# st: RE: adjusted r square

 From "Schaffer, Mark E" To Subject st: RE: adjusted r square Date Tue, 20 Feb 2007 13:39:33 -0000

```Hi all.

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Kit Baum
> Sent: Tuesday, February 20, 2007 1:28 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: adjusted r square
>
> Ranjita said
>
> I saw your note in Stata re: adjusted R square and that while
> -areg- calculates the adjusted R^2 statistic, but, it is not
> statistically equivalent to the FE model in -xtreg, fe-:
> Therefore, my question is if I wanted to stay with xtreg, fe
> how whould I calculate adjusted R square? Thank you for your help
>
> The model estimated by xtreg,fe is certainly 'statistically
> equivalent' to that estimated by areg:
>
> webuse grunfeld
> xtreg invest mvalue kstock,fe
> areg invest mvalue kstock,absorb(company)
>
> These models have identical coefficients, standard errors, F-
> statistics and RMSEs. What is not equivalent? These are just
> two different ways of implementing the LSDV (least squares dummy
> variable) approach, taking into account the loss of d.f.

Using Kit's example,

webuse grunfeld
qui areg invest mvalue kstock,absorb(company)
di e(r2)
di e(ar2)
qui xi: reg invest mvalue kstock i.company
di e(r2)
di e(r2_a)
qui xtreg invest mvalue kstock, fe
di e(r2)
di e(r2_a)

the R2 and adjusted R2 for areg is identical to that for the LSDV
approach, and much higher (96%) than that for the FE model (75-76%).

I suppose what is happening is that the areg R2 and adj R2 refer to the
total variation in the dependent variable, whereas the FE R2 and adj R2
refer to the variation in the demeaned dependent variable.

So the question for Ranjita is, which R2 do you want?

--Mark

> Kit Baum, Boston College Economics
> 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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