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Re: st: Robust OLS and adjusted R-square


From   Richard Williams <Richard.A.Williams.5@nd.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Robust OLS and adjusted R-square
Date   Wed, 05 May 2004 21:02:06 -0500

At 02:11 AM 5/6/2004 +0100, Mark Schaffer wrote:
Ayako,

Quoting Ayako Saiki <smap@brandeis.edu>:

> Dear all,
>
> If anybody can help me on this, that'll be great - I ran OLS
> with robust standard errors (reg.... , robust), but it does not
> provide adjusted R-square.  Can anybody tell me what is causing
> this?
>

It should be there, if you look in the right place:

. sysuse auto, replace
(1978 Automobile Data)

. regress price mpg, robust

Regression with robust standard errors                 Number of obs

<snip>

. ereturn list r2_a
scalar e(r2_a)     =  .2087437291901012
Also -- note that the R^2 and adjusted R^2 values are the same regardless of whether or not you use robust standard errors. So, if you also run regression without the robust option the value is already reported for you.

This raises an interesting question: when using robust standard errors, is adjusted R^2 not reported (a) because there is something that makes it inappropriate when using robust standard errors, or (b) because whoever wrote the programming code did not bother to include it in the output?

The omission of the Anova table when using robust standard errors is quite intentional by the way. From p. 337, Stata 8 Reference Manual N-R, "When you specify robust, regress purposefully suppresses displaying the ANOVA table, as it is no longer appropriate in a statistical sense even though, mechanically, the numbers would be unchanged. That is, sums of squares remain unchanged, but the meaning you might be tempted to give those sums is no longer relevant. The F statistic, for instance, is no longer based on sums of squares; it becomes a Wald test based on the robustly estimated variance matrix."

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