##zestaw5
#zadanie1
library(faraway)
summary(data)
?star

data=star
m1=lm(temp~light,star)
summary(m1)
library(car)
boxCox(m1,lambda = seq(-2, 25))
m2=lm(temp^(14)~light,star)
summary(m2)


#wykresy
plot(star$temp~star$light)

par(mfrow=c(3,2))
plot(m1,1)
plot(m1,2)
plot(m1,3)
plot(m1,4)
plot(m1,5)
plot(m1,6)
par(mfrow=c(3,2))
plot(m2,1)
plot(m2,2)
plot(m2,3)
plot(m2,4)
plot(m2,5)
plot(m2,6)


###porównanie modeli m1 i m2
data
r1=0
r2=0

for( j in (1:length(data)))
{
  training=data[-j,]
  test=data[j,]
  
  m1=lm(temp~light,training)
  m2=lm(temp^(14)~light,training)
  
  r1=r1+abs((predict(m1,test) )- test$temp    )
  r2=r2+abs((predict(m2,test) )^(1/14)- test$temp    )
  
}


rmse1=r1/length(data)
rmse2=r2/length(data)
rmse1
rmse2
##Wygrywa model 2, bo ma mniejsze rmse. Ale jest trudniejszy do interpretacji

par(mfrow=c(1,1))
rstudent(m1)
plot(abs(rstudent(m1)))
which(abs(rstudent(m1))>2)
###gwiazdy podejrzane: 11,20,30,34 
#nie możemy je usunąć!