5.,  1.],\n",
       "       [ 1., 15.,  2.],\n",
       "       [ 1., 25.,  5.],\n",
       "       [ 1., 35., 11.],\n",
       "       [ 1., 45., 15.],\n",
       "       [ 1., 55., 34.],\n",
       "       [ 1., 60., 35.]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sm.add_constant(x)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "0a016320",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = sm.OLS(y,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "f4df2d1a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.862\n",
      "Model:                            OLS   Adj. R-squared:                  0.806\n",
      "Method:                 Least Squares   F-statistic:                     15.56\n",
      "Date:                Thu, 22 Sep 2022   Prob (F-statistic):            0.00713\n",
      "Time:                        21:45:08   Log-Likelihood:                -24.316\n",
      "No. Observations:                   8   AIC:                             54.63\n",
      "Df Residuals:                       5   BIC:                             54.87\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          5.5226      4.431      1.246      0.268      -5.867      16.912\n",
      "x1             0.4471      0.285      1.567      0.178      -0.286       1.180\n",
      "x2             0.2550      0.453      0.563      0.598      -0.910       1.420\n",
      "==============================================================================\n",
      "Omnibus:                        0.561   Durbin-Watson:                   3.268\n",
      "Prob(Omnibus):                  0.755   Jarque-Bera (JB):                0.534\n",
      "Skew:                           0.380   Prob(JB):                        0.766\n",
      "Kurtosis:                       1.987   Cond. No.                         80.1\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\User\\anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1541: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=8\n",
      "  warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n"
     ]
    }
   ],
   "source": [
    "results = model.fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "446f0da6",
   "metadata": {},
   "source": [
    "- R^2 : 0.862\n",
    "- b0 : 5.5226\n",
    "- b1 : 0.4471\n",
    "- b2 : 0.2550"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "65783f7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8615939258756777"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "55b830b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8062314962259488"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.rsquared_adj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "c5c2c92b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.52257928, 0.44706965, 0.25502548])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "585986bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.77760476,  8.012953  , 12.73867497, 17.9744479 , 23.97529728,\n",
       "       29.4660957 , 38.78227633, 41.27265006])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.fittedvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "6af87b42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.77760476,  8.012953  , 12.73867497, 17.9744479 , 23.97529728,\n",
       "       29.4660957 , 38.78227633, 41.27265006])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "5a2489df",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_new = sm.add_constant(np.arange(10).reshape((-1,2)))\n",
    "\n",
    "y_new = results.predict(x_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "55cf05e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 1.],\n",
       "       [1., 2., 3.],\n",
       "       [1., 4., 5.],\n",
       "       [1., 6., 7.],\n",
       "       [1., 8., 9.]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "428fa67c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.77760476,  7.18179502,  8.58598528,  9.99017554, 11.3943658 ])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_new"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8206d31a",
   "metadata": {},
   "source": [
    "# LinReg on Real Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "16ff9381",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "data = datasets.load_boston()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "4c606345",
   "metadata": {
    "scrolled": true
   },
   "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 black people 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(data.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "6c687084",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "62ac9fb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(data.data,columns=data.feature_names)\n",
    "\n",
    "target = pd.DataFrame(data.target,columns=[\"MEDV\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "9fe918cc",
   "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>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  "
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "072baac8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 13)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "1728a378",
   "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>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   MEDV\n",
       "0  24.0\n",
       "1  21.6\n",
       "2  34.7\n",
       "3  33.4\n",
       "4  36.2"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "target.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "b151e356",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared (uncentered):</th>      <td>   0.901</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.901</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   4615.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 22 Sep 2022</td> <th>  Prob (F-statistic):</th>          <td>3.74e-256</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>21:45:08</td>     <th>  Log-Likelihood:    </th>          <td> -1747.1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th>          <td>   3496.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   505</td>      <th>  BIC:               </th>          <td>   3500.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th> <td>    3.6534</td> <td>    0.054</td> <td>   67.930</td> <td> 0.000</td> <td>    3.548</td> <td>    3.759</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>83.295</td> <th>  Durbin-Watson:     </th> <td>   0.493</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 152.507</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.955</td> <th>  Prob(JB):          </th> <td>7.65e-34</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.894</td> <th>  Cond. No.          </th> <td>    1.00</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                   MEDV   R-squared (uncentered):                   0.901\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.901\n",
       "Method:                 Least Squares   F-statistic:                              4615.\n",
       "Date:                Thu, 22 Sep 2022   Prob (F-statistic):                   3.74e-256\n",
       "Time:                        21:45:08   Log-Likelihood:                         -1747.1\n",
       "No. Observations:                 506   AIC:                                      3496.\n",
       "Df Residuals:                     505   BIC:                                      3500.\n",
       "Df Model:                           1                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "RM             3.6534      0.054     67.930      0.000       3.548       3.759\n",
       "==============================================================================\n",
       "Omnibus:                       83.295   Durbin-Watson:                   0.493\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              152.507\n",
       "Skew:                           0.955   Prob(JB):                     7.65e-34\n",
       "Kurtosis:                       4.894   Cond. No.                         1.00\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = df[\"RM\"]\n",
    "y = target[\"MEDV\"]\n",
    "\n",
    "model = sm.OLS(y,X).fit()\n",
    "predictions = model.predict(X)\n",
    "\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "2b36fcf1",
   "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,alpha=0.5)\n",
    "\n",
    "plt.plot(X,predictions)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "45337295",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df\n",
    "\n",
    "lm = LinearRegression()\n",
    "model = lm.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "9780da3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([30.00384338, 25.02556238, 30.56759672, 28.60703649, 27.94352423,\n",
       "       25.25628446, 23.00180827, 19.53598843, 11.52363685, 18.92026211,\n",
       "       18.99949651, 21.58679568, 20.90652153, 19.55290281, 19.28348205,\n",
       "       19.29748321, 20.52750979, 16.91140135, 16.17801106, 18.40613603,\n",
       "       12.52385753, 17.67103669, 15.83288129, 13.80628535, 15.67833832,\n",
       "       13.38668561, 15.46397655, 14.70847428, 19.54737285, 20.8764282 ,\n",
       "       11.45511759, 18.05923295,  8.81105736, 14.28275814, 13.70675891,\n",
       "       23.81463526, 22.34193708, 23.10891142, 22.91502612, 31.35762569,\n",
       "       34.21510225, 28.02056414, 25.20386628, 24.60979273, 22.94149176,\n",
       "       22.09669817, 20.42320032, 18.03655088,  9.10655377, 17.20607751,\n",
       "       21.28152535, 23.97222285, 27.6558508 , 24.04901809, 15.3618477 ,\n",
       "       31.15264947, 24.85686978, 33.10919806, 21.77537987, 21.08493555,\n",
       "       17.8725804 , 18.51110208, 23.98742856, 22.55408869, 23.37308644,\n",
       "       30.36148358, 25.53056512, 21.11338564, 17.42153786, 20.78483633,\n",
       "       25.20148859, 21.7426577 , 24.55744957, 24.04295712, 25.50499716,\n",
       "       23.9669302 , 22.94545403, 23.35699818, 21.26198266, 22.42817373,\n",
       "       28.40576968, 26.99486086, 26.03576297, 25.05873482, 24.78456674,\n",
       "       27.79049195, 22.16853423, 25.89276415, 30.67461827, 30.83110623,\n",
       "       27.1190194 , 27.41266734, 28.94122762, 29.08105546, 27.03977365,\n",
       "       28.62459949, 24.72744978, 35.78159518, 35.11454587, 32.25102801,\n",
       "       24.58022019, 25.59413475, 19.79013684, 20.31167129, 21.43482591,\n",
       "       18.53994008, 17.18755992, 20.75049026, 22.64829115, 19.7720367 ,\n",
       "       20.64965864, 26.52586744, 20.77323638, 20.71548315, 25.17208881,\n",
       "       20.43025591, 23.37724626, 23.69043261, 20.33578364, 20.79180873,\n",
       "       21.91632071, 22.47107777, 20.55738556, 16.36661977, 20.56099819,\n",
       "       22.48178446, 14.61706633, 15.17876684, 18.93868592, 14.05573285,\n",
       "       20.03527399, 19.41013402, 20.06191566, 15.75807673, 13.25645238,\n",
       "       17.26277735, 15.87841883, 19.36163954, 13.81483897, 16.44881475,\n",
       "       13.57141932,  3.98885508, 14.59495478, 12.1488148 ,  8.72822362,\n",
       "       12.03585343, 15.82082058,  8.5149902 ,  9.71844139, 14.80451374,\n",
       "       20.83858153, 18.30101169, 20.12282558, 17.28601894, 22.36600228,\n",
       "       20.10375923, 13.62125891, 33.25982697, 29.03017268, 25.56752769,\n",
       "       32.70827666, 36.77467015, 40.55765844, 41.84728168, 24.78867379,\n",
       "       25.37889238, 37.20347455, 23.08748747, 26.40273955, 26.65382114,\n",
       "       22.5551466 , 24.29082812, 22.97657219, 29.07194308, 26.5219434 ,\n",
       "       30.72209056, 25.61669307, 29.13740979, 31.43571968, 32.92231568,\n",
       "       34.72440464, 27.76552111, 33.88787321, 30.99238036, 22.71820008,\n",
       "       24.7664781 , 35.88497226, 33.42476722, 32.41199147, 34.51509949,\n",
       "       30.76109485, 30.28934141, 32.91918714, 32.11260771, 31.55871004,\n",
       "       40.84555721, 36.12770079, 32.6692081 , 34.70469116, 30.09345162,\n",
       "       30.64393906, 29.28719501, 37.07148392, 42.03193124, 43.18949844,\n",
       "       22.69034796, 23.68284712, 17.85447214, 23.49428992, 17.00587718,\n",
       "       22.39251096, 17.06042754, 22.73892921, 25.21942554, 11.11916737,\n",
       "       24.51049148, 26.60334775, 28.35518713, 24.91525464, 29.68652768,\n",
       "       33.18419746, 23.77456656, 32.14051958, 29.7458199 , 38.37102453,\n",
       "       39.81461867, 37.58605755, 32.3995325 , 35.45665242, 31.23411512,\n",
       "       24.48449227, 33.28837292, 38.0481048 , 37.16328631, 31.71383523,\n",
       "       25.26705571, 30.10010745, 32.71987156, 28.42717057, 28.42940678,\n",
       "       27.29375938, 23.74262478, 24.12007891, 27.40208414, 16.3285756 ,\n",
       "       13.39891261, 20.01638775, 19.86184428, 21.2883131 , 24.0798915 ,\n",
       "       24.20633547, 25.04215821, 24.91964007, 29.94563374, 23.97228316,\n",
       "       21.69580887, 37.51109239, 43.30239043, 36.48361421, 34.98988594,\n",
       "       34.81211508, 37.16631331, 40.98928501, 34.44634089, 35.83397547,\n",
       "       28.245743  , 31.22673593, 40.8395575 , 39.31792393, 25.70817905,\n",
       "       22.30295533, 27.20340972, 28.51169472, 35.47676598, 36.10639164,\n",
       "       33.79668274, 35.61085858, 34.83993382, 30.35192656, 35.30980701,\n",
       "       38.79756966, 34.33123186, 40.33963075, 44.67308339, 31.59689086,\n",
       "       27.3565923 , 20.10174154, 27.04206674, 27.2136458 , 26.91395839,\n",
       "       33.43563311, 34.40349633, 31.8333982 , 25.81783237, 24.42982348,\n",
       "       28.45764337, 27.36266999, 19.53928758, 29.11309844, 31.91054611,\n",
       "       30.77159449, 28.94275871, 28.88191022, 32.79887232, 33.20905456,\n",
       "       30.76831792, 35.56226857, 32.70905124, 28.64244237, 23.58965827,\n",
       "       18.54266897, 26.87889843, 23.28133979, 25.54580246, 25.48120057,\n",
       "       20.53909901, 17.61572573, 18.37581686, 24.29070277, 21.32529039,\n",
       "       24.88682244, 24.86937282, 22.86952447, 19.45123791, 25.11783401,\n",
       "       24.66786913, 23.68076177, 19.34089616, 21.17418105, 24.25249073,\n",
       "       21.59260894, 19.98446605, 23.33888   , 22.14060692, 21.55509929,\n",
       "       20.61872907, 20.16097176, 19.28490387, 22.1667232 , 21.24965774,\n",
       "       21.42939305, 30.32788796, 22.04734975, 27.70647912, 28.54794117,\n",
       "       16.54501121, 14.78359641, 25.27380082, 27.54205117, 22.14837562,\n",
       "       20.45944095, 20.54605423, 16.88063827, 25.40253506, 14.32486632,\n",
       "       16.59488462, 19.63704691, 22.71806607, 22.20218887, 19.20548057,\n",
       "       22.66616105, 18.93192618, 18.22846804, 20.23150811, 37.4944739 ,\n",
       "       14.28190734, 15.54286248, 10.83162324, 23.80072902, 32.6440736 ,\n",
       "       34.60684042, 24.94331333, 25.9998091 ,  6.126325  ,  0.77779806,\n",
       "       25.30713064, 17.74061065, 20.23274414, 15.83331301, 16.83512587,\n",
       "       14.36994825, 18.47682833, 13.4276828 , 13.06177512,  3.27918116,\n",
       "        8.06022171,  6.12842196,  5.6186481 ,  6.4519857 , 14.20764735,\n",
       "       17.21225183, 17.29887265,  9.89116643, 20.22124193, 17.94181175,\n",
       "       20.30445783, 19.29559075, 16.33632779,  6.55162319, 10.89016778,\n",
       "       11.88145871, 17.81174507, 18.26126587, 12.97948781,  7.37816361,\n",
       "        8.21115861,  8.06626193, 19.98294786, 13.70756369, 19.85268454,\n",
       "       15.22308298, 16.96071981,  1.71851807, 11.80578387, -4.28131071,\n",
       "        9.58376737, 13.36660811,  6.89562363,  6.14779852, 14.60661794,\n",
       "       19.6000267 , 18.12427476, 18.52177132, 13.1752861 , 14.62617624,\n",
       "        9.92374976, 16.34590647, 14.07519426, 14.25756243, 13.04234787,\n",
       "       18.15955693, 18.69554354, 21.527283  , 17.03141861, 15.96090435,\n",
       "       13.36141611, 14.52079384,  8.81976005,  4.86751102, 13.06591313,\n",
       "       12.70609699, 17.29558059, 18.740485  , 18.05901029, 11.51474683,\n",
       "       11.97400359, 17.68344618, 18.12695239, 17.5183465 , 17.22742507,\n",
       "       16.52271631, 19.41291095, 18.58215236, 22.48944791, 15.28000133,\n",
       "       15.82089335, 12.68725581, 12.8763379 , 17.18668531, 18.51247609,\n",
       "       19.04860533, 20.17208927, 19.7740732 , 22.42940768, 20.31911854,\n",
       "       17.88616253, 14.37478523, 16.94776851, 16.98405762, 18.58838397,\n",
       "       20.16719441, 22.97718032, 22.45580726, 25.57824627, 16.39147632,\n",
       "       16.1114628 , 20.534816  , 11.54272738, 19.20496304, 21.86276391,\n",
       "       23.46878866, 27.09887315, 28.56994302, 21.08398783, 19.45516196,\n",
       "       22.22225914, 19.65591961, 21.32536104, 11.85583717,  8.22386687,\n",
       "        3.66399672, 13.75908538, 15.93118545, 20.62662054, 20.61249414,\n",
       "       16.88541964, 14.01320787, 19.10854144, 21.29805174, 18.45498841,\n",
       "       20.46870847, 23.53334055, 22.37571892, 27.6274261 , 26.12796681,\n",
       "       22.34421229])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions = lm.predict(X)\n",
    "predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "e7f4aa39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7406426641094095"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_sq = lm.score(X,y)\n",
    "r_sq"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c6e2752",
   "metadata": {},
   "source": [
    "# SKlearn Example 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "94437b5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "aa22ad2f",
   "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>horsepower</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>111</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>111</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>154</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>102</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>115</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   horsepower    price\n",
       "0         111  13495.0\n",
       "1         111  16500.0\n",
       "2         154  16500.0\n",
       "3         102  13950.0\n",
       "4         115  17450.0"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"https://raw.githubusercontent.com/ardhiraka/PFDS_sources/master/CarPrice_Assignment.csv\",usecols=[\"horsepower\",\"price\"])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "6c0e0b36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(205, 2)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "6fba1f45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = plt.figure(figsize=(12,4))\n",
    "\n",
    "f.add_subplot(1,2,1)\n",
    "df[\"horsepower\"].plot(kind=\"kde\")\n",
    "\n",
    "f.add_subplot(1,2,2)\n",
    "plt.boxplot(df[\"horsepower\"])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "987238e4",
   "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(df[\"horsepower\"],df[\"price\"])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "876922fe",
   "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>horsepower</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.808139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.808139</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            horsepower     price\n",
       "horsepower    1.000000  0.808139\n",
       "price         0.808139  1.000000"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "ee7d7ba1",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = df[\"horsepower\"].values.reshape(-1,1)\n",
    "y = df[\"price\"].values.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "5de930be",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train,x_test,y_train,y_test = train_test_split(x,y,test_size=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "93473dda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(164, 1)"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "c635974a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(41, 1)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "f753340b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(x_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "a480c37e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[166.59767818]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "d5f09ca0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3903.14421945])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "5b4f632a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7435159635185311"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.score(x_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "f81570ec",
   "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": [
    "y_pred = lin_reg.predict(x_test)\n",
    "\n",
    "plt.scatter(x_test,y_test)\n",
    "plt.plot(x_test,y_pred,c=\"r\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "731d0b4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[112715.23050799]])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict([[700]])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}