Polynomial regression in R with multiple independent variables

Question

I want to do a polynomial regression in R with one dependent variable y and two independent variables x1 and x2. In my mind the model shou

Answer 1

you can use polym

y ~ polym(x1, x2, degree=2, raw=TRUE) # is equivalent to
y ~ x1 + x2 + I(x1^2) + I(x2^2) + x1:x2

But be careful with the order of the coefficients they are not the same as the second formula.

If you use degree=3 then it will add interactions of higher order like this I(x1^2):x2 +I(x2^2):x1, thus you have to adapt your formula.

NB : polym is a wrapper for poly, so you can use this latter with the same call.