Project

# Load necessary packages
library(caret)

## Loading required package: ggplot2

## Loading required package: lattice

library(ggplot2)

# Load data (replace "path/to/advertising.csv" with your actual file path)
f <- read.csv("C://Users//hp//Desktop//advertising.csv")
# View the structure and summary of the data
str(f)

## 'data.frame':    200 obs. of  4 variables:
##  $ TV       : num  230.1 44.5 17.2 151.5 180.8 ...
##  $ Radio    : num  37.8 39.3 45.9 41.3 10.8 48.9 32.8 19.6 2.1 2.6 ...
##  $ Newspaper: num  69.2 45.1 69.3 58.5 58.4 75 23.5 11.6 1 21.2 ...
##  $ Sales    : num  22.1 10.4 12 16.5 17.9 7.2 11.8 13.2 4.8 15.6 ...

summary(f)

##        TV             Radio          Newspaper          Sales      
##  Min.   :  0.70   Min.   : 0.000   Min.   :  0.30   Min.   : 1.60  
##  1st Qu.: 74.38   1st Qu.: 9.975   1st Qu.: 12.75   1st Qu.:11.00  
##  Median :149.75   Median :22.900   Median : 25.75   Median :16.00  
##  Mean   :147.04   Mean   :23.264   Mean   : 30.55   Mean   :15.13  
##  3rd Qu.:218.82   3rd Qu.:36.525   3rd Qu.: 45.10   3rd Qu.:19.05  
##  Max.   :296.40   Max.   :49.600   Max.   :114.00   Max.   :27.00

# Fit the regression model
model <- lm(Sales ~ TV + Radio + Newspaper, data = f)
# Print the model summary
summary(model)

## 
## Call:
## lm(formula = Sales ~ TV + Radio + Newspaper, data = f)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.3034 -0.8244 -0.0008  0.8976  3.7473 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.6251241  0.3075012  15.041   <2e-16 ***
## TV          0.0544458  0.0013752  39.592   <2e-16 ***
## Radio       0.1070012  0.0084896  12.604   <2e-16 ***
## Newspaper   0.0003357  0.0057881   0.058    0.954    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.662 on 196 degrees of freedom
## Multiple R-squared:  0.9026, Adjusted R-squared:  0.9011 
## F-statistic: 605.4 on 3 and 196 DF,  p-value: < 2.2e-16

##Assumptions

# Check linearity visually using scatterplots
plot(f$TV, model$residuals, main = "Residuals vs TV", xlab = "TV", ylab = "Residuals")
abline(h = 0, col = "red")

# Check normality of residuals using a Q-Q plot
qqnorm(model$residuals)
qqline(model$residuals, col = "red")

# Check homoscedasticity using residuals vs fitted values plot
plot(model$fitted.values, model$residuals, main = "Residuals vs Fitted Values", xlab = "Fitted Values", ylab = "Residuals")
abline(h = 0, col = "red")

# Function to calculate VIF
calculate_vif <- function(model) {
  # Extract predictor variables
  X <- model.matrix(model)
  vif_values <- sapply(2:ncol(X), function(i) {
    vif_i <- 1 / (1 - summary(lm(X[, i] ~ X[, -i]))$r.squared)
    return(vif_i)
  })
  # Assign variable names to VIF values
  names(vif_values) <- colnames(X)[-1]
  return(vif_values)
}

# Calculate and print VIF values
vif_values <- calculate_vif(model)
print(vif_values)

##        TV     Radio Newspaper 
##  1.004611  1.144952  1.145187