[Gretl-users] QR versus Cholesky decomposition

[Allin Cottrell]

On Thu, 20 Jul 2006, Talha Yalta wrote:

> I want to draw attention to gretl's results in calculating the 
> R^2 for the noint1 a noint2 data sets. Results are very poor 
> with both QR and Cholesky methods. Can there be a bug that 
> affects calculating the R^2 in regressions without the 
> constant term?

Have you read the section dealing with this at

http://gretl.sourceforge.net/nist/index.html

<quote>

In the NoInt1 and NoInt2 datasets there is a methodological 
disagreement over the calculation of the coefficient of 
determination, R^2, where the regression does not have an 
intercept. gretl reports the square of the correlation 
coefficient between the fitted and actual values of the 
dependent variable in this case, while the NIST figure is

R^2 = 1 - ESS / sum(y^2)

There is no universal agreement among statisticians on the 
"correct" formula (see for instance the discussion in 
Ramanathan, 2002, pp. 163-4). Eviews 3.1 produces a different 
figure again (which has a negative value for the NoInt test 
files). The figure chosen by NIST was obtained for these 
regressions using the command

genr r2alt = 1 - $ess/sum(y * y)

and the numbers thus obtained were in agreement with the 
certified values, up to gretl's precision.

</quote>

Allin Cottrell