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st: r-squared in rreg output


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: r-squared in rreg output
Date   Fri, 7 Jul 2006 18:27:31 -0400

It is quite interesting that OLS and rreg come up with very similar r^2 measures, but coefficient estimates VERY different:

. reg price mpg rep78 headroom

Source | SS df MS Number of obs = 69
-------------+------------------------------ F( 3, 65) = 7.51
Model | 148497605 3 49499201.8 Prob > F = 0.0002
Residual | 428299354 65 6589220.82 R-squared = 0.2575
-------------+------------------------------ Adj R-squared = 0.2232
Total | 576796959 68 8482308.22 Root MSE = 2566.9

------------------------------------------------------------------------ ------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------------- +----------------------------------------------------------------
mpg | -289.3462 62.53921 -4.63 0.000 -414.2456 -164.4467
rep78 | 670.8971 343.5213 1.95 0.055 -15.16242 1356.957
headroom | -300.0293 398.0516 -0.75 0.454 -1094.993 494.9346
_cons | 10921.33 2153.003 5.07 0.000 6621.487 15221.17
------------------------------------------------------------------------ ------


Robust regression Number of obs = 69
F( 3, 65) = 7.40
Prob > F = 0.0002

------------------------------------------------------------------------ ------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------------- +----------------------------------------------------------------
mpg | -113.8438 26.05671 -4.37 0.000 -165.8826 -61.80491
rep78 | 464.9123 143.1268 3.25 0.002 179.0684 750.7562
headroom | -176.2006 165.8466 -1.06 0.292 -507.4191 155.0179
_cons | 6395.867 897.0398 7.13 0.000 4604.355 8187.379
------------------------------------------------------------------------ ------


The interesting thing is that the weights derived by -rreg-, which are designed to lie in the unit interval, essentially throw out the data on the high-priced cars (almost every car with a price >= 9300 is given a weight of zero). Nevertheless, the procedure is not quite the same as running OLS on that subsample in terms of the point estimates.

Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html


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