####Lack of Fit Test
data = read.table('bank.txt',header=F)
y = data[,2]
x = data[,1]
Reduced=lm(y~x)
Full=lm(y~as.factor(x)-1)
anova(Reduced, Full)


####Box-Cox transformation
n = 1000
x = rnorm(n)
eps = rnorm(n)/10
sy = x + eps + 6
y = sy^2
logk2 = mean(log(y))
k2 = exp(logk2)
 
lamList = seq(from=-2, to=2, by=0.25)
sseList = rep(0,length(lamList))
for(i in 1:length(lamList)){
lam = lamList[i]
k1 = 1/lam/k2^(lam-1)
if(lam == 0) w = k2*log(y)
if(lam != 0) w = k1*(y^lam-1)
fit = lm(w~x)
sseList[i] = sum((w-fitted(fit))^2)
 
}
plot(lamList,sseList)
lamList[which.min(sseList)] ###best transformation parameter

###direct function
library(MASS)
fit = lm(y~x)
a = boxcox(fit)
a$x[which.max(a$y)] ###best transformation paramete