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Multicollinearity problem could arise when we add quadratic variable in regression like this: enter image description here So, one of the possible solutions to eliminate the problem is to add centered variables: enter image description here 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: enter image description here

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?

[a]https://online.stat.psu.edu/stat501/lesson/12/12.6

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    $\begingroup$ Are you sure it’s even a problem? $\endgroup$
    – Dave
    Jul 22 '21 at 23:42
  • $\begingroup$ Without the answers on questions in post, yes, that’s the issue $\endgroup$ Jul 23 '21 at 14:46