09-03a_scikit_learn_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": [],
   "source": [
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": [
    "np.random.seed(1)\n",
    "x = 10 * np.random.rand(50)\n",
    "y = 1 + 0.8 * x + np.random.randn(50)\n",
    "plt.scatter(x, y)\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50,)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)\n"
     ]
    }
   ],
   "source": [
    "print(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.17022005e+00 7.20324493e+00 1.14374817e-03 3.02332573e+00\n",
      " 1.46755891e+00 9.23385948e-01 1.86260211e+00 3.45560727e+00\n",
      " 3.96767474e+00 5.38816734e+00 4.19194514e+00 6.85219500e+00\n",
      " 2.04452250e+00 8.78117436e+00 2.73875932e-01 6.70467510e+00\n",
      " 4.17304802e+00 5.58689828e+00 1.40386939e+00 1.98101489e+00\n",
      " 8.00744569e+00 9.68261576e+00 3.13424178e+00 6.92322616e+00\n",
      " 8.76389152e+00 8.94606664e+00 8.50442114e-01 3.90547832e-01\n",
      " 1.69830420e+00 8.78142503e+00 9.83468338e-01 4.21107625e+00\n",
      " 9.57889530e+00 5.33165285e+00 6.91877114e+00 3.15515631e+00\n",
      " 6.86500928e+00 8.34625672e+00 1.82882773e-01 7.50144315e+00\n",
      " 9.88861089e+00 7.48165654e+00 2.80443992e+00 7.89279328e+00\n",
      " 1.03226007e+00 4.47893526e+00 9.08595503e+00 2.93614148e+00\n",
      " 2.87775339e+00 1.30028572e+00]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50,)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50, 1)\n"
     ]
    }
   ],
   "source": [
    "# we create an X matrix using the x values\n",
    "X = x.reshape([50,1])\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)\n"
     ]
    }
   ],
   "source": [
    "# now we fit the model\n",
    "model.fit(X, y)\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.82720881]\n"
     ]
    }
   ],
   "source": [
    "print(model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.001422914446795\n"
     ]
    }
   ],
   "source": [
    "print(model.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21,)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction_x  = np.linspace(0, 10, 21)\n",
    "prediction_x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction_x = prediction_x.reshape([-1,1])\n",
    "# -1 tells numpy to figure out what value it should use because the human was too lazy to figure it out themselves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00142291, 1.41502732, 1.82863172, 2.24223613, 2.65584054,\n",
       "       3.06944494, 3.48304935, 3.89665375, 4.31025816, 4.72386256,\n",
       "       5.13746697, 5.55107137, 5.96467578, 6.37828018, 6.79188459,\n",
       "       7.20548899, 7.6190934 , 8.0326978 , 8.44630221, 8.85990661,\n",
       "       9.27351102])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(prediction_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(prediction_x, model.predict(prediction_x), color = 'red', marker = '.')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "residuals = y - model.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.80206234 -1.04262028 -0.67270017 -0.09634861 -1.1586638   0.20786855\n",
      "  1.60770007  0.64659828 -0.30121418 -1.0356575  -0.86263905  1.50459161\n",
      " -0.00624418 -0.87734387  0.18204073  1.91640599  0.00519237  0.46376734\n",
      "  0.26054979 -0.40757382 -1.36181418 -0.61421809 -0.29559614  0.39682753\n",
      "  0.59910544  0.68626734  0.26102489  0.87309191 -0.80202969  1.01251311\n",
      "  0.4847479  -0.41409412  0.22646489 -0.22206256  0.94195494  1.43254585\n",
      "  1.99736376 -1.62501097 -1.45051274 -0.70999412 -0.11044318  0.67117903\n",
      "  0.23790656 -2.23837765 -0.3357135   0.70468523 -0.01854621  0.68069935\n",
      " -0.3020513  -0.23756021]\n"
     ]
    }
   ],
   "source": [
    "print(residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.39648317751562e-16"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.,  2.,  4.,  7.,  8., 11.,  9.,  3.,  2.,  3.]),\n",
       " array([-2.23837765, -1.81480351, -1.39122937, -0.96765523, -0.54408108,\n",
       "        -0.12050694,  0.3030672 ,  0.72664134,  1.15021548,  1.57378962,\n",
       "         1.99736376]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 34,
     "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": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x26c7989e438>]"
      ]
     },
     "execution_count": 35,
     "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": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "boston = load_boston()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sklearn.utils.Bunch"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(boston)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename'])"
      ]
     },
     "execution_count": 38,
     "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": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 13)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.data.shape  # the x matrix, 506 rows 13 columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506,)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.target.shape # the one-dimensional target y values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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": 42,
   "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": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C:\\\\ProgramData\\\\Anaconda3\\\\lib\\\\site-packages\\\\sklearn\\\\datasets\\\\data\\\\boston_house_prices.csv'"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.filename"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(boston.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "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": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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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",
       "      <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": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bos.columns = boston.feature_names\n",
    "bos.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "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": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.target[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we will add the array of values to the bos dataframe\n",
    "bos['PRICE'] = boston.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <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",
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       "      <th>LSTAT</th>\n",
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       "      <th>1</th>\n",
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       "      <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",
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       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
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       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
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       "      <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",
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       "  </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": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bos.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "bosmodel = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <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": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = bos.loc[:, 'CRIM':'LSTAT']\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.series.Series"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(bos.loc[:,'PRICE'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bosmodel.fit(X, boston.target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "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": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bosmodel.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "yhat = bosmodel.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "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": 57,
   "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": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7406426641094095"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bosmodel.score(X, boston.target)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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