R Notebook

# Importing the dataset
dataset <-  read.csv("G:\\RStudio\\udemy\\ml\\Machine Learning AZ\\Part 2 - Regression\\Section 5 - Multiple Linear Regression\\Multiple_Linear_Regression\\50_Startups.csv")
head(dataset)

# taking care of missing values
# Test for missing values
sum(is.na(dataset$R.D.Spend))

[1] 0

sum(is.na(dataset$Administration))

[1] 0

sum(is.na(dataset$Marketing.Spend))

[1] 0

sum(is.na(dataset$State))

[1] 0

sum(is.na(dataset$Profit))

[1] 0

# if all zeros, then there are no missing numbers. 
# no need to work with miss

# convert variables into factors
dataset$State <-  factor(dataset$State,
                           levels = c("New York", "California","Florida"),
                           labels = c(1,2,3))

# feature scaling
# skipped.
training_set

test_set

# fitting mulitple linear regression to the training set
regressor = lm(formula = Profit ~ R.D.Spend+ Administration + Marketing.Spend + State, data = training_set)
# you can also use the dot 
# regressor = lm(formula = Profit ~ ., data=training_set)
View(training_set)
View(test_set)
summary(regressor)

Call:
lm(formula = Profit ~ R.D.Spend + Administration + Marketing.Spend + 
    State, data = training_set)

Residuals:
   Min     1Q Median     3Q    Max 
-33128  -4865      5   6098  18065 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)      4.965e+04  7.637e+03   6.501 1.94e-07 ***
R.D.Spend        7.986e-01  5.604e-02  14.251 6.70e-16 ***
Administration  -2.942e-02  5.828e-02  -0.505    0.617    
Marketing.Spend  3.268e-02  2.127e-02   1.537    0.134    
State2           1.213e+02  3.751e+03   0.032    0.974    
State3           2.376e+02  4.127e+03   0.058    0.954    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9908 on 34 degrees of freedom
Multiple R-squared:  0.9499,    Adjusted R-squared:  0.9425 
F-statistic:   129 on 5 and 34 DF,  p-value: < 2.2e-16

# Preditcing the Test set results
y_pred = predict(regressor, newdata = test_set)
y_pred

        4         5         8        11        16        20        21        24        31 
173981.09 172655.64 160250.02 135513.90 146059.36 114151.03 117081.62 110671.31  98975.29 
       32 
 96867.03 

# Building the optimal model using backward elimination
regressor = lm(formula = Profit ~ R.D.Spend + Administration + Marketing.Spend + State, 
               data = dataset)
# we used dataset to see the whole effect and find the most significant variables
summary(regressor)

Call:
lm(formula = Profit ~ R.D.Spend + Administration + Marketing.Spend + 
    State, data = dataset)

Residuals:
   Min     1Q Median     3Q    Max 
-33504  -4736     90   6672  17338 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)      5.008e+04  6.953e+03   7.204 5.76e-09 ***
R.D.Spend        8.060e-01  4.641e-02  17.369  < 2e-16 ***
Administration  -2.700e-02  5.223e-02  -0.517    0.608    
Marketing.Spend  2.698e-02  1.714e-02   1.574    0.123    
State2           4.189e+01  3.256e+03   0.013    0.990    
State3           2.407e+02  3.339e+03   0.072    0.943    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9439 on 44 degrees of freedom
Multiple R-squared:  0.9508,    Adjusted R-squared:  0.9452 
F-statistic: 169.9 on 5 and 44 DF,  p-value: < 2.2e-16

# remove the highest P value to build a new regressor
regressor = lm(formula = Profit ~ R.D.Spend + Administration + Marketing.Spend, 
               data = dataset)
summary(regressor)

Call:
lm(formula = Profit ~ R.D.Spend + Administration + Marketing.Spend, 
    data = dataset)

Residuals:
   Min     1Q Median     3Q    Max 
-33534  -4795     63   6606  17275 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)      5.012e+04  6.572e+03   7.626 1.06e-09 ***
R.D.Spend        8.057e-01  4.515e-02  17.846  < 2e-16 ***
Administration  -2.682e-02  5.103e-02  -0.526    0.602    
Marketing.Spend  2.723e-02  1.645e-02   1.655    0.105    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9232 on 46 degrees of freedom
Multiple R-squared:  0.9507,    Adjusted R-squared:  0.9475 
F-statistic:   296 on 3 and 46 DF,  p-value: < 2.2e-16

# remove the highest P value to build a new regressor
regressor = lm(formula = Profit ~ R.D.Spend  + Marketing.Spend, 
               data = dataset)
summary(regressor)

Call:
lm(formula = Profit ~ R.D.Spend + Marketing.Spend, data = dataset)

Residuals:
   Min     1Q Median     3Q    Max 
-33645  -4632   -414   6484  17097 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)     4.698e+04  2.690e+03  17.464   <2e-16 ***
R.D.Spend       7.966e-01  4.135e-02  19.266   <2e-16 ***
Marketing.Spend 2.991e-02  1.552e-02   1.927     0.06 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9161 on 47 degrees of freedom
Multiple R-squared:  0.9505,    Adjusted R-squared:  0.9483 
F-statistic: 450.8 on 2 and 47 DF,  p-value: < 2.2e-16

# remove the highest P value to build a new regressor
regressor = lm(formula = Profit ~ R.D.Spend , 
               data = dataset)
summary(regressor)

Call:
lm(formula = Profit ~ R.D.Spend, data = dataset)

Residuals:
   Min     1Q Median     3Q    Max 
-34351  -4626   -375   6249  17188 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 4.903e+04  2.538e+03   19.32   <2e-16 ***
R.D.Spend   8.543e-01  2.931e-02   29.15   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9416 on 48 degrees of freedom
Multiple R-squared:  0.9465,    Adjusted R-squared:  0.9454 
F-statistic: 849.8 on 1 and 48 DF,  p-value: < 2.2e-16