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Re: st: R2's from xtreg


From   Daifeng He <dhe.statlist@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: R2's from xtreg
Date   Thu, 17 Nov 2011 23:24:10 -0500

Kit,

Thanks so much for the help.  Great info!

Best,
Daifeng

On Thu, Nov 17, 2011 at 9:51 AM, Christopher Baum <kit.baum@bc.edu> wrote:
> <>
> On Nov 17, 2011, at 2:33 AM, Daifeng wrote:
>
>>
>> Here is what the Manual Says:  the overall R2 corresponds to Eq(1),
>> the between R2 corresponds to Eq(2), and the within R2 corresponds to
>> Eq(3).  (Sorry, the equations are uly and hard to read, but Statlist
>> does not allow formatting..)
>>
>>
>> y_it_hat = a + b*x_it                       (1)
>> y_it_bar = a + b*x_it_bar                 (2)
>> (y_it-y_i_bar)= b*(x_it - xi_bar)         (3 )
>
> In linear regression with a constant term (or with many constant terms), R^2 can always be written as the squared correlation of Y and Yhat. If you do
>
> webuse grunfeld
> xtreg invest mvalue, fe
> predict ihat, xb
> corr ihat invest
> di r(rho)^2
>
> you will see that the 'overall' R^2 is this measure: the squared correlation of actual and predicted values.
>
> If you do the same thing with areg -- areg invest mvalue, absorb(company) -- it gives you a different R^2. However if you save the predicted values and look at their squared correlation with invest, you will get the same R^2 as you do in xtreg, fe as the 'overall' R^2.
>
> Note that the 'xb' predictions after areg are not the same as those from an equivalent regression; you need the 'xbd' predict option for that. Likewise, for xtreg, fe, it is the xbu option that produces the same predicted values as those from a regression including the dummy variables.
>
> Kit
>
> Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
>                             An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
>  An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html
>
>
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