Re: st: Re: adjusted r square

[Richard Williams <Richard.A.Williams.5@ND.edu>]

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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