Multicollinearity problem could arise when we add quadratic variable in regression like this:
So, one of the possible solutions to eliminate the problem is to add centered variables:
This was suggested here: [a]
Then the author concludes without general proof that estimates in the original regression and in the regression with centered variables are similar after the transformations:
How could we prove that for general case? Could centering always solve this problem of multicollinearity? Is it necessary to eliminate the problem or we do not need to divide an influence between quadratic and first degree variable?
