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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 07:32:03 -0400

Marcello says

Unless, of course, you use an r^2 that accounts for the number of
covariates you include. That is why I asked about which r^2 you are
interested in. To say that "R-squared is not a statistical concept." is
silly.

Silly, perhaps. But I also think talking about 'which r^2' is a bit silly. r^2 is a distinct concept: the squared Pearson correlation between observed and predicted. Marcello is certainly correct in suggesting that we _could_ speak of a confidence interval around a correlation coefficient. Strangely enough a significance level cannot be produced by -correlate-, although it can by -pwcorr-. There is, as Nick Cox points out, an entire bestiary of R^2-type measures, pseudo- r^2s, r^2 from a model lacking a constant term, etc. But when we speak of r^2 arising from linear regression with a constant term included I don't think there is room for disagreement about "which one".

Of course, what you may observe in this dialogue is the difference between a real statistician and a nominal statistician. Marcello has a much stronger claim on the subject than do I. I just use the stuff.

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


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