Using Orthogonal Polynomials to remove multicollinearity


New Member
I have a homework about using orthogonal polynomials to remove multicollinearity in polynomial models. I've found the concept of polynomial orthogonality and how to produce them in a math book (apostol), But I can't find anything about how to use them in a regression model to reduce multicollinearity between independent variables. Many references just say that it can be used to reduce multicollinearity but they don't give any further information.
I used Legendre polynomials and checked their collinearity by some random data but these polynomials still had high collinearity. To be more specific, I generated a set of random data (x) between 0 and 100. Then I regressed P2(x) on P1(x) (P's are Legendre polynomials) and they had a high regression coefficient.
I think there must be some method to use these polynomials, something more than just replacing x and x^2 by P1(x) and P2(x) in the model without any other changes.
Anyone can help, please? and sorry for my awful English!