R help - Apr 2005 - R-squared in summary(lm...)

What is the difference between the two R-squareds returned for a linear
regression by summary(lm...)?  When might one report multiple vs. adjusted
R-squared?
Thank you,
Ben Osborne

-- 
Botany Department
University of Vermont
109 Carrigan Drive
Burlington, VT 05405

benjamin.osborne at uvm.edu
phone: 802-656-0297
fax: 802-656-0440

Please consult any basic book on linear regression/linear models; for
example, APPLIED REGRESSION ANALYSIS by Draper and Smith. Or google on
"adjusted R-Squared."

In brief, Adjusted R-squared arrempts to compensate for the property that
adding extra regressors -- even random ones -- to a linear model **always**
increases R-squared. It does so by penalizing for extra regressors. So
R-squared is almost never useful as an indication of the quality of fit.
Adjusted R-squared might be (but often isn't either because of selection
bias among other reasons).

-- Bert Gunter
Genentech Non-Clinical Statistics
South San Francisco, CA
 
"The business of the statistician is to catalyze the scientific learning
process."  - George E. P. Box
 
 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of 
> Benjamin M. Osborne
> Sent: Monday, April 18, 2005 3:52 PM
> To: R help
> Subject: [R] R-squared in summary(lm...)
> 
> What is the difference between the two R-squareds returned 
> for a linear
> regression by summary(lm...)?  When might one report multiple 
> vs. adjusted
> R-squared?
> Thank you,
> Ben Osborne
> 
> -- 
> Botany Department
> University of Vermont
> 109 Carrigan Drive
> Burlington, VT 05405
> 
> benjamin.osborne at uvm.edu
> phone: 802-656-0297
> fax: 802-656-0440
> 
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