8-3_sklearn_basics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.24.1'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sklearn\n",
    "sklearn.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import linear_model\n",
    "from sklearn.metrics import mean_squared_error, r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "olympic = pd.read_csv(\"https://raw.githubusercontent.com/sdrogers/fcmlcode/master/R/data/olympics/male100.csv\", names = [\"year\",\"time\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>year</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1896</td>\n",
       "      <td>12.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1900</td>\n",
       "      <td>11.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1904</td>\n",
       "      <td>11.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1906</td>\n",
       "      <td>11.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1908</td>\n",
       "      <td>10.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1912</td>\n",
       "      <td>10.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1920</td>\n",
       "      <td>10.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1924</td>\n",
       "      <td>10.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1928</td>\n",
       "      <td>10.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1932</td>\n",
       "      <td>10.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1936</td>\n",
       "      <td>10.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1948</td>\n",
       "      <td>10.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1952</td>\n",
       "      <td>10.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1956</td>\n",
       "      <td>10.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1960</td>\n",
       "      <td>10.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1964</td>\n",
       "      <td>10.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1968</td>\n",
       "      <td>9.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1972</td>\n",
       "      <td>10.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1976</td>\n",
       "      <td>10.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1980</td>\n",
       "      <td>10.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1984</td>\n",
       "      <td>9.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1988</td>\n",
       "      <td>9.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1992</td>\n",
       "      <td>9.96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1996</td>\n",
       "      <td>9.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2000</td>\n",
       "      <td>9.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>2004</td>\n",
       "      <td>9.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>2008</td>\n",
       "      <td>9.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2012</td>\n",
       "      <td>9.63</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    year   time\n",
       "0   1896  12.00\n",
       "1   1900  11.00\n",
       "2   1904  11.00\n",
       "3   1906  11.20\n",
       "4   1908  10.80\n",
       "5   1912  10.80\n",
       "6   1920  10.80\n",
       "7   1924  10.60\n",
       "8   1928  10.80\n",
       "9   1932  10.30\n",
       "10  1936  10.30\n",
       "11  1948  10.30\n",
       "12  1952  10.40\n",
       "13  1956  10.50\n",
       "14  1960  10.20\n",
       "15  1964  10.00\n",
       "16  1968   9.95\n",
       "17  1972  10.14\n",
       "18  1976  10.06\n",
       "19  1980  10.25\n",
       "20  1984   9.99\n",
       "21  1988   9.92\n",
       "22  1992   9.96\n",
       "23  1996   9.84\n",
       "24  2000   9.87\n",
       "25  2004   9.85\n",
       "26  2008   9.69\n",
       "27  2012   9.63"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "olympic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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('year', 'time', data = olympic)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28,)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = olympic.time\n",
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creates an instance of a linear regression model where we will estimate the intercept\n",
    "model = linear_model.LinearRegression(fit_intercept = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# SciKit Learn requires that the features (x) be a matrix\n",
    "# and the response y be a one-dimension array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(28, 1)\n"
     ]
    }
   ],
   "source": [
    "# we create an X matrix using the x values\n",
    "x = olympic.year.values\n",
    "X = x.reshape([-1,1]) # alternatively I could write x.reshape((28, 1))\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now we fit the model to the data\n",
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.01327532]\n"
     ]
    }
   ],
   "source": [
    "print(model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "36.30912040967222\n"
     ]
    }
   ],
   "source": [
    "print(model.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101,)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction_x  = np.linspace(1900, 2000, 101)\n",
    "prediction_x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction_x = prediction_x.reshape([-1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11.08600515, 11.07272982, 11.0594545 , 11.04617918, 11.03290385,\n",
       "       11.01962853, 11.00635321, 10.99307788, 10.97980256, 10.96652723,\n",
       "       10.95325191, 10.93997659, 10.92670126, 10.91342594, 10.90015061,\n",
       "       10.88687529, 10.87359997, 10.86032464, 10.84704932, 10.833774  ,\n",
       "       10.82049867, 10.80722335, 10.79394802, 10.7806727 , 10.76739738,\n",
       "       10.75412205, 10.74084673, 10.72757141, 10.71429608, 10.70102076,\n",
       "       10.68774543, 10.67447011, 10.66119479, 10.64791946, 10.63464414,\n",
       "       10.62136881, 10.60809349, 10.59481817, 10.58154284, 10.56826752,\n",
       "       10.5549922 , 10.54171687, 10.52844155, 10.51516622, 10.5018909 ,\n",
       "       10.48861558, 10.47534025, 10.46206493, 10.4487896 , 10.43551428,\n",
       "       10.42223896, 10.40896363, 10.39568831, 10.38241299, 10.36913766,\n",
       "       10.35586234, 10.34258701, 10.32931169, 10.31603637, 10.30276104,\n",
       "       10.28948572, 10.2762104 , 10.26293507, 10.24965975, 10.23638442,\n",
       "       10.2231091 , 10.20983378, 10.19655845, 10.18328313, 10.1700078 ,\n",
       "       10.15673248, 10.14345716, 10.13018183, 10.11690651, 10.10363119,\n",
       "       10.09035586, 10.07708054, 10.06380521, 10.05052989, 10.03725457,\n",
       "       10.02397924, 10.01070392,  9.99742859,  9.98415327,  9.97087795,\n",
       "        9.95760262,  9.9443273 ,  9.93105198,  9.91777665,  9.90450133,\n",
       "        9.891226  ,  9.87795068,  9.86467536,  9.85140003,  9.83812471,\n",
       "        9.82484939,  9.81157406,  9.79829874,  9.78502341,  9.77174809,\n",
       "        9.75847277])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(prediction_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AgPhWS6SY9HT4zW8gJ8fPuO3Xz1/ZZ2VBr15+cbW9e0v9NvGSlHkJImVU1puxjZxzXwGEHg+PcJwD3jCzZWY2vKRvaGbDzSzHzHK2aky1RGIGJ58Mzz7rb9LefrtfZ+fss/2et/fdB98Vvy6Jv6TPSxCJQaJH3XR2znUAegNXm1mXSAc65yY75zo65zo2bNgwwdWSQGjUCG691a+t8+KLfpTOmDG+W+eKK2DFioSdOmXmJYhEoaxB/7WZNQYIPW4Jd5BzbnPocQswG+hUxvOJRFajBgweDIsX+71thwzxG563bw+nneb3wN21K66nTLl5CSIlKGvQzwWGhp4PBeYUP8DM6phZvf3PgR7A6uLHicTVccfBE0/4MfkPPOC3O7zwQjjySBg/HjZvjstpUnpegkgxpY6jN7MZQDfgMOBr4DYgG3gRaA5sBAY7574zsybAX51zfczsKPxVPEB14Dnn3J3RVErj6CVu9u2D11/3Y/JffdXPyB00yI/J79xZY/IlMEoaR68JU1J1rF/vR+pMmeJn37Zr5wP/oougdu1k106kXMo1YUokMI4+2u9+lZ/vu3ecgyuv9AuqjR4Nn38OaCKUBI+CXqqeOnVg+HA/KmfJEjjrLHjoITj6aP51+lnMm/g3Nn+/QxOhJDDUdSMC/ubtE0/w7YOPcuiP3/PFIY2Z3r4fLx13Jj/UqktG/XSWjj0j2bUUiaikrpvqFV0ZkZSUkQF/+hOnFHagV94/GLrsZf6w6ElGv/M0s9t0Z3qHfoCCXionBb1IEQ0PPZi5rbsyt3VX2vxrPUOWz2PQ6kVcvOJ1+Ozv/uZt//5+7L5IJaE+epEiik6EWnPE0dzc5zq6Xzud1dfdAl9+6SdmtWgBd9wBX3+d5NqKREdBL1JEuIlQN1/SmbYP3eGHZ86Z4zdK+f3voXlzuPRSv/l5Ct7rEtlPN2NFyiIvDx57zC+dvH273/z86qvhggv8UsoiFUwTpiRhsnMLmDg/j83bCmlSP50xPbMiLgMQy7HJrGdMtm+HZ56BRx+FtWvh0EP92PwRI/yyCyIVRBOmJCFi2XwjmRt1JPTc9erByJGwerXf/rBLF7j3XjjqKL/5+cKF6taRpFPQS5nFsvlGMjfqqJBzm/mtDmfNgi++gJtvhnff9ZOx9m9+vn17/M4nEgMFvZRZLJtvJHOjjgo/d/PmcNddfmOUqVOhbl0/LDMjA665Bj7+ODHnFYlAQS9lFsvmG8ncqCNp565VC4YOhQ8/hPff9+PvJ0+GY4/1m5/PmVOh2x/Gk9YDqlwU9FJmsWy+kcyNOlJik5BOnWD6dH+Vf+ed/qp+wADflz9hAnzzTcXVpZy0MXrlo6CXMotl841kbtSRUpuEHH44/O53vh9/5kwf9OPG+RU0L7sMli2r+DrFSBujVz4aXimSbGvW+Ju1Tz8NO3b4zc9HjYLzzoOaNZNdu//RYuw8wqWGAV9M6FvR1ZEQDa8USbIS+7TbtPGTrwoK4OGH4dtv4ZJL/E3d3//el6cQbYxe+SjoRRIs6j7tX/wCrr3W99/Pnw8nneT784888r+bn6fAX+Apcc9DYqKgF0mwmPu0q1WDHj1g7lz47DO44QY/8apbNzj+eL871o4dia94BCl1z0Oioj56kQSLS5/2Tz/BjBl+qYUVK/zV/7BhcNVVfotEqfLURy+SRHHp065dGy6/HJYv9zNu+/SBP/8ZWrb0z+fNg3374lRjCRoFvUiCxbVP2ww6d4bnnoONG2H8eH+F36+fD/3774fvvz/gI5rcJAp6kQRLWJ9248Zw221+Q5QXXoAmTWD0aL/UwvDhsHKlJjcJoD56kWBZudL34z/7LBQWsiLzOJ48vg/zW53CnrT/7hyqzc6DR330IlVFu3bw5JOQnw/33UeD77cwae49vPv4MK5dOoOGP/punYpYTE5ShzYHFwmiBg3gxhu5+OfjOTp3KUOXvcIN7z7LqH+8wGtZnXm16yA/Jt8s2TWVCqCgFwmwG3u3ZlzhXt765f8j87sCLs19lfNXLaD/usXw/t/8UgsXXgjpmtUaZOq6EQmwojeCv2yQwZRB1/L2wlx4/HHYvdsP2WzaFG66yS+0JoGkm7EiVZVzflmFSZNg9mzYt4+vTj+Le395FnMaHkvjQ+pU6L6+Uj4l3YxV141IVWXml1Xo1g3y88n7430cOmMaDy5ZwKgGGUxv35c7v+0BnKywr+TUdSMi0LQpw355DqeO+BvX97uRf9eqy/iFk3n74UvYN/Iqv5SyVFoKehEB/JDLXdVrkN2mOwMvvZ+zhzzIa1md6ZvzGrRtC2ee6bt49uxJdlUlRgp6EQH+d+2dVY1bMrrv/+fccS/A3XfD+vUwcKDfFeuuu2DLliTVVGJVatCb2RQz22Jmq4uUNTCzBWb2aejxkAif7WVmeWa23szGxrPiIkGUzHVpIq3JM3xgJxg7Fj7/HLKzoVUruOUWaNYMhgzxm59LSovmin4q0KtY2VhgoXOuJbAw9PoAZpYGTAJ6A62BC82sdblqKxJgyV6XptQ1edLSoH9/ePNNWLsWrrzSd+V06uQ3SZk+HXbuDNsuLaqWXFENrzSzTOAV51zb0Os8oJtz7iszawy87ZzLKvaZU4DxzrmeodfjAJxzd5d2Pg2vlKqo84RFFIRZmiCl16X54Qe/1+2jj0JeHjRs6H8BjBgBzZr955dX0Y1X0mukaaOSBEjEWjeNnHNfAYQeDw9zTAawqcjr/FBZpEoON7McM8vZunVrGaslUnlFWn8mpdelOfhgP7t23TpYsABOPRUmTIDMTBg0iIWPPU/hrgNv3pa4u1aU9FdCbBI5jj7cIhoR/3xwzk0GJoO/ok9UpURSVZP66WGv6CNtUJKdW8DE+Xls3lZIk/rpyZ3cZAZnneW/NmzwM2//+lf+/O0srjm0OU936MvsNt3ZUbM2UL5fXsX/StjfxQXor4QIynpF/3Woy4bQY7jb7/lAsyKvmwKby3g+kcCLZYOSZPfnlygz01/Vb9rEnYPG8HP1Gtyx4C+899hvuO3NJzjq2/zYdtcqJuY9eKXMV/RzgaHAhNDjnDDHfAi0NLMWQAFwAXBRGc8nEnj7r0ajuUovKexS5qo2PZ02t1zH+TO7c+yXa7h0+Twuzn2Ny5a9zNcnd4U2O/w2iGlppX+vIiplF1eSlRr0ZjYD6AYcZmb5wG34gH/RzC4HNgKDQ8c2Af7qnOvjnNtjZqOA+UAaMMU5p+l1IiUY0D4jqqCuLGH3319eNbkh41ieGnA19277gNZznoNzzvFX/1ddBcOGkb1xZ1S/5GLt4hItaiZSKVXKETpF7d7tx+RPmgSLF7O3Zk2yj+nKlPZ9WdPol0Dk0TkayROedpgSCZi4bjieDDVqwODB8Pbb8NFHvNzuLHqvXcy8qdfx0jNjOHvtYvbs3Bm23z1he/AGmK7oRSqplBp1U04txs6j3s4fOW/VQi7NfYUW33/FljqHMKNdL677+31+43MpUUlX9Ap6EUm6ol1R5vbR5Ytchi57mW5fLKNaWppfY2fUKDjttIRtf1jZf3Gq60ZEUlrRrihn1Vh81IlcfdHtvJn9Dlx7LbzxBnTpAiec4Dc/37EjrudP6eGqcaCgF5Gki9Tv3uOcznD//ZCfD5Mn+4OHD/fbH954I3z2WYnfN9oZtLGMza+Ms3LVdSMilYdzsHSpX1tn5kzYuxd694ZrroEePaDaf69dYxmd02LsvLDT9g34YkLfMn3PiqauGxEJBjPfT//88/Dll/CHP8Dy5T7ss7LgwQdh2zYgtqv0SGPwi5dX1lm5CnoRqZyaNIHx433gP/ccNGoEN9wAGRkwYgT1Pl0X9mPhJpVFO1y1skxUK06bg4tI5XbQQXDhhf4rN9d360ybxus7d/LPZm2Z1qEfC1qezJ40H3fhrt6jXX6iss7KVR+9iATPt9+y+k8PUH/aUzT999d8VfdQnm3fm+wT+zB6SJcy96dX1j56Bb2IBFZ2zkbee+Rp+r4ziy4bctlXvQbVfn2+H5N/0kllGpOfquPtFfQiInl5fm2dqVNh+3Y48UQf+L/+NaSndtdLNDTqRkQkKwseeQQKCuCxx6CwEC67zG9yPnasv6kbUAp6Eala6tWDkSNh9WpYtMjPuJ04EY46CgYMgPffT3YN405BLyJVkxl07w6zZsEXX/ir+qVLYf36ZNcs7tRHLyKy386dfserGjWSXZOYldRHr3H0IiL71aqV7BokhIJeRCRBUmUopoJeRCQBik+u2r/0MVDhYa+bsSIiCZBKC6Ap6EVEEiCVFkBT0IuIJEC0Sx9XBAW9iEgCRLv0MSR+1yrdjBURSYBolz6uiJu2CnoRkQQZ0D6j1LAu6aZtvIJeXTciIklUETdtFfQiIklUETdtFfQiIkkUy03bslIfvYhIEkV707Y8FPQiIkkWzU3b8lDXjYhIwCnoRUQCTkEvIhJwCnoRkYBT0IuIBFxK7hlrZluBLxN8msOAbxJ8jooWtDYFrT0QvDYFrT1Qedt0pHOuYbg3UjLoK4KZ5UTaSLeyClqbgtYeCF6bgtYeCGab1HUjIhJwCnoRkYCrykE/OdkVSICgtSlo7YHgtSlo7YEAtqnK9tGLiFQVVfmKXkSkSlDQi4gEXKCC3symmNkWM1tdpKydmb1nZqvM7GUzO7jIe+PMbL2Z5ZlZzyLlJ4aOX29mj5iZVXRbQvWIuj1m9iszWxYqX2ZmZ6Rae0J1ienfKPR+czP70cxGFylLiTaV4Wfu+NB7a0Lv10ql9oTqEsvPXQ0zmxYqX2dm44p8JiXaZGbNzOytUP3WmNl1ofIGZrbAzD4NPR5S5DMpnQ0xc84F5gvoAnQAVhcp+xDoGno+DLg99Lw1sBKoCbQAPgPSQu99AJwCGPAa0LsStKc90CT0vC1QUOQzKdGeWNtU5P2ZwN+B0anWphj/jaoDHwHtQq8PTbWfuTK06SLg+dDz2sAGIDOV2gQ0BjqEntcDPgn9/78XGBsqHwvcE3qe8tkQ61egruidc0uA74oVZwFLQs8XAINCz/vjf0B/ds59AawHOplZY+Bg59x7zv/LPg0MSHjlw4ilPc65XOfc5lD5GqCWmdVMpfaE6hnLvxFmNgD4HN+m/WUp06YY29MD+Mg5tzL02W+dc3tTqT2hesXSJgfUMbPqQDqwC/ghldrknPvKObc89Hw7sA7IwGfAtNBh04rUL+WzIVaBCvoIVgPnhJ4PBpqFnmcAm4oclx8qywg9L16eKiK1p6hBQK5z7mdSvz0QoU1mVge4GfhjseNTvU2R/o1aAc7M5pvZcjO7KVSe6u2ByG16CdgBfAVsBO5zzn1HirbJzDLxf/2+DzRyzn0F/pcBcHjosMqaDRFVhaAfBlxtZsvwf7btCpWH61tzJZSnikjtAcDM2gD3AL/dXxTme6RSeyBym/4IPOic+7HY8anepkjtqQ6cBlwcejzXzM4k9dsDkdvUCdgLNMF3c9xoZkeRgm0ys7r4bsDrnXM/lHRomLLKkA0RBX4rQefcx/g/mTGzVkDf0Fv5HHg13BTYHCpvGqY8JZTQHsysKTAbGOKc+yxUnNLtgRLbdBJwnpndC9QH9pnZTvx/1pRtUyk/c4udc9+E3nsV3xf+DCncHiixTRcBrzvndgNbzGwp0BF4hxRqk5nVwP/cPOucmxUq/trMGjvnvgp1y2wJlVfKbChJ4K/ozezw0GM14Fbg8dBbc4ELQv3YLYCWwAehP+G2m9nJoTvqQ4A5Sah6WJHaY2b1gXnAOOfc0v3Hp3p7IHKbnHOnO+cynXOZwEPAXc65R1O9TSX8zM0Hjjez2qE+7a7A2lRvD5TYpo3AGebVAU4GPk6lNoXO/xSwzjn3QJG35gJDQ8+H8t/6VcpsKFGy7wbH8wuYge8r3I3/7Xs5cB3+LvsnwARCs4FDx9+Cv6OeR5G75/grktWh9x4t+plUbQ/+P98OYEWRr8NTqT1l+Tcq8rnxHDjqJiXaVIafuUvwN5ZXA/emWnvK8HNXFz8iag2wFhiTam3Cd5M5/Iin/f83+uBHPS0EPg09NijymZTOhli/tASCiEjABb7rRkSkqlPQi4gEnIJeRCTgFPQiIgGnoBcRCTgFvYhIwCnoRUQC7v8A/ZYi4msvsIQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(prediction_x, model.predict(prediction_x), color = 'red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "residuals = y - model.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0     0.860894\n",
      "1    -0.086005\n",
      "2    -0.032904\n",
      "3     0.193647\n",
      "4    -0.179803\n",
      "5    -0.126701\n",
      "6    -0.020499\n",
      "7    -0.167397\n",
      "8     0.085704\n",
      "9    -0.361195\n",
      "10   -0.308093\n",
      "11   -0.148790\n",
      "12    0.004312\n",
      "13    0.157413\n",
      "14   -0.089486\n",
      "15   -0.236384\n",
      "16   -0.233283\n",
      "17    0.009818\n",
      "18   -0.017081\n",
      "19    0.226021\n",
      "20    0.019122\n",
      "21    0.002223\n",
      "22    0.095325\n",
      "23    0.028426\n",
      "24    0.111527\n",
      "25    0.144629\n",
      "26    0.037730\n",
      "27    0.030831\n",
      "Name: time, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9032394707859825e-16"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2., 6., 7., 8., 4., 0., 0., 0., 0., 1.]),\n",
       " array([-0.36119479, -0.23898595, -0.11677712,  0.00543172,  0.12764055,\n",
       "         0.24984939,  0.37205822,  0.49426705,  0.61647589,  0.73868472,\n",
       "         0.86089356]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17abe3d3ec8>]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, residuals, \"o\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Boston Housing Data set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many problems with this dataset, especially with its usage of race. Just the fact that the creators of the dataset decided to include the proportion of Black residents as a variable suggests that they believed this could have been a factor in housing prices and the data could be perpetuating known problems of systemic racism in the real estate market.\n",
    "\n",
    "I want to take my mistake and this moment and encourage all students who decide to use any data set to take the time to investigate its collection and its historical context. Please be aware of any possible biases that could exist or be perpetuated simply from the variables that the authors chose to consider or failed to consider.\n",
    "\n",
    "This linked article provides another person's perspective on this data. https://www.linkedin.com/pulse/its-time-retire-boston-housing-dataset-colleen-e-crangle/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "boston = load_boston()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sklearn.utils.Bunch"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(boston)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename'])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.keys()  # boston is a dictionary, the x variables are in 'data' and the y values are in 'target'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 13)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.data.shape  # the x matrix, 506 rows 13 columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506,)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.target.shape # the one-dimensional target y values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['CRIM' 'ZN' 'INDUS' 'CHAS' 'NOX' 'RM' 'AGE' 'DIS' 'RAD' 'TAX' 'PTRATIO'\n",
      " 'B' 'LSTAT']\n"
     ]
    }
   ],
   "source": [
    "print(boston.feature_names)  # the names of the x variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "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)  # data dictionary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C:\\\\Users\\\\miles\\\\anaconda3\\\\lib\\\\site-packages\\\\sklearn\\\\datasets\\\\data\\\\boston_house_prices.csv'"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.filename"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(boston.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        0     1     2    3      4      5     6       7    8      9     10  \\\n",
      "0  0.00632  18.0  2.31  0.0  0.538  6.575  65.2  4.0900  1.0  296.0  15.3   \n",
      "1  0.02731   0.0  7.07  0.0  0.469  6.421  78.9  4.9671  2.0  242.0  17.8   \n",
      "2  0.02729   0.0  7.07  0.0  0.469  7.185  61.1  4.9671  2.0  242.0  17.8   \n",
      "3  0.03237   0.0  2.18  0.0  0.458  6.998  45.8  6.0622  3.0  222.0  18.7   \n",
      "4  0.06905   0.0  2.18  0.0  0.458  7.147  54.2  6.0622  3.0  222.0  18.7   \n",
      "\n",
      "       11    12  \n",
      "0  396.90  4.98  \n",
      "1  396.90  9.14  \n",
      "2  392.83  4.03  \n",
      "3  394.63  2.94  \n",
      "4  396.90  5.33  \n"
     ]
    }
   ],
   "source": [
    "# we will convert to pandas dataframe\n",
    "bos = pd.DataFrame(boston.data)\n",
    "print(bos.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\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": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bos.columns = boston.feature_names\n",
    "bos.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([24. , 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.target[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we will add the array of values to the bos dataframe\n",
    "bos['PRICE'] = boston.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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",
       "      <th>PRICE</th>\n",
       "    </tr>\n",
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       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
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       "      <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",
       "      <td>24.0</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",
       "      <td>21.6</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",
       "      <td>34.7</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",
       "      <td>33.4</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",
       "      <td>36.2</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  PRICE  \n",
       "0     15.3  396.90   4.98   24.0  \n",
       "1     17.8  396.90   9.14   21.6  \n",
       "2     17.8  392.83   4.03   34.7  \n",
       "3     18.7  394.63   2.94   33.4  \n",
       "4     18.7  396.90   5.33   36.2  "
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bos.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "bosmodel = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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",
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       "      <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": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = bos.loc[:, 'CRIM':'LSTAT']\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.series.Series"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(bos.loc[:,'PRICE'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bosmodel.fit(X, boston.target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.08011358e-01,  4.64204584e-02,  2.05586264e-02,  2.68673382e+00,\n",
       "       -1.77666112e+01,  3.80986521e+00,  6.92224640e-04, -1.47556685e+00,\n",
       "        3.06049479e-01, -1.23345939e-02, -9.52747232e-01,  9.31168327e-03,\n",
       "       -5.24758378e-01])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bosmodel.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "yhat = bosmodel.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "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.plot(yhat, boston.target, 'o')\n",
    "plt.xlabel('predicted')\n",
    "plt.ylabel('actual')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "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": [
    "residuals = boston.target - yhat\n",
    "plt.plot(yhat, residuals, 'o')\n",
    "plt.xlabel('predicted')\n",
    "plt.ylabel('residual')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7406426641094095"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bosmodel.score(X, boston.target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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