Plan <- read.table("https://husson.github.io/livre_exo/chap12_ex3.csv", header = TRUE, sep=";",row.names=1, encoding = "latin1")
for (i in 1:2) Plan[,i] <- as.factor(Plan[,i])

X <- model.matrix(~ F1+F2, Plan, contrasts = "contr.sum")
t(X)%*%X
solve(t(X)%*%X)

library(FactoMineR)
AovSum(Y ~F1 + F2, data = Plan)