Hello I have two questions.

Question 1: How/does mean-centering of continuous variables help with outlier detection/diagnostics?

Question 2: I now know that in multivariate regression analyses (y = x1A+x2B+x3AB+e), if I have interaction terms, I need to do mean-centering to avoid collinearity issues of interaction terms (A*B).

Do I need to do mean-centering in a general multivariate regression (y = x1A+x2B+e)? If yes, what is the rationale for such decisions?

Thank you very much!