George MacKenzie wrote in message ...
>
>SAS has a paper on their website discussing the matter of
>ill-conditioning and numerical accuracy.
>
>http://www.sas.com/rnd/app/papers/papers_da.html
>
>--
>George MacKenzie
>Multivariate Models R&D
>SAS
>
The paper refered to indicates that the SAS REG procedure
failed on the filip.dat datset. It reported a false singularity.
At first sight, it looked as if the problem was very badly
ill-conditioned, and that this was not a serious fault.
The problem is to fit a polynomial:
Y = a0 + a1.X + a2.X^2 + ... + a10.X^10
to a set of 82 (x,y) pairs of observations.
While this is a pretty silly thing to do - fitting splines, or local
polynomials would probably be more sensible, nevertheless
the problem is not badly ill-conditioned. Using no more than
double precision and a standard least squares package from
the Applied Statistics algorithms, I was able to calculate all
the regression coefficients to at least 7 decimal digits, with
not a suggestion of a singularity.
The paper referred to above indicates that orthogonal
reduction algorithms are not used in SAS for least-squares calculations
unless specifically requested. WHY NOT?
If you use ORTHREG, then Morven Gentleman's algorithm AS75
is used. Why is this not the default? Even Numerical Recipes
recommends an orthogonal reduction method (they use the SVD
which is very slow and gives no better accuracy) for linear regression,
but they strangely don't take their own advice for nonlinear regression.
--
Alan Miller, Retired Scientist (Statistician)
CSIRO Mathematical & Information Sciences
Alan.Miller -at- vic.cmis.csiro.au
http://www.ozemail.com.au/~milleraj
http://users.bigpond.net.au/amiller/
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