Consider a polynomial regression of the form
$y = α*x_1^2 + β*x_1 + ɣ*x_2$
My question is: how to deal with multicollinearity between $x_1^2$ and $x2$? Or in other words, how to control for a quadratic correlation between two independent variables in polynomial regression analyses?
I guess that such correlations must have consequences for model fitting. I know that it is not perfect, but for "normal" multicollinearity in (non-polynomial) regression analyses, scientists in my research field would drop one of the correlated variables in order to avoid multicollinearity issues. Perhaps someone can indicate a sensible approach?
Here I include two example plots, $x_1$ vs $x_2$ and $x_1^2$ vs $x_2$.
type = "Spearman" (in
R) yields a correlation coefficient between $x_1^2$ vs $x_2$ of $-0.58$. The variables are scaled variables from a use case.