#uvek treba podeliti uzorak na deo za treniranje i deo za testiranje. Ovde to izostavljamo jer je baza koju imamo mala, a zelimo da prikazemo pstupke ocenjivanja.

 x <- as.matrix(longley[,1:6])
 y <- as.matrix(longley[,7])
fitOLS=lm(y~x)
#centiramo i skaliramo model
xc=scale(x,center=TRUE,scale=TRUE)
yc=y-mean(y)
fitOLSc=lm(yc~xc-1)
summary(fitOLSc)
kappa(xc)
install.packages('HH')
library(HH)
vif(fitOLS)
rmse<-function (x, y) sqrt (mean ( (x-y)^2) )
prcomp(x,scale=TRUE,center=TRUE)
pc=prcomp(xc,scale=TRUE,center=TRUE)
summary(pc)
xnovo=pc$x
fitPC=lm(yc~xnovo-1)
rmse(fitPC$fitted.values+mean(y),y)
rmse(fitOLSc$fitted.values+mean(y),y)

fitPC1=lm(yc~xnovo[,1:3]-1)
plot(pc$sdev,type='l')



#nazubljena regresija i LASSO

install.packages('lars')
library(lars)
plot(lm.ridge(yc~xc-1,lambda=seq(from=0,to=0.5,by=0.01)))
select(lm.ridge(yc~xc-1,lambda=seq(from=0,to=0.1,by=0.01)))

#pravimo model sa odabranim lambda 
fitRIDGE=lm.ridge(yc~xc-1,lambda=0.03)
yR=mean(y)+xc%*%matrix(fitRIDGE$coef,ncol=1)
rmse(yR,y)



fit.lasso=lars(x=xc,y=yc,type="lasso")
coef.lars(fit.lasso,s=0,mode="lambda")
plot(fit.lasso)
coef.max=coef.lars(fit.lasso,s=0,mode="lambda")
maxL1norm=sum(abs(coef.max))
coef.P=coef.lars(fit.lasso,s=0.3,mode="lambda")
L1norm=sum(abs(coef.P))
yLassoC=xc%*%matrix(coef.P,ncol=1)+mean(y)
yLassoC
rmse(yLassoC,y)
cv.lars(x=xc,y=yc,intercept=FALSE,type="lasso",plot.it = TRUE)