Multiple  Regression Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import Library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import DataSet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = pd.read_csv(r'F:\\multi linear\\insurance.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>bmi</th>\n",
       "      <th>children</th>\n",
       "      <th>smoker</th>\n",
       "      <th>region</th>\n",
       "      <th>charges</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>female</td>\n",
       "      <td>27.900</td>\n",
       "      <td>0</td>\n",
       "      <td>yes</td>\n",
       "      <td>southwest</td>\n",
       "      <td>16884.92400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>18</td>\n",
       "      <td>male</td>\n",
       "      <td>33.770</td>\n",
       "      <td>1</td>\n",
       "      <td>no</td>\n",
       "      <td>southeast</td>\n",
       "      <td>1725.55230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>28</td>\n",
       "      <td>male</td>\n",
       "      <td>33.000</td>\n",
       "      <td>3</td>\n",
       "      <td>no</td>\n",
       "      <td>southeast</td>\n",
       "      <td>4449.46200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>33</td>\n",
       "      <td>male</td>\n",
       "      <td>22.705</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>northwest</td>\n",
       "      <td>21984.47061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>32</td>\n",
       "      <td>male</td>\n",
       "      <td>28.880</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>northwest</td>\n",
       "      <td>3866.85520</td>\n",
       "    </tr>\n",
       "    <tr>\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",
       "      <td>1333</td>\n",
       "      <td>50</td>\n",
       "      <td>male</td>\n",
       "      <td>30.970</td>\n",
       "      <td>3</td>\n",
       "      <td>no</td>\n",
       "      <td>northwest</td>\n",
       "      <td>10600.54830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1334</td>\n",
       "      <td>18</td>\n",
       "      <td>female</td>\n",
       "      <td>31.920</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>northeast</td>\n",
       "      <td>2205.98080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1335</td>\n",
       "      <td>18</td>\n",
       "      <td>female</td>\n",
       "      <td>36.850</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>southeast</td>\n",
       "      <td>1629.83350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1336</td>\n",
       "      <td>21</td>\n",
       "      <td>female</td>\n",
       "      <td>25.800</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>southwest</td>\n",
       "      <td>2007.94500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1337</td>\n",
       "      <td>61</td>\n",
       "      <td>female</td>\n",
       "      <td>29.070</td>\n",
       "      <td>0</td>\n",
       "      <td>yes</td>\n",
       "      <td>northwest</td>\n",
       "      <td>29141.36030</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1338 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      age     sex     bmi  children smoker     region      charges\n",
       "0      19  female  27.900         0    yes  southwest  16884.92400\n",
       "1      18    male  33.770         1     no  southeast   1725.55230\n",
       "2      28    male  33.000         3     no  southeast   4449.46200\n",
       "3      33    male  22.705         0     no  northwest  21984.47061\n",
       "4      32    male  28.880         0     no  northwest   3866.85520\n",
       "...   ...     ...     ...       ...    ...        ...          ...\n",
       "1333   50    male  30.970         3     no  northwest  10600.54830\n",
       "1334   18  female  31.920         0     no  northeast   2205.98080\n",
       "1335   18  female  36.850         0     no  southeast   1629.83350\n",
       "1336   21  female  25.800         0     no  southwest   2007.94500\n",
       "1337   61  female  29.070         0    yes  northwest  29141.36030\n",
       "\n",
       "[1338 rows x 7 columns]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Split Data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = dataset.iloc[:, :-1].values\n",
    "y = dataset.iloc[:, 6].values\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Encoding categorical data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\RADHA.K\\Anaconda3\\lib\\site-packages\\sklearn\\preprocessing\\_encoders.py:415: FutureWarning: The handling of integer data will change in version 0.22. Currently, the categories are determined based on the range [0, max(values)], while in the future they will be determined based on the unique values.\n",
      "If you want the future behaviour and silence this warning, you can specify \"categories='auto'\".\n",
      "In case you used a LabelEncoder before this OneHotEncoder to convert the categories to integers, then you can now use the OneHotEncoder directly.\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "C:\\Users\\RADHA.K\\Anaconda3\\lib\\site-packages\\sklearn\\preprocessing\\_encoders.py:451: DeprecationWarning: The 'categorical_features' keyword is deprecated in version 0.20 and will be removed in 0.22. You can use the ColumnTransformer instead.\n",
      "  \"use the ColumnTransformer instead.\", DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import LabelEncoder, OneHotEncoder\n",
    "labelencoder = LabelEncoder()\n",
    "X[:, 1] = labelencoder.fit_transform(X[:, 1])\n",
    "X[:, 4] = labelencoder.fit_transform(X[:, 4])\n",
    "X[:, 5] = labelencoder.fit_transform(X[:, 5])\n",
    "onehotencoder = OneHotEncoder(categorical_features = [5])\n",
    "X = onehotencoder.fit_transform(X).toarray()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avoiding the Dummy Variable Trap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = X[:, 1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Building the optimal model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.750</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.749</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   998.1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 02 Feb 2020</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>14:28:34</td>     <th>  Log-Likelihood:    </th> <td> -13551.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1338</td>      <th>  AIC:               </th> <td>2.711e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1333</td>      <th>  BIC:               </th> <td>2.714e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td> -1.21e+04</td> <td>  941.984</td> <td>  -12.848</td> <td> 0.000</td> <td> -1.4e+04</td> <td>-1.03e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>  257.8495</td> <td>   11.896</td> <td>   21.675</td> <td> 0.000</td> <td>  234.512</td> <td>  281.187</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>  321.8514</td> <td>   27.378</td> <td>   11.756</td> <td> 0.000</td> <td>  268.143</td> <td>  375.559</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>  473.5023</td> <td>  137.792</td> <td>    3.436</td> <td> 0.001</td> <td>  203.190</td> <td>  743.814</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td> 2.381e+04</td> <td>  411.220</td> <td>   57.904</td> <td> 0.000</td> <td>  2.3e+04</td> <td> 2.46e+04</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>301.480</td> <th>  Durbin-Watson:     </th> <td>   2.087</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 722.157</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.215</td>  <th>  Prob(JB):          </th> <td>1.53e-157</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.654</td>  <th>  Cond. No.          </th> <td>    292.</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.750\n",
       "Model:                            OLS   Adj. R-squared:                  0.749\n",
       "Method:                 Least Squares   F-statistic:                     998.1\n",
       "Date:                Sun, 02 Feb 2020   Prob (F-statistic):               0.00\n",
       "Time:                        14:28:34   Log-Likelihood:                -13551.\n",
       "No. Observations:                1338   AIC:                         2.711e+04\n",
       "Df Residuals:                    1333   BIC:                         2.714e+04\n",
       "Df Model:                           4                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const       -1.21e+04    941.984    -12.848      0.000    -1.4e+04   -1.03e+04\n",
       "x1           257.8495     11.896     21.675      0.000     234.512     281.187\n",
       "x2           321.8514     27.378     11.756      0.000     268.143     375.559\n",
       "x3           473.5023    137.792      3.436      0.001     203.190     743.814\n",
       "x4          2.381e+04    411.220     57.904      0.000     2.3e+04    2.46e+04\n",
       "==============================================================================\n",
       "Omnibus:                      301.480   Durbin-Watson:                   2.087\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              722.157\n",
       "Skew:                           1.215   Prob(JB):                    1.53e-157\n",
       "Kurtosis:                       5.654   Cond. No.                         292.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.formula.api as sm\n",
    "import statsmodels.regression.linear_model as sm\n",
    "X = np.append(arr = np.ones((1338, 1)).astype(int), values = X, axis = 1)\n",
    "X_opt = X[:, [0, 1, 2, 3, 4, 5, 6, 7, 8]]\n",
    "regressor_OLS = sm.OLS(endog = y, exog = X_opt).fit()\n",
    "regressor_OLS.summary()\n",
    "X_opt = X[:, [0, 1, 2, 3, 4, 6, 7, 8]]\n",
    "regressor_OLS = sm.OLS(endog = y, exog = X_opt).fit()\n",
    "regressor_OLS.summary()\n",
    "X_opt = X[:, [0, 2, 3, 4, 6, 7, 8]]\n",
    "regressor_OLS = sm.OLS(endog = y, exog = X_opt).fit()\n",
    "regressor_OLS.summary()\n",
    "X_opt = X[:, [0, 2, 4, 6, 7, 8]]\n",
    "regressor_OLS = sm.OLS(endog = y, exog = X_opt).fit()\n",
    "regressor_OLS.summary()\n",
    "X_opt = X[:, [0, 4, 6, 7, 8]]\n",
    "regressor_OLS = sm.OLS(endog = y, exog = X_opt).fit()\n",
    "regressor_OLS.summary()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the optimized model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_opt = X[:, [0, 2, 3, 4, 6, 7, 8]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Splitting X-opt into training and Split test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X_opt, y, test_size = 0.2, random_state = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fitting Multiple Linear Regression to the Training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "regressor = LinearRegression()\n",
    "regressor.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predicting the Test set results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "         299.50423428,  9025.72206318, 15276.09781154,  9662.1673571 ,\n",
       "       35162.90263391,  7385.96064263, 16983.07399387,  9527.49591954,\n",
       "        8241.24368233,  3057.92362293, 32780.20120856, 31623.11986276,\n",
       "       39643.82383769,  5742.0543952 ,  9300.99445519,  3594.7666032 ,\n",
       "        7637.1733989 ,  8505.08175931, 31746.49421702, 29984.33274291,\n",
       "       29791.9846019 ,  8716.88189042, 32429.43545169,  3493.09846988,\n",
       "        3827.79872618, 11276.77129632, 13158.43287155, 12747.12551451,\n",
       "        5583.323348  , 15576.42079545, 14928.1855411 ,  2524.47631929,\n",
       "         157.37754964, 10724.8040594 ,  7269.38329855, 31862.30245327,\n",
       "       12262.14133802,  2337.72181888,  6596.58081255,  7849.16017028,\n",
       "        4580.28930461,  2115.89038635, 11475.94843546, 12662.05261258,\n",
       "        7137.40851772, 16399.64737587, 11939.50097606, 14118.93115341,\n",
       "        3042.7369801 ,  7163.30885251, 23117.53272925,  7450.46634422,\n",
       "        5364.49511911,  5191.91114596,  6892.67995404,  5071.09263435,\n",
       "       10124.58874121,  5384.20859504,  5738.99011488,  6643.89251564,\n",
       "        3570.36938248,  5703.2382345 , 37944.67480412,  1372.28951218,\n",
       "       12760.75090908,  9101.47351628, 13923.86220204,  5406.41350874,\n",
       "        5061.72514477, 36343.68775549,  4271.70017702,  2032.2614585 ,\n",
       "       15349.79615216, 12541.92268019, 35021.35089255,  4768.10822786,\n",
       "        5672.42245357, 31241.32683531,  6342.48475929,  2155.92928655,\n",
       "        8313.93015937,  9905.97555821,  8006.86891322,  5939.24019429,\n",
       "       13023.78436015, 38483.00681954, 13873.62703271, 28884.69015462,\n",
       "        6921.48773946, 35527.63758511,  3638.91369118, 11901.32631479,\n",
       "        9049.52018699,  6264.09640318, 11500.4983159 , 14426.940472  ,\n",
       "        5283.89091608,  4456.47083556,  7916.54136064,  1349.2695319 ,\n",
       "        7730.03264049,  4275.74303612, 12880.02552364,  4099.13294133,\n",
       "       10104.190546  ,  7054.81297465,  9291.00897996,  2255.40866907,\n",
       "       13241.47362434, 17010.17081381, 14935.59992318, 10586.21859863,\n",
       "        5293.23813807,  2236.67430365,  1938.38346888, 13387.50744776,\n",
       "       14048.21242063,  4873.69604135,  3747.68540768,  9495.61960181,\n",
       "        9840.12365425, 28165.00244517,  7524.82555419, 10332.48823225,\n",
       "        6315.25820578, 29991.06271575, 11142.54993421,  7368.08159505,\n",
       "       10369.31730489, 12386.73996931,  2878.83191732, 10997.42004594,\n",
       "        1397.97480108,  6913.46645225, 28438.76755314, 38690.05399114,\n",
       "        6359.62095339,  8181.79846685,  2394.05853474,   318.59020768,\n",
       "       10578.99572255,  4193.66969959,  5086.27927719,  2330.39274912,\n",
       "        6811.60185174, 33407.19277679, 38131.78354496, 14884.46731742,\n",
       "        8414.18970413, 16031.26081106, 32897.66288984,  9342.86453755])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = regressor.predict(X_test)\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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