#Problem 1
datadir = "http://www.uio.no/studier/emner/matnat/math/STK2100/data/"
nuclear = read.table(paste(datadir,"nuclear.dat",sep=""),header=T)
n = nrow(nuclear)

#Fit with all covariates
fit = lm(log(cost)~.,data=nuclear)

#Fit with t1 taken away.
fit2 = lm(log(cost)~.-t1,data=nuclear)

d.new = data.frame(date=70.0,t1=13,t2=50,cap=800,pr=1,
                   ne=0,ct=0,bw=1,cum.n=8,pt=1)

predict(fit,d.new,interval="confidence")
predict(fit,d.new,interval="predict")

x = model.matrix(log(cost)~.,data=nuclear)
y = log(nuclear$cost)

library(glmnet)
grid=10^seq(1,-5,length=100)
lasso.mod=glmnet(x,y,alpha=1,lambda=grid)
plot(lasso.mod,xvar="lambda")

set.seed(1)
cv.out=cv.glmnet(x,y,alpha=1)
plot(cv.out)
cv.out


#Problem 2
datadir = "http://www.uio.no/studier/emner/matnat/math/STK2100/data/"
Fe <- read.table(paste(datadir,"fe.dat",sep=""),header=T,sep=",")
fit <- lm(Fe~form,data=Fe)
summary(fit)

Fe$form <- as.factor(Fe$form)

fit1 <- lm(Fe~form,data=Fe)
summary(fit1)

fit2 <- lm(Fe~form+0,data=Fe)
summary(fit2)

options(contrasts=c("contr.sum","contr.sum"))
fit3 <- lm(Fe~form,data=Fe)
summary(fit3)

newdata = data.frame(form=as.factor(c(1,2,3,4)))
pred1 = predict(fit1,newdata)
pred2 = predict(fit2,newdata)
pred3 = predict(fit3,newdata)