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


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Goodness of fit measure akin to R-squared for 0-constant or noconstant
Date   Fri, 24 Apr 2009 13:10:05 +0100

I don't understand the substantive reasoning here, as regressing GDP on
demand for jewellery seems a backward way to predict the latter. Perhaps
"on" has a differing meaning here. Or perhaps you mean GDP growth and
jewellery demand growth: your posting appears contradictoru on this and
in any case is not very clear to me. 

On general grounds the origin of zero GDP and zero jewellery demand
would seem likely to be a long way away from the bulk of the data!

On one very specific and one very general technical point:  

My recollection is that the Durbin-Watson test is only defined for a
model with intercept, but I can't find chapter and verse for that
possibly garbled memory. 

Although its title is not your exact question, the material in 

FAQ     . . . . . . . . . . . . . . . . . . . . . . . Do-it-yourself
R-squared
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N.
J. Cox
        9/03    How can I get an R-squared value when a Stata command
                does not supply one?
                http://www.stata.com/support/faqs/stat/rsquared.html

has much bearing on your situation. 

It pushes various simple ideas. Here's one: in many models, and yours
seems to be among them, it is simple and natural to think of 

correlation between observed and predicted 

or its square as one measure of model merit. Naturally, _no_ single
measure can ever tell the complete story. 

Nick 
n.j.cox@durham.ac.uk

P.S. later contributions to this thread mentioned a paper without ever
giving a proper full reference. Here it is:  

Kv{\aa}lseth, T.O. 1985. Cautionary note about $R^2$. American
Statistician 39: 279-285.

Bas de Goei
===========

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??


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