Linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression on Boston's Housing Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression\n",
    "\n",
    "Linear regression is used to find the linear relationhip between target variable and one and more predictive variable .It is useful for finding relationship between two continous variable .One is predictor variable (also called independent variable) and other is the target variable (also called dependent variable). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np#numpy for operating mathmatical functions\n",
    "\n",
    "import pandas as pd#pandas for data retrival and manipulation\n",
    "\n",
    "import matplotlib.pyplot as plt#matplotlib for visualising data\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston# importing data from scikit learn library\n",
    "\n",
    "boston = load_boston()#making an istance of data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['data', 'target', 'feature_names', 'DESCR'])\n"
     ]
    }
   ],
   "source": [
    "print(boston.keys())#for printing out the key functionalitis provided by data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[6.3200e-03 1.8000e+01 2.3100e+00 ... 1.5300e+01 3.9690e+02 4.9800e+00]\n",
      " [2.7310e-02 0.0000e+00 7.0700e+00 ... 1.7800e+01 3.9690e+02 9.1400e+00]\n",
      " [2.7290e-02 0.0000e+00 7.0700e+00 ... 1.7800e+01 3.9283e+02 4.0300e+00]\n",
      " ...\n",
      " [6.0760e-02 0.0000e+00 1.1930e+01 ... 2.1000e+01 3.9690e+02 5.6400e+00]\n",
      " [1.0959e-01 0.0000e+00 1.1930e+01 ... 2.1000e+01 3.9345e+02 6.4800e+00]\n",
      " [4.7410e-02 0.0000e+00 1.1930e+01 ... 2.1000e+01 3.9690e+02 7.8800e+00]]\n"
     ]
    }
   ],
   "source": [
    "print(boston.data)# first key printing data values of the boston data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[24.  21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 15.  18.9 21.7 20.4\n",
      " 18.2 19.9 23.1 17.5 20.2 18.2 13.6 19.6 15.2 14.5 15.6 13.9 16.6 14.8\n",
      " 18.4 21.  12.7 14.5 13.2 13.1 13.5 18.9 20.  21.  24.7 30.8 34.9 26.6\n",
      " 25.3 24.7 21.2 19.3 20.  16.6 14.4 19.4 19.7 20.5 25.  23.4 18.9 35.4\n",
      " 24.7 31.6 23.3 19.6 18.7 16.  22.2 25.  33.  23.5 19.4 22.  17.4 20.9\n",
      " 24.2 21.7 22.8 23.4 24.1 21.4 20.  20.8 21.2 20.3 28.  23.9 24.8 22.9\n",
      " 23.9 26.6 22.5 22.2 23.6 28.7 22.6 22.  22.9 25.  20.6 28.4 21.4 38.7\n",
      " 43.8 33.2 27.5 26.5 18.6 19.3 20.1 19.5 19.5 20.4 19.8 19.4 21.7 22.8\n",
      " 18.8 18.7 18.5 18.3 21.2 19.2 20.4 19.3 22.  20.3 20.5 17.3 18.8 21.4\n",
      " 15.7 16.2 18.  14.3 19.2 19.6 23.  18.4 15.6 18.1 17.4 17.1 13.3 17.8\n",
      " 14.  14.4 13.4 15.6 11.8 13.8 15.6 14.6 17.8 15.4 21.5 19.6 15.3 19.4\n",
      " 17.  15.6 13.1 41.3 24.3 23.3 27.  50.  50.  50.  22.7 25.  50.  23.8\n",
      " 23.8 22.3 17.4 19.1 23.1 23.6 22.6 29.4 23.2 24.6 29.9 37.2 39.8 36.2\n",
      " 37.9 32.5 26.4 29.6 50.  32.  29.8 34.9 37.  30.5 36.4 31.1 29.1 50.\n",
      " 33.3 30.3 34.6 34.9 32.9 24.1 42.3 48.5 50.  22.6 24.4 22.5 24.4 20.\n",
      " 21.7 19.3 22.4 28.1 23.7 25.  23.3 28.7 21.5 23.  26.7 21.7 27.5 30.1\n",
      " 44.8 50.  37.6 31.6 46.7 31.5 24.3 31.7 41.7 48.3 29.  24.  25.1 31.5\n",
      " 23.7 23.3 22.  20.1 22.2 23.7 17.6 18.5 24.3 20.5 24.5 26.2 24.4 24.8\n",
      " 29.6 42.8 21.9 20.9 44.  50.  36.  30.1 33.8 43.1 48.8 31.  36.5 22.8\n",
      " 30.7 50.  43.5 20.7 21.1 25.2 24.4 35.2 32.4 32.  33.2 33.1 29.1 35.1\n",
      " 45.4 35.4 46.  50.  32.2 22.  20.1 23.2 22.3 24.8 28.5 37.3 27.9 23.9\n",
      " 21.7 28.6 27.1 20.3 22.5 29.  24.8 22.  26.4 33.1 36.1 28.4 33.4 28.2\n",
      " 22.8 20.3 16.1 22.1 19.4 21.6 23.8 16.2 17.8 19.8 23.1 21.  23.8 23.1\n",
      " 20.4 18.5 25.  24.6 23.  22.2 19.3 22.6 19.8 17.1 19.4 22.2 20.7 21.1\n",
      " 19.5 18.5 20.6 19.  18.7 32.7 16.5 23.9 31.2 17.5 17.2 23.1 24.5 26.6\n",
      " 22.9 24.1 18.6 30.1 18.2 20.6 17.8 21.7 22.7 22.6 25.  19.9 20.8 16.8\n",
      " 21.9 27.5 21.9 23.1 50.  50.  50.  50.  50.  13.8 13.8 15.  13.9 13.3\n",
      " 13.1 10.2 10.4 10.9 11.3 12.3  8.8  7.2 10.5  7.4 10.2 11.5 15.1 23.2\n",
      "  9.7 13.8 12.7 13.1 12.5  8.5  5.   6.3  5.6  7.2 12.1  8.3  8.5  5.\n",
      " 11.9 27.9 17.2 27.5 15.  17.2 17.9 16.3  7.   7.2  7.5 10.4  8.8  8.4\n",
      " 16.7 14.2 20.8 13.4 11.7  8.3 10.2 10.9 11.   9.5 14.5 14.1 16.1 14.3\n",
      " 11.7 13.4  9.6  8.7  8.4 12.8 10.5 17.1 18.4 15.4 10.8 11.8 14.9 12.6\n",
      " 14.1 13.  13.4 15.2 16.1 17.8 14.9 14.1 12.7 13.5 14.9 20.  16.4 17.7\n",
      " 19.5 20.2 21.4 19.9 19.  19.1 19.1 20.1 19.9 19.6 23.2 29.8 13.8 13.3\n",
      " 16.7 12.  14.6 21.4 23.  23.7 25.  21.8 20.6 21.2 19.1 20.6 15.2  7.\n",
      "  8.1 13.6 20.1 21.8 24.5 23.1 19.7 18.3 21.2 17.5 16.8 22.4 20.6 23.9\n",
      " 22.  11.9]\n"
     ]
    }
   ],
   "source": [
    "print(boston.target)# printing out the values of the target(dependent) variable "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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)# printing out the names of columns of the dataset "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boston House Prices dataset\n",
      "===========================\n",
      "\n",
      "Notes\n",
      "------\n",
      "Data Set Characteristics:  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive\n",
      "    \n",
      "    :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",
      "http://archive.ics.uci.edu/ml/datasets/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",
      "**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",
      "   - many more! (see http://archive.ics.uci.edu/ml/datasets/Housing)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(boston.DESCR)# printing the whole description about the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(506, 13)\n"
     ]
    }
   ],
   "source": [
    "print(boston.data.shape)# printing the dimensions of data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
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       "      <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",
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       "      <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",
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       "        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",
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       "\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  "
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     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(boston.data)# converting boston data into dataframe\n",
    "\n",
    "df.head()#printing 5 rows of the data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <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",
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       "      <td>0.00632</td>\n",
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       "      <td>0.538</td>\n",
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       "      <td>0.02731</td>\n",
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       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
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       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>7.185</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",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
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       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
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       "      <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": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns = boston.feature_names# assigning name to the columns of dataframe\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
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       "      <td>0.538</td>\n",
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       "      <td>24.0</td>\n",
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       "    <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",
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       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
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       "    <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",
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       "    <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": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['PRICE'] = boston.target#adding price column to the data \n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df.drop('PRICE',axis = 1)#droping Price column\n",
    "\n",
    "Y = df['PRICE']#creating a target vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>CRIM</th>\n",
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       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
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       "      <th>RM</th>\n",
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       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
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       "      <td>396.90</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
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       "      <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",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
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       "      <td>6.0622</td>\n",
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       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
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       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
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       "      <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": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    24.0\n",
       "1    21.6\n",
       "2    34.7\n",
       "3    33.4\n",
       "4    36.2\n",
       "Name: PRICE, dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split#spliting dataset "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train , x_test , y_train , y_test = train_test_split(X,Y,test_size = 0.3,random_state = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>445</th>\n",
       "      <td>0.67180</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>24.0</td>\n",
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       "    <tr>\n",
       "      <th>428</th>\n",
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       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.679</td>\n",
       "      <td>6.193</td>\n",
       "      <td>78.1</td>\n",
       "      <td>1.9356</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>96.73</td>\n",
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       "      <th>481</th>\n",
       "      <td>5.70818</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.532</td>\n",
       "      <td>6.750</td>\n",
       "      <td>74.9</td>\n",
       "      <td>3.3317</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>393.07</td>\n",
       "      <td>7.74</td>\n",
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       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>0.01311</td>\n",
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       "      <td>0.403</td>\n",
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       "      <td>226.0</td>\n",
       "      <td>17.9</td>\n",
       "      <td>395.93</td>\n",
       "      <td>4.81</td>\n",
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       "      <th>488</th>\n",
       "      <td>0.15086</td>\n",
       "      <td>0.0</td>\n",
       "      <td>27.74</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.609</td>\n",
       "      <td>5.454</td>\n",
       "      <td>92.7</td>\n",
       "      <td>1.8209</td>\n",
       "      <td>4.0</td>\n",
       "      <td>711.0</td>\n",
       "      <td>20.1</td>\n",
       "      <td>395.09</td>\n",
       "      <td>18.06</td>\n",
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       "</table>\n",
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      ],
      "text/plain": [
       "        CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS   RAD    TAX  \\\n",
       "445  0.67180   0.0  18.10   0.0  0.740  6.459  94.8  1.9879  24.0  666.0   \n",
       "428  7.36711   0.0  18.10   0.0  0.679  6.193  78.1  1.9356  24.0  666.0   \n",
       "481  5.70818   0.0  18.10   0.0  0.532  6.750  74.9  3.3317  24.0  666.0   \n",
       "55   0.01311  90.0   1.22   0.0  0.403  7.249  21.9  8.6966   5.0  226.0   \n",
       "488  0.15086   0.0  27.74   0.0  0.609  5.454  92.7  1.8209   4.0  711.0   \n",
       "\n",
       "     PTRATIO       B  LSTAT  \n",
       "445     20.2   43.06  23.98  \n",
       "428     20.2   96.73  21.52  \n",
       "481     20.2  393.07   7.74  \n",
       "55      17.9  395.93   4.81  \n",
       "488     20.1  395.09  18.06  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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>60</th>\n",
       "      <td>0.14932</td>\n",
       "      <td>25.0</td>\n",
       "      <td>5.13</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.453</td>\n",
       "      <td>5.741</td>\n",
       "      <td>66.2</td>\n",
       "      <td>7.2254</td>\n",
       "      <td>8.0</td>\n",
       "      <td>284.0</td>\n",
       "      <td>19.7</td>\n",
       "      <td>395.11</td>\n",
       "      <td>13.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>108</th>\n",
       "      <td>0.12802</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.56</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.520</td>\n",
       "      <td>6.474</td>\n",
       "      <td>97.1</td>\n",
       "      <td>2.4329</td>\n",
       "      <td>5.0</td>\n",
       "      <td>384.0</td>\n",
       "      <td>20.9</td>\n",
       "      <td>395.24</td>\n",
       "      <td>12.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>298</th>\n",
       "      <td>0.06466</td>\n",
       "      <td>70.0</td>\n",
       "      <td>2.24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.400</td>\n",
       "      <td>6.345</td>\n",
       "      <td>20.1</td>\n",
       "      <td>7.8278</td>\n",
       "      <td>5.0</td>\n",
       "      <td>358.0</td>\n",
       "      <td>14.8</td>\n",
       "      <td>368.24</td>\n",
       "      <td>4.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>138</th>\n",
       "      <td>0.24980</td>\n",
       "      <td>0.0</td>\n",
       "      <td>21.89</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.624</td>\n",
       "      <td>5.857</td>\n",
       "      <td>98.2</td>\n",
       "      <td>1.6686</td>\n",
       "      <td>4.0</td>\n",
       "      <td>437.0</td>\n",
       "      <td>21.2</td>\n",
       "      <td>392.04</td>\n",
       "      <td>21.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>370</th>\n",
       "      <td>6.53876</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.631</td>\n",
       "      <td>7.016</td>\n",
       "      <td>97.5</td>\n",
       "      <td>1.2024</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>392.05</td>\n",
       "      <td>2.96</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS   RAD    TAX  \\\n",
       "60   0.14932  25.0   5.13   0.0  0.453  5.741  66.2  7.2254   8.0  284.0   \n",
       "108  0.12802   0.0   8.56   0.0  0.520  6.474  97.1  2.4329   5.0  384.0   \n",
       "298  0.06466  70.0   2.24   0.0  0.400  6.345  20.1  7.8278   5.0  358.0   \n",
       "138  0.24980   0.0  21.89   0.0  0.624  5.857  98.2  1.6686   4.0  437.0   \n",
       "370  6.53876   0.0  18.10   1.0  0.631  7.016  97.5  1.2024  24.0  666.0   \n",
       "\n",
       "     PTRATIO       B  LSTAT  \n",
       "60      19.7  395.11  13.15  \n",
       "108     20.9  395.24  12.27  \n",
       "298     14.8  368.24   4.97  \n",
       "138     21.2  392.04  21.32  \n",
       "370     20.2  392.05   2.96  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_test.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression#importing linear regrssion module from sklearn\n",
    "\n",
    "LR = LinearRegression()\n",
    "\n",
    "LR.fit(x_train, y_train)#fitting the training data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = LR.predict(x_test)#predicting values of testing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Predicted prices')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(y_test,y_pred)#pl\n",
    "\n",
    "plt.xlabel('Prices')\n",
    "\n",
    "plt.ylabel('Predicted prices')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6771045545035987"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "r2_score(y_test,y_pred)"
   ]
  },
  {
   "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
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}