multiple_linear_regression.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
@author: sudarshan
"""
# Multiple Linear Regression

# Importing the libraries
import statsmodels.api as sm
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import LabelEncoder, OneHotEncoder
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

# Importing the dataset
dataset = pd.read_csv('50_Startups.csv')
X = dataset.iloc[:, :-1].values
y = dataset.iloc[:, 4].values

# Encoding categorical data
# Encoding the Independent Variable
labelencoder_X = LabelEncoder()
X[:, 3] = labelencoder_X.fit_transform(X[:, 3])
onehotencoder = OneHotEncoder(categorical_features=[3])
X = onehotencoder.fit_transform(X).toarray()

# Avoiding the dummy variable Trap
# Good practice to remove one of the dummy variable but the library is gonna do it anyway
X = X[:, 1:]

# Splitting the dataset into the Training set and Test set
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=0)

# Fitting Multiple Linear Regression to the Training set
regressor = LinearRegression()
regressor.fit(X_train, y_train)

# Predicting the Test set results
y_pred = regressor.predict(X_test)

# Building the optimal model using Backward Elimination
# adding column at the first with ones values to work for BW Elimination
X = np.append(arr=np.ones((50, 1)).astype(int), values=X, axis=1)
# fitting the model with all possible predictors
# We assume that our significance level threshold (P value) is 0.05 (5%)
X_opt = X[:, [0, 1, 2, 3, 4, 5]]
regressor_OLS = sm.OLS(endog=y, exog=X_opt).fit()
regressor_OLS.summary()

# As the second variable has highest P value, we omit that and run the model
X_opt = X[:, [0, 1, 3, 4, 5]]
regressor_OLS = sm.OLS(endog=y, exog=X_opt).fit()
regressor_OLS.summary()

# The first variable has the highest P value so now we omit that
X_opt = X[:, [0, 3, 4, 5]]
regressor_OLS = sm.OLS(endog=y, exog=X_opt).fit()
regressor_OLS.summary()

# it shows that fourth variable has more P values than others, so we omit that
X_opt = X[:, [0, 3, 5]]
regressor_OLS = sm.OLS(endog=y, exog=X_opt).fit()
regressor_OLS.summary()

# it seems more step needed as fifth variable has slight more P value
X_opt = X[:, [0, 3]]
regressor_OLS = sm.OLS(endog=y, exog=X_opt).fit()
regressor_OLS.summary()

# from this model, we knew that the profit has the highest statistical significance with R&D.