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

 From "Nick Cox" To Subject RE: st: RE: Goodness of fit measure akin to R-squared for 0-constant or noconstant Date Fri, 24 Apr 2009 14:44:06 +0100

```Thanks for the clarification. As a long ago student of economics (A level Economics, Grade A, for those who know precisely what and how little that means), I didn't know there were any pure economic grounds, just lots of economists who if put end to end would not reach a conclusion. (No answer expected.)

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

Bas de Goei

oops...well, I should have been clearer indeed. You're right that it
is supposed to be growth of GDP predicting growth of Jewellery demand.

0 growth of GDP should be on pure economic grounds equal 0 growth in
jewellery demand, or at least never positive - the forecast resulting
from this corresponds very well with our expectations on where it
would sit amongst other countries.

Durbin Watson has been defined without intercept (as far as I
understand), but you'd have to use a different table for the upper and
lower bound. Please see here for a reference:

http://www.nd.edu/~wevans1/econ30331/Durbin_Watson_tables.pdf

I re-calculated R-squared with Kvalseth's preferred method (see
reference below: thanks Nick), which works fine for normal OLS without
a constant.

I am now trying to make it work with the AR(1) regression that results
from the Prais command in Stata. I have some problems with how to
treat the Rho in Kvalseths formula. Any ideas?

On Fri, Apr 24, 2009 at 1:10 PM, Nick Cox <n.j.cox@durham.ac.uk> wrote:

> 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??

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```