In principle components regression, we mean center(or standardize) X and using this X we decompose it so that:
X = T.P' + E
And regression to Y becomes(with using a certain portion of T):
Y = T.b where b is a vector without intercept term
Similarly in PLS, after mean centering both X and Y the equations(shortly) are
X = T.P' + E and
Y = U.Q' while the inner relation to be solved is
U = T * b where b is, again, a vector having linear regression coefficents.
Does it make any sense to add a intercept term to the
b vectors I have mentioned above? In other words, do PLS and/or PCA themselves make sure the scores(T and/or U) are bias free mathematically or due to initial mean centering of the data?