It was stated in Sect. 9.8 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....

It was stated in Sect. 9.8 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 − X) and (X − X)2? What are the VIFs of (X − X) and (X − X)2?