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st: Goodness of fit measure akin to R-squared for 0-constant or noconstant


From   Bas de Goei <bas.degoei@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Goodness of fit measure akin to R-squared for 0-constant or noconstant
Date   Fri, 24 Apr 2009 09:53:32 +0100

Dear all,

I am currently creating forecasts for jewellery demand in India by
regressing GDP on demand for jewellery.

Let me first give the required background:
I have data going back to 1980. In a regression based on GDP over
time, you obviously run into the problem of serial autocorrelation,
though this is neccesarily a problem for a forecast, my boss wants
"only regressions that pass Durbin Watson test".

I really have two problems:

The first is that the normal OLS regression result indicated a
positive intercept. However, economically this would mean that even
when there is no growth in GDP, there would still be growth in the
demand for jewellery. Of course, there was the problem that the model
did not pass the Durbin Watson test. Fitting the model with the GLS
approach (the prais command in Stata), did improve the model, but it
kept (as expected) the intercept positive.

I decided to inspect the data more closely, and to drop two outliers
from the data. The intercept under the Prais command is now still
positive, but it has become insignificant. I decided that there is
justification to re-run the regression with a 0 intercept. However,
this balloons the F statistic and the R-squared. I now understand why
that is, given the mathematics behind the R squared calculation.

My question is, how would you calculate in Stata a "correct" or
"alternative" R-squared, or a goodness of fit measure, which you can
use to compare it to the model with a constant??

Thanks!!

Bastiaan
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