[Gretl-users] eigen values

[Talha Yalta]

I have somehow missed that he was referring to Appendix 7.A.5. I
thought the example being mentioned was the one presented a couple of
pages earlier (Table 10.5).

Thanks very much for your help.
Cheers
Talha





On Feb 18, 2008 8:47 PM, Allin Cottrell <cottrell at wfu.edu> wrote:
> 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.
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