# Lab: Linear Regression


## Libraries

###
library(MASS)
library(ISLR2)

## Simple Linear Regression

###
head(Boston)
###
lm.fit <- lm(medv ~ lstat)
###
lm.fit <- lm(medv ~ lstat, data = Boston)
attach(Boston)
lm.fit <- lm(medv ~ lstat)
###
lm.fit
summary(lm.fit)
###
names(lm.fit)
coef(lm.fit)
###
confint(lm.fit)
###
predict(lm.fit, data.frame(lstat = (c(5, 10, 15))),
    interval = "confidence")
predict(lm.fit, data.frame(lstat = (c(5, 10, 15))),
    interval = "prediction")
###
plot(lstat, medv)
abline(lm.fit)
###
abline(lm.fit, lwd = 3)
abline(lm.fit, lwd = 3, col = "red")
plot(lstat, medv, col = "red")
plot(lstat, medv, pch = 20)
plot(lstat, medv, pch = "+")
plot(1:20, 1:20, pch = 1:20)
###
par(mfrow = c(2, 2))
plot(lm.fit)
###
plot(predict(lm.fit), residuals(lm.fit))
plot(predict(lm.fit), rstudent(lm.fit))
###
plot(hatvalues(lm.fit))
which.max(hatvalues(lm.fit))

## Multiple Linear Regression

###
lm.fit <- lm(medv ~ lstat + age, data = Boston)
summary(lm.fit)
###
lm.fit <- lm(medv ~ ., data = Boston)
summary(lm.fit)
###
library(car)
vif(lm.fit)
###
lm.fit1 <- lm(medv ~ . - age, data = Boston)
summary(lm.fit1)
###
lm.fit1 <- update(lm.fit, ~ . - age)

## Interaction Terms

###
summary(lm(medv ~ lstat * age, data = Boston))

## Non-linear Transformations of the Predictors

###
lm.fit2 <- lm(medv ~ lstat + I(lstat^2))
summary(lm.fit2)
###
lm.fit <- lm(medv ~ lstat)
anova(lm.fit, lm.fit2)
###
par(mfrow = c(2, 2))
plot(lm.fit2)
###
lm.fit5 <- lm(medv ~ poly(lstat, 5))
summary(lm.fit5)
###
summary(lm(medv ~ log(rm), data = Boston))

## Qualitative Predictors

###
head(Carseats)
###
lm.fit <- lm(Sales ~ . + Income:Advertising + Price:Age, 
    data = Carseats)
summary(lm.fit)
###
attach(Carseats)
contrasts(ShelveLoc)

## Writing  Functions

###
LoadLibraries
LoadLibraries()
###
LoadLibraries <- function() {
 library(ISLR2)
 library(MASS)
 print("The libraries have been loaded.")
}
###
LoadLibraries
###
LoadLibraries()
###