Plan <- read.table("https://husson.github.io/livre_exo/chap14_ex1.csv", header = TRUE, sep=";",row.names=1, encoding = "latin1")

Plan[,1] <- (Plan[,1]-20)/10
Plan[,2] <- (Plan[,2]-45)/15

Plan

X <- model.matrix(~ T1+T2+I(T1*T2)+I(T1^2)+I(T2^2), Plan)
t(X)%*%X
cor(X)
solve(t(X)%*%X)