# Load the library, and the data (also info on the data)
library(ISLR)
data("Credit")
help(Credit)

# Scatterplot
with(Credit, plot(Limit, Balance))
# Boxplot
with(Credit, plot(Balance ~ Student))

# Scatterplot including the information on the Student's status
with(Credit, plot(Limit, Balance, col = ifelse(Student == "Yes", "green", "red")))

# Fit the lm model 
lmFit <- lm(Balance ~ Limit + Student, data = Credit)
lmFit

# Model matrix
X <- model.matrix(Balance ~ Limit + Student, data = Credit)
# Outcome
y <- Credit$Balance 

# LS by hand 
beta_OLS <- solve(t(X)%*%X)%*%t(X)%*%y
beta_OLS
# Check
lmFit$coefficients

# Explore the summary
summary(lmFit)

# Residuals:
head(residuals(lmFit))
head(Credit$Balance - predict(lmFit))

# Extract the table of coefficients 
summary(lmFit)$coefficients 

# Summary of the Residuals 
summary(residuals(lmFit)) 

# Estimate of the square root of the variance of the error term
sqrt(sum(residuals(lmFit)^2)/(nrow(Credit)-ncol(X)))
summary(lmFit)$sigma 


# R2 coefficient 
summary(lmFit)$r.squared
# By hand 
1 - sum(residuals(lmFit)^2)/(var(Credit$Balance)*(nrow(Credit) - 1))

# Adjusted R squared
Rsq <- 1 - sum(residuals(lmFit)^2)/(var(Credit$Balance)*(nrow(Credit) - 1))
Rsq 

summary(lmFit)$adj.r.squared
Rsq - (1-Rsq)*(ncol(X)-1)/(nrow(Credit)-ncol(X))

# Fitted regression lines 
with(Credit, plot(Limit, Balance, col = ifelse(Student == "Yes", "green", "red")))
abline(lmFit$coefficients[1:2], col = "red")
abline(c(lmFit$coefficients[1] + lmFit$coefficients[3], 
         lmFit$coefficients[2]), col = "green")