Solved – Multicollinearity in polynomial regression

Question

How to deal with multicollinearity in polynomial regression? Suppose I have $x$, $x^2$ and $x^3$ as independent variables in my regression equation. How can I calculate and remove multicollinearity from my model?

Answer 1

Don't use polynomial transformations "as such", because they will be collinear, as you note. Instead, transform them into orthogonal polynomials. In R, use the poly() command.

Even better, don't use higher order polynomials at all, since they will become unstable at the boundaries of your data space. Instead, use splines. In R, look at the splines package. For more information, look at Frank Harrell's Regression Modeling Strategies.