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st: RE: interpreting R-squared when constant has been supressed


From   "Brent Fulton" <fultonb@berkeley.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: interpreting R-squared when constant has been supressed
Date   Thu, 27 Sep 2007 08:21:53 -0700

Lloyd, for your clarity in reporting goal, another option is to run a
constrained regression where all three dummies (as well as the constant
term) are included in the model, but the parameter estimates on the three
dummies are constrained to sum to zero. The interpretation of the dummy
parameters are how the prediction deviates from the average (instead of how
they deviate from the omitted category). This is explained in Suits (1984),
and Stata can estimate this using -cnsreg-.

Suits, Daniel B.(1984), "Dummy Variables: Mechanics V. Interpretation," The
Review of Economics and Statistics, 66(1): 177-180. 

-Brent Fulton




-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Lloyd Dumont
Sent: Thursday, September 27, 2007 5:05 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: interpreting R-squared when constant has been supressed

Hello.  I am running an OLS model in which
observations fall into one of three mutually-exclusive
and collectively-exhaustive categories.  For clarity
in reporting, I thought it would be a good idea to
suppress the constant and report slope estimates for
all three dummies.
 
If I run the model both ways (either with two dummies
and the constant vs. with all three dummies and no
constant), the estimates and the standard errors are
what they should be, i.e., are the same in relative
terms to one another in both models, same t-stats,
etc.  But, without the constant, the R2 shoots up from
something like .11 to something like .68.
 
I sort of understand conceptually how this could
happen--fit is now relative to zero than to the mean. 
But...
 
1.  Is my understanding correct?
2.  How can I explain this succinctly?
3.  Am I being deceptive to report the .68?
 
Thank you.  Lloyd Dumont



 
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