DS4_simple_linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2caebf52",
   "metadata": {},
   "source": [
    "# 4) Data Analytics I\n",
    "Create a Linear Regression Model using Python/R to predict home prices using Boston Housing Dataset (https://www.kaggle.com/c/boston-housing). The Boston Housing dataset contains \n",
    "information about various houses in Boston through different parameters. There are 506 samples and 13 feature variables in this dataset.\n",
    "\n",
    "The objective is to predict the value of prices of the house using the given features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "80f5b843",
   "metadata": {},
   "outputs": [],
   "source": [
    "#import dependencies\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn import datasets\n",
    "from sklearn import linear_model\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a6db6e9e",
   "metadata": {},
   "outputs": [
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       "<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>MEDV</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</td>\n",
       "      <td>296</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</td>\n",
       "      <td>242</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</td>\n",
       "      <td>242</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</td>\n",
       "      <td>222</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</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>NaN</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>0.06263</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.593</td>\n",
       "      <td>69.1</td>\n",
       "      <td>2.4786</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>391.99</td>\n",
       "      <td>NaN</td>\n",
       "      <td>22.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>0.04527</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.120</td>\n",
       "      <td>76.7</td>\n",
       "      <td>2.2875</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.08</td>\n",
       "      <td>20.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>0.06076</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.976</td>\n",
       "      <td>91.0</td>\n",
       "      <td>2.1675</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.64</td>\n",
       "      <td>23.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>0.10959</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.794</td>\n",
       "      <td>89.3</td>\n",
       "      <td>2.3889</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>393.45</td>\n",
       "      <td>6.48</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>505</th>\n",
       "      <td>0.04741</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.030</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.5050</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>7.88</td>\n",
       "      <td>11.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>506 rows × 14 columns</p>\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  296   \n",
       "1    0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671    2  242   \n",
       "2    0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671    2  242   \n",
       "3    0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622    3  222   \n",
       "4    0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622    3  222   \n",
       "..       ...   ...    ...   ...    ...    ...   ...     ...  ...  ...   \n",
       "501  0.06263   0.0  11.93   0.0  0.573  6.593  69.1  2.4786    1  273   \n",
       "502  0.04527   0.0  11.93   0.0  0.573  6.120  76.7  2.2875    1  273   \n",
       "503  0.06076   0.0  11.93   0.0  0.573  6.976  91.0  2.1675    1  273   \n",
       "504  0.10959   0.0  11.93   0.0  0.573  6.794  89.3  2.3889    1  273   \n",
       "505  0.04741   0.0  11.93   0.0  0.573  6.030   NaN  2.5050    1  273   \n",
       "\n",
       "     PTRATIO       B  LSTAT  MEDV  \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    NaN  36.2  \n",
       "..       ...     ...    ...   ...  \n",
       "501     21.0  391.99    NaN  22.4  \n",
       "502     21.0  396.90   9.08  20.6  \n",
       "503     21.0  396.90   5.64  23.9  \n",
       "504     21.0  393.45   6.48  22.0  \n",
       "505     21.0  396.90   7.88  11.9  \n",
       "\n",
       "[506 rows x 14 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston = pd.read_csv(r'ds4_housing_data.csv')\n",
    "boston"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "17b61dc6",
   "metadata": {},
   "outputs": [
    {
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       "      <th>RM</th>\n",
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       "      <th>PTRATIO</th>\n",
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       "      <td>6.575</td>\n",
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       "      <th>1</th>\n",
       "      <td>6.421</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>21.6</td>\n",
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       "      <th>2</th>\n",
       "      <td>7.185</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>34.7</td>\n",
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       "      <th>3</th>\n",
       "      <td>6.998</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7.147</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "      RM  TAX  PTRATIO  MEDV\n",
       "0  6.575  296     15.3  24.0\n",
       "1  6.421  242     17.8  21.6\n",
       "2  7.185  242     17.8  34.7\n",
       "3  6.998  222     18.7  33.4\n",
       "4  7.147  222     18.7  36.2"
      ]
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   "source": [
    "# Transform the data set into a data frame\n",
    "# data = the data we want or independent variables also known as the x values\n",
    "# feature_names = the column names of the data \n",
    "\n",
    "# RM - average number of rooms\n",
    "# TAX - full-value property-tax rate per dollar 10,000\n",
    "# PTRATIO - pupil-teacher ratio by town\n",
    "\n",
    "df_x = boston[['RM','TAX','PTRATIO','MEDV']] \n",
    "df_x.head()\n",
    "     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "96ef4f6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RM         0\n",
       "TAX        0\n",
       "PTRATIO    0\n",
       "MEDV       0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_x.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fe1beb2a",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>24.0</td>\n",
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       "      <th>1</th>\n",
       "      <td>21.6</td>\n",
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       "      <th>2</th>\n",
       "      <td>34.7</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>36.2</td>\n",
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      "text/plain": [
       "   MEDV\n",
       "0  24.0\n",
       "1  21.6\n",
       "2  34.7\n",
       "3  33.4\n",
       "4  36.2"
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     "execution_count": 5,
     "metadata": {},
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   ],
   "source": [
    "# target = the target of variable or the price of the houses or dependent variables also known as the y value \n",
    "df_y = pd.DataFrame(boston.MEDV)\n",
    "df_y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "10c6da21",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RM</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>6.284634</td>\n",
       "      <td>408.237154</td>\n",
       "      <td>18.455534</td>\n",
       "      <td>22.532806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.702617</td>\n",
       "      <td>168.537116</td>\n",
       "      <td>2.164946</td>\n",
       "      <td>9.197104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>3.561000</td>\n",
       "      <td>187.000000</td>\n",
       "      <td>12.600000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.885500</td>\n",
       "      <td>279.000000</td>\n",
       "      <td>17.400000</td>\n",
       "      <td>17.025000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.208500</td>\n",
       "      <td>330.000000</td>\n",
       "      <td>19.050000</td>\n",
       "      <td>21.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>6.623500</td>\n",
       "      <td>666.000000</td>\n",
       "      <td>20.200000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>8.780000</td>\n",
       "      <td>711.000000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               RM         TAX     PTRATIO        MEDV\n",
       "count  506.000000  506.000000  506.000000  506.000000\n",
       "mean     6.284634  408.237154   18.455534   22.532806\n",
       "std      0.702617  168.537116    2.164946    9.197104\n",
       "min      3.561000  187.000000   12.600000    5.000000\n",
       "25%      5.885500  279.000000   17.400000   17.025000\n",
       "50%      6.208500  330.000000   19.050000   21.200000\n",
       "75%      6.623500  666.000000   20.200000   25.000000\n",
       "max      8.780000  711.000000   22.000000   50.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get some Statistics from the data set, count, mean \n",
    "df_x.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "eba2df2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Intialise the linear regression model\n",
    "from sklearn.linear_model import LinearRegression\n",
    "reg = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f2b850bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Split the data into 67% training and 33% testing data\n",
    "x_train, x_test, y_train, y_test = train_test_split(df_x, df_y, test_size= 0.33, random_state= 42)\n",
    "     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "75838de8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train the model with our training data\n",
    "reg.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ebf23b7f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9.40554071e-18  5.55111512e-17 -1.21430643e-15  1.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "# Print the co-efficients/weights for each feature/coloum of our model\n",
    "print(reg.coef_) #f(x) = mx + da + b = y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1d83b6a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[23.6]\n",
      " [32.4]\n",
      " [13.6]\n",
      " [22.8]\n",
      " [16.1]\n",
      " [20. ]\n",
      " [17.8]\n",
      " [14. ]\n",
      " [19.6]\n",
      " [16.8]\n",
      " [21.5]\n",
      " [18.9]\n",
      " [ 7. ]\n",
      " [21.2]\n",
      " [18.5]\n",
      " [29.8]\n",
      " [18.8]\n",
      " [10.2]\n",
      " [50. ]\n",
      " [14.1]\n",
      " [25.2]\n",
      " [29.1]\n",
      " [12.7]\n",
      " [22.4]\n",
      " [14.2]\n",
      " [13.8]\n",
      " [20.3]\n",
      " [14.9]\n",
      " [21.7]\n",
      " [18.3]\n",
      " [23.1]\n",
      " [23.8]\n",
      " [15. ]\n",
      " [20.8]\n",
      " [19.1]\n",
      " [19.4]\n",
      " [34.7]\n",
      " [19.5]\n",
      " [24.4]\n",
      " [23.4]\n",
      " [19.7]\n",
      " [28.2]\n",
      " [50. ]\n",
      " [17.4]\n",
      " [22.6]\n",
      " [15.1]\n",
      " [13.1]\n",
      " [24.2]\n",
      " [19.9]\n",
      " [24. ]\n",
      " [18.9]\n",
      " [35.4]\n",
      " [15.2]\n",
      " [26.5]\n",
      " [43.5]\n",
      " [21.2]\n",
      " [18.4]\n",
      " [28.5]\n",
      " [23.9]\n",
      " [18.5]\n",
      " [25. ]\n",
      " [35.4]\n",
      " [31.5]\n",
      " [20.2]\n",
      " [24.1]\n",
      " [20. ]\n",
      " [13.1]\n",
      " [24.8]\n",
      " [30.8]\n",
      " [12.7]\n",
      " [20. ]\n",
      " [23.7]\n",
      " [10.8]\n",
      " [20.6]\n",
      " [20.8]\n",
      " [ 5. ]\n",
      " [20.1]\n",
      " [48.5]\n",
      " [10.9]\n",
      " [ 7. ]\n",
      " [20.9]\n",
      " [17.2]\n",
      " [20.9]\n",
      " [ 9.7]\n",
      " [19.4]\n",
      " [29. ]\n",
      " [16.4]\n",
      " [25. ]\n",
      " [25. ]\n",
      " [17.1]\n",
      " [23.2]\n",
      " [10.4]\n",
      " [19.6]\n",
      " [17.2]\n",
      " [27.5]\n",
      " [23. ]\n",
      " [50. ]\n",
      " [17.9]\n",
      " [ 9.6]\n",
      " [17.2]\n",
      " [22.5]\n",
      " [21.4]\n",
      " [12. ]\n",
      " [19.9]\n",
      " [19.4]\n",
      " [13.4]\n",
      " [18.2]\n",
      " [24.6]\n",
      " [21.1]\n",
      " [24.7]\n",
      " [ 8.7]\n",
      " [27.5]\n",
      " [20.7]\n",
      " [36.2]\n",
      " [31.6]\n",
      " [11.7]\n",
      " [39.8]\n",
      " [13.9]\n",
      " [21.8]\n",
      " [23.7]\n",
      " [17.6]\n",
      " [24.4]\n",
      " [ 8.8]\n",
      " [19.2]\n",
      " [25.3]\n",
      " [20.4]\n",
      " [23.1]\n",
      " [37.9]\n",
      " [15.6]\n",
      " [45.4]\n",
      " [15.7]\n",
      " [22.6]\n",
      " [14.5]\n",
      " [18.7]\n",
      " [17.8]\n",
      " [16.1]\n",
      " [20.6]\n",
      " [31.6]\n",
      " [29.1]\n",
      " [15.6]\n",
      " [17.5]\n",
      " [22.5]\n",
      " [19.4]\n",
      " [19.3]\n",
      " [ 8.5]\n",
      " [20.6]\n",
      " [17. ]\n",
      " [17.1]\n",
      " [14.5]\n",
      " [50. ]\n",
      " [14.3]\n",
      " [12.6]\n",
      " [28.7]\n",
      " [21.2]\n",
      " [19.3]\n",
      " [23.1]\n",
      " [19.1]\n",
      " [25. ]\n",
      " [33.4]\n",
      " [ 5. ]\n",
      " [29.6]\n",
      " [18.7]\n",
      " [21.7]\n",
      " [23.1]\n",
      " [22.8]\n",
      " [21. ]\n",
      " [48.8]]\n"
     ]
    }
   ],
   "source": [
    "# print the predictions on our test data\n",
    "y_pred = reg.predict(x_test)\n",
    "print(y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9db71fd1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     MEDV\n",
      "173  23.6\n",
      "274  32.4\n",
      "491  13.6\n",
      "72   22.8\n",
      "452  16.1\n",
      "..    ...\n",
      "110  21.7\n",
      "321  23.1\n",
      "265  22.8\n",
      "29   21.0\n",
      "262  48.8\n",
      "\n",
      "[167 rows x 1 columns]\n"
     ]
    }
   ],
   "source": [
    "# Print the actual values\n",
    "print(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b6900163",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.911777469612269e-29\n"
     ]
    }
   ],
   "source": [
    "# Check the model performance/accuracy using Mean Squared error(MSE)\n",
    "print( np.mean((y_pred - y_test)**2 ))\n",
    "     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "843f9cbd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.911777469612269e-29\n"
     ]
    }
   ],
   "source": [
    "# Check the model performance/accuracy using Mean Squared error (MSE) and sklearn.metrics\n",
    "from sklearn.metrics import mean_squared_error\n",
    "print( mean_squared_error(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cd1c2c40",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Squared Error: 9.911777469612269e-29\n",
      "Mean Absolute Error: 8.674365284616194e-15\n",
      "Root Mean Squared Error: 9.95579101307991e-15\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "mse = metrics.mean_squared_error(y_test,y_pred)\n",
    "mae = metrics.mean_absolute_error(y_test,y_pred)\n",
    "rmse = np.sqrt(metrics.mean_squared_error(y_test,y_pred))\n",
    "print(f'Mean Squared Error: {mse}',f'Mean Absolute Error: {mae}',f'Root Mean Squared Error: {rmse}',sep='\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b127b63f",
   "metadata": {},
   "source": [
    "From above *Evaluation Metrices*, we can notice that Root Mean Squared Error is low for our  Regression Model and that is good thing for us."
   ]
  }
 ],
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