# The Validation Set Approach

library(ISLR)
set.seed(1)
train=sample(392,196)
lm.fit=lm(mpg~horsepower,data=Auto,subset=train)
attach(Auto)
mean((mpg-predict(lm.fit,Auto))[-train]^2)
lm.fit2=lm(mpg~poly(horsepower,2),data=Auto,subset=train)
mean((mpg-predict(lm.fit2,Auto))[-train]^2)
lm.fit3=lm(mpg~poly(horsepower,3),data=Auto,subset=train)
mean((mpg-predict(lm.fit3,Auto))[-train]^2)
set.seed(2)
train=sample(392,196)
lm.fit=lm(mpg~horsepower,subset=train)
mean((mpg-predict(lm.fit,Auto))[-train]^2)
lm.fit2=lm(mpg~poly(horsepower,2),data=Auto,subset=train)
mean((mpg-predict(lm.fit2,Auto))[-train]^2)
lm.fit3=lm(mpg~poly(horsepower,3),data=Auto,subset=train)
mean((mpg-predict(lm.fit3,Auto))[-train]^2)

# Leave-One-Out Cross-Validation

glm.fit=glm(mpg~horsepower,data=Auto)
coef(glm.fit)
lm.fit=lm(mpg~horsepower,data=Auto)
coef(lm.fit)
library(boot)
glm.fit=glm(mpg~horsepower,data=Auto)
cv.err=cv.glm(Auto,glm.fit)
cv.err$delta
cv.error=rep(0,5)
for (i in 1:5){
 glm.fit=glm(mpg~poly(horsepower,i),data=Auto)
 cv.error[i]=cv.glm(Auto,glm.fit)$delta[1]
 }
cv.error

# k-Fold Cross-Validation

set.seed(17)
cv.error.10=rep(0,10)
for (i in 1:10){
 glm.fit=glm(mpg~poly(horsepower,i),data=Auto)
 cv.error.10[i]=cv.glm(Auto,glm.fit,K=10)$delta[1]
 }
cv.error.10

# The Bootstrap

alpha.fn=function(data,index){
 X=data$X[index]
 Y=data$Y[index]
 return((var(Y)-cov(X,Y))/(var(X)+var(Y)-2*cov(X,Y)))
 }
alpha.fn(Portfolio,1:100)
set.seed(1)
alpha.fn(Portfolio,sample(100,100,replace=T))
boot(Portfolio,alpha.fn,R=1000)

# Estimating the Accuracy of a Linear Regression Model

boot.fn=function(data,index)
 return(coef(lm(mpg~horsepower,data=data,subset=index)))
boot.fn(Auto,1:392)
set.seed(1)
boot.fn(Auto,sample(392,392,replace=T))
boot.fn(Auto,sample(392,392,replace=T))
boot(Auto,boot.fn,1000)

summary(lm(mpg~horsepower,data=Auto))$coef

boot.fn=function(data,index)
coefficients(lm(mpg~horsepower+I(horsepower^2),data=data,subset=index))

set.seed(1)
boot(Auto,boot.fn,1000)
summary(lm(mpg~horsepower+I(horsepower^2),data=Auto))$coef