#Multiple linear regression

#Importing Libraries

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

#Importing Dataset

Startup = pd.read_csv("50_Startups.csv")

#Seperating Dependent and Independent Variables

X = Startup.iloc[:,:-1].values

Y= Startup.iloc[:,-1].values

#Encoding categorical variables

from sklearn.preprocessing import OneHotEncoder, LabelEncoder

labelencoder = LabelEncoder()

X[:,-1] = labelencoder.fit_transform(X[:,-1])

onehotencoder = OneHotEncoder(categorical_features=[-1])

X = onehotencoder.fit_transform(X).toarray()

#Avoiding the Dummy Variable Trap

X= X[:,1:]

#Splitting data into training and test sets

from sklearn.cross_validation import train_test_split

train_X,test_X,train_Y,test_Y = train_test_split(X,Y,test_size=0.2,random_state=0)

#Fitting Multiple leniar regression to the training set

from sklearn.linear_model import LinearRegression

regressor = LinearRegression()

regressor.fit(train_X,train_Y)

#predicting the test set results

Y_Pred = regressor.predict(test_X)

#Building optimal model using Backward elimination

import statsmodels.formula.api as sm

X = np.append(arr=np.ones((50,1)).astype(int),values=X, axis=1)

X_opt = X[:,[0,1,2,3,4,5]]

SL = 0.05

regressor_OLS = sm.OLS(endog=Y, exog=X_opt).fit()

regressor_OLS.summary()

#variable X3 has highest P value and more than SL of 5% so remove that

X_opt = X[:,[0,1,3,4,5]]

regressor_OLS = sm.OLS(endog=Y, exog=X_opt).fit()

regressor_OLS.summary()

#variable X1 has highest P value and more than SL of 5% so remove that

X_opt = X[:,[0,3,4,5]]

regressor_OLS = sm.OLS(endog=Y, exog=X_opt).fit()

regressor_OLS.summary()

#variable X2 has highest P value and more than SL of 5% so remove that

X_opt = X[:,[0,3,5]]

regressor_OLS = sm.OLS(endog=Y, exog=X_opt).fit()

regressor_OLS.summary()

#variable X2 has highest P value and more than SL of 5% so remove that

X_opt = X[:,[0,3]]

regressor_OLS = sm.OLS(endog=Y, exog=X_opt).fit()

regressor_OLS.summary()