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From   Richard Williams <[email protected]>
To   [email protected]
Date   Wed, 29 Oct 2003 09:20:44 -0500

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.

Richard Williams, Associate Professor
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