Question: It was stated in Section 12.8 that centering reduces collinearity. As an illustration, consider the example of quadratic polynomial regression where X takes 30 equally

It was stated in Section 12.8 that centering reduces collinearity. As an illustration, consider the example of quadratic polynomial regression where X takes 30 equally spaced values between 1 and 15.
(a) What is the correlation between X and X2? What are the VIFs of X and X2?
(b) Now suppose that we center X before squaring. What is the correlation between (X -) and (X-)2? What are the VIFs of (X -) and (X - )2?

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