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Re: st: Re: adjusted r square


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Re: adjusted r square
Date   Tue, 20 Feb 2007 21:11:45 -0500

At 10:34 AM 2/20/2007, Ulrich Kohler wrote:
It is just a simple fact that I can explain more variance with an additional variable.
One other point: It is true that in a sample, R^2 will always go up as you add more variables. This is because, even if the population coefficient is zero, sampling variability will cause the estimated coefficient to be non-zero. But, if we had the entire population, there would be no requirement that adding another variable result in more explained variance.

By way of analogy, suppose we had an estimation procedure that we knew produced coefficients with an upward bias. Would we complain that we were being "punished" if a correction was applied that reduced or eliminated that upward bias?

Incidentally, I'm assuming adjusted R^2 does what it purports to do. Its formula is something I've always just taken on blind faith. But regardless of how well it works, I think the rationale for it makes sense.


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Richard Williams, Notre Dame Dept of Sociology
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