At 05:09 AM 10/29/2003 +0000, Clive Nicholas wrote:
unlikely to vote Labour and vice versa. Because this overlap is carried
forward to the computation of R^2, R^2 has been upwardly biased.
To put it one other (and hopefully last) way: It is important to understand
that R^2 is not just a function of the interrelationships between the Xs
and the Ys. It is also a function of the intercorrelations of the Xs with
each other (as well as other things, such as the exogenous variances and
the residual variances.) Hence, while I could be wrong, I don't think it is
technically correct to say that correlated Xs will "upwardly bias"
R^2. But, it is certainly correct to note that the correlations of the Xs
will affect R^2. Because R^2 is a function of so many different things,
only part of which is the effect of the Xs on the Ys, it is a potentially
misleading statistic, especially when you get into the business of
comparing R^2 across populations or times or whatever. Just looking at R^2
could cause two populations to look much more different (or much more
similar) than they really are.
