[19195] in s-news-athena
[S] Model explains __% of the dispersion?
daemon@ATHENA.MIT.EDU (John Thaden)
Sun Sep 12 14:39:06 1999
Message-Id: <3.0.3.32.19990912123809.009ee070@pop.flash.net>
Date: Sun, 12 Sep 1999 12:38:09 -0500
To: s-news@wubios.wustl.edu
From: John Thaden <jjthaden@flash.net>
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On 9/3/99, I asked s-news a question under the same subject line. I
received three responses, all from others asking for a summary. Since the
issue apparently is of some general interest, I repeat the question below:
#############
Greetings,
I'd like to report in a publication that my weighted multiple regression
model explains a certain percentage, of the variation, or variance, or
deviance, or dispersion in the data. I'm uncertain how to calculate
something like this (or whether in fact this is an appropriate thing to
report, or even exactly what these various terms mean). I would be
grateful for a hint from a real statistician on this list.
In S-Plus 4.5 for Windows, the summary reports for lm(), glm(), and
lmRobMM() contain the following statements, when I fit my data with my
model formula and my weightings:
>summary(lm.object)
<snip>
Residual standard error: 0.5206 on 130 degrees of freedom
Multiple R-Squared: 0.9451
F-statistic: 279.8 on 8 and 130 degrees of freedom, the p-value is 0
<snip>
>summary(glm.object)
<snip>
(Dispersion Parameter for Gaussian family taken to be 0.2710143 )
Null Deviance: 641.8048 on 138 degrees of freedom
Residual Deviance: 35.23186 on 130 degrees of freedom
Number of Fisher Scoring Iterations: 1
<snip>
> 100 * (641.80 - 35.23)/641.80
[1] 94.51075
# So it looks like my model explains 94.5% of the deviance
summary(lmRobmm.object)
<snip>
Residual scale estimate: 0.5102 on 130 degrees of freedom
Proportion of variation in response explained by model: 0.7315
<snip>
#So it looks like my model only explaind 73% of the variation in response
What do I say? How do I relate these two percentages?
************************************************************
John J. Thaden, Ph.D., Instructor jjthaden@life.uams.edu
Department of Geriatrics (501) 257-5583
University of Arkansas for Medical Sciences FAX: (501) 257-4822
mail & ship to: J. L. McClellan V.A. Medical Center
Research-151 (Room GB103 or GC124)
4300 West 7th Street
Little Rock AR 72205 USA
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