Plan <- read.table("https://husson.github.io/livre_exo/chap14_ex4.csv", header = TRUE, sep=";",row.names=1, encoding = "latin1")

X <- model.matrix(~ X1+X2+I(X1^2)+I(X2^2)+I(X1*X2), Plan)
X
t(X)%*%X
cor(X)
solve(t(X)%*%X)

## Question 5 : (ajout de 2 points au centre)
Plan2 <- Plan[c(1,1,1:7),]
X <- model.matrix(~ X1+X2+I(X1^2)+I(X2^2)+I(X1*X2), Plan2)
X
t(X)%*%X
cor(X)
solve(t(X)%*%X)