# Hitters data - Ridge regression

library(ISLR)
names(Hitters)
dim(Hitters)
sum(is.na(Hitters$Salary))
Hitters=na.omit(Hitters)
dim(Hitters)
sum(is.na(Hitters))


Hitters2 = Hitters
Hitters2$PutOuts = (Hitters2$PutOuts-mean(Hitters2$PutOuts))/sd(Hitters2$PutOuts)
Hitters2$Hits = (Hitters2$Hits-mean(Hitters2$Hits))/sd(Hitters2$Hits)
fit.lm = lm(Salary~PutOuts+Hits,data=Hitters2)

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

#For understanding the following commands, you can look at the help pages or 
#Look at section 6.5 in the ISLR book (James et al)
library(glmnet)
grid=10^seq(10,-2,length=100)
ridge.mod=glmnet(x,y,alpha=0,lambda=grid)
plot(ridge.mod)
class(ridge.mod)
help(plot.elnet)
help(plot.glmnet)
plot(ridge.mod,xvar="lambda")
dim(coef(ridge.mod))
ridge.mod$lambda[50]
coef(ridge.mod)[,50]
sqrt(sum(coef(ridge.mod)[-1,50]^2))
ridge.mod$lambda[60]
coef(ridge.mod)[,60]
sqrt(sum(coef(ridge.mod)[-1,60]^2))
predict(ridge.mod,s=50,type="coefficients")[1:20,]
set.seed(1)
train=sample(1:nrow(x), nrow(x)/2)
test=(-train)
y.test=y[test]
ridge.mod=glmnet(x[train,],y[train],alpha=0,lambda=grid, thresh=1e-12)
ridge.pred=predict(ridge.mod,s=4,newx=x[test,])
mean((ridge.pred-y.test)^2)
mean((mean(y[train])-y.test)^2)
ridge.pred=predict(ridge.mod,s=1e10,newx=x[test,])
mean((ridge.pred-y.test)^2)
ridge.pred=predict(ridge.mod,s=0,newx=x[test,],exact=T,x=x[train,],y=y[train])
mean((ridge.pred-y.test)^2)
lm(y~x, subset=train)
predict(ridge.mod,s=0,exact=T,x=x[train,],y=y[train],type="coefficients")[1:20,]
set.seed(1)
cv.out=cv.glmnet(x[train,],y[train],alpha=0)
plot(cv.out)
bestlam=cv.out$lambda.min
bestlam
ridge.pred=predict(ridge.mod,s=bestlam,newx=x[test,])
mean((ridge.pred-y.test)^2)
out=glmnet(x,y,alpha=0)
#Coefficients
predict(out,type="coefficients",s=bestlam)[,1]