library(ISLR2)
summary(Hitters)

names(Hitters)


Hitters=na.omit(Hitters)
with(Hitters,sum(is.na(Salary)))

library(leaps)
regfit.full=regsubsets(Salary~.,data=Hitters)
summary(regfit.full)

regfit.full=regsubsets(Salary~.,data=Hitters,nvmax=19)
reg.summary=summary(regfit.full)
names(reg.summary)
reg.summary$rsq
library(ggplot2)
plot(reg.summary$cp,xlab = "Number of variables",ylab = "Cp")

which.min(reg.summary$cp)
points(10,reg.summary$cp[10],pch=20,col="red")
plot(regfit.full,scale="Cp")
coef(regfit.full,10)

regfit.fwd=regsubsets(Salary~.,data=Hitters,nvmax=19,method="forward")
summary(regfit.fwd)
plot(regfit.fwd,scale="Cp")


dim(Hitters)
set.seed(1)
train=sample(seq(263),180,replace=FALSE)
train
regfit.fwd=regsubsets(Salary~.,data=Hitters[train,],nvmax=19,method="forward")

val.errors=rep(NA,19)
x.test=model.matrix(Salary~.,data=Hitters[-train,])# notice the -index!
for(i in 1:19){
  coefi=coef(regfit.fwd,id=i)
  pred=x.test[,names(coefi)]%*%coefi
  val.errors[i]=mean((Hitters$Salary[-train]-pred)^2)
}
plot(sqrt(val.errors),ylab="Root MSE",ylim=c(300,400),pch=19,type="b")
points(sqrt(regfit.fwd$rss[-1]/180),col="blue",pch=19,type="b")
legend("topright",legend=c("Training","Validation"),col=c("blue","black"),pch=19)


predict.regsubsets=function(object,newdata,id,...){
  form=as.formula(object$call[[2]])
  mat=model.matrix(form,newdata)
  coefi=coef(object,id=id)
  mat[,names(coefi)]%*%coefi
}

set.seed(11)
folds=sample(rep(1:10,length=nrow(Hitters)))
folds

#install.packages("glmnet")

library(glmnet)
x=model.matrix(Salary~.-1,data=Hitters)
y=Hitters$Salary


fit.ridge=glmnet(x,y,alpha=0)
plot(fit.ridge,xvar="lambda",label=TRUE)
cv.ridge=cv.glmnet(x,y,alpha=0)
plot(cv.ridge)
fit.lasso=glmnet(x,y)
plot(fit.lasso,xvar="lambda",label=TRUE)

cv.lasso=cv.glmnet(x,y)
plot(cv.lasso)
coef(cv.lasso)

lasso.tr=glmnet(x[train,],y[train])
lasso.tr
pred=predict(lasso.tr,x[-train,])
dim(pred)
rmse= sqrt(apply((y[-train]-pred)^2,2,mean))
plot(log(lasso.tr$lambda),rmse,type="b",xlab="Log(lambda)")
lam.best=lasso.tr$lambda[order(rmse)[1]]
lam.best
coef(lasso.tr,s=lam.best)