(1) When doing PCA, do you assume the variables to be bell-shaped? Say if I have a bunch of variables, some are bell-shaped but some have characteristic long (right) tails (highly skewed and asymmetric with the median close to the minimum and and a few extremely large values). Should I do log transformation on those long-tailed variables or leave them like that? What are the implications to the results of the PCA with and without transformation?
(2) The second question is, when I do principal component regression (PCR), the response variable have a long tail & one of the PC scores also have long tail. Should I log transform either or both of them?
NB: Tails in this question are all one-sided.