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st: Re: confidence intervals on r-squared


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: confidence intervals on r-squared
Date   Tue, 16 Oct 2007 06:09:36 -0400

Marcello indicates that one can indeed provide confidence intervals for the r^2 statistic. My point is that as one can arbitrarily increase r^2 by tossing anything lying around (e.g. interactions, polynomial terms, anything not completely random) into the regression, you can with probability 1 place r^2=1 in such a confidence interval. But what does that mean? I agree with Nick. "Improving your model" is not a matter of maximizing r^2 (we all know how to do that without any reference to the underlying discipline- specific theory). The model should be a tradeoff between explanatory power and parsimony, and r^2 is not made for that objective. Adjusted r^2, although imperfect, at least penalizes the inclusion of lots of junk.


Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


On Oct 16, 2007, at 2:33 AM, statalist-digest wrote:


Oblique answer: You can do this, but it is better
to devote the surplus energy you would spend on it
thinking about the interpretation of your model,
whether you can improve it, and so forth.

Nick
n.j.cox@durham.ac.uk

Marcello Pagano

Correct answer: R-squared is a statistic around which you can set a
confidence interval.  It is just somewhat complicated to give the
general formula, although it is available in particular cases.

Which case are you interested in?

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