[Gretl-users] eigen values

[Allin Cottrell]

On Mon, 18 Feb 2008, Talha Yalta wrote:

> While preparing the notes for my econometrics class, I noticed that
> for Table_10.5.gdt from the Gujarati dataset, Gujarati reports that
> the Condition Index is found by SAS as \sqrt{3.0/0.00002422} (the
> squareroot of the biggest eigenvalue divided by the smallest)
> 
> When I choose from the menu: View--Principal components, I see the
> eigen values reported as 2.9720 and 0.0009 (instead of 0.00002422)
> 
> Can this be due to an accuracy error?

Yes: the inaccuracy consists in using the wrong dataset, and not 
taking logs ;-)

If you look carefully at Appendix 7A.5 you'll see that the SAS 
output is based on data from Table_7.3.gdt, with logs taken of all 
variables.  Repeat what Jack suggested with the right data

open Table_7.3.gdt
logs Y X2 X3
ols l_Y 0 l_X2 l_X3
matrix X = { const l_X2 l_X3 }
l = sqrt(diag(X'X))
matrix X = X ./ l'
l = eigensym(X'X, null)
CN = maxc(l)/minc(l)
printf "CN = %g, (square root = %g)\n", CN, sqrt(CN)

and you'll find the same results as given by SAS (apart from the 
slightly inaccurate reporting of the largest eigenvalue as 3.0 in 
Gujarati, rather than 2.9996).

Allin.