Plan <- read.table("https://husson.github.io/livre_exo/chap14_ex3.csv", header = TRUE, sep=";",row.names=1, encoding = "latin1")

# modèle sans interaction
res <- lm(Y ~ X1 + X2 + I(X1^2) + I(X2^2), data = Plan)
anova(res)[5,]
## question 2 
CM_pure <- var(Plan[5:8,3])

## Question 3
CM_ajust <- (anova(res)[5,2] - CM_pure*3) / 4
pf( CM_ajust/CM_pure,4,3,lower.tail=FALSE)