#########################################
# Domaci uloha 4 (jedno z moznych reseni)
#########################################

fullmoon <- read.table("fullmoon.txt", header=TRUE)
fullmoon$Moon <- factor(fullmoon$Moon, levels=c("Before", "During", "After"))
fullmoon$Month <- factor(fullmoon$Month, levels=c("Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"))

C <- rbind(
  c(rep(1/12, 12)),
  c(rep(0, 10), -1, 1), # Listopad vs Vanoce   
  c(-1, rep(0, 10), 1), # Leden vs Vanoce   
  c(0, -1, rep(0, 9), 1), # Unor vs Vanoce   
  c(rep(0, 4), -1, 0, 1/2, 1/2, rep(0, 4)), # Kveten vs prazdniny   
  c(rep(0, 5), -1, 1/2, 1/2, rep(0, 4)), # Cerven vs prazdniny   
  c(rep(0, 2), -1, rep(0, 8), 1),
  c(rep(0, 3), -1, rep(0, 7), 1),
  c(rep(0, 4), -1, rep(0, 6), 1),
  c(rep(0, 7), -1, rep(0, 3), 1),
  c(rep(0, 8), -1, rep(0, 2), 1),
  c(rep(0, 9), -1, 0, 1)
)  
# prvni radky C jsou kontrasty, ktere chceme videt, vsechny radky se scitaji na 0 a matice ma plnou hodnost

round(C, 3)
C.cont <- solve(C)  
C.cont
# matice ma prvni sloupec 1

model.hw <- lm(Admission~Month, data=fullmoon, contrasts=list(Month=C.cont[, -1]))
summary(model.hw)

C%*%tapply(fullmoon$Admission, fullmoon$Month, mean)
# dostali jsme, co jsme zadali