On Mon, 14 Feb 2000 [EMAIL PROTECTED] wrote in part:
> I am a lowly computer programmer who has only one recipe for making
> multiple linear regressions in SQL: via a sequence of simple ones.
> This is my aforementioned schedule is so important: it is an algorithm.
> Aha! I'm found out!
Does SQL not permit matrix operations? It is much simpler than the
sequence you suggested to consider the (p+1)x(p+1) submatrix of variances
and covariances among the p predictors (Xs) and the response variable
(Y), and apply the sweep operator p times (successively, in any
convenient order, to the row and column identified with each predictor).
A good reference if you can find it is Albert Beaton's 1964 paper "Special
Matrix Operators" (I think I'm remembering the title right), published as
a Research Bulletin by the Educational Testing Service, Princeton, NJ.
But there should be independent references to the sweep operator
-- I'm fairly sure it wasn't invented by Beaton -- in the literature on
computing algorithms.
(In practice, one would carry out the successive sweeps on the
complete matrix of variances and covariances for all variables in the
active file; it's just easier to conceptualize in terms of the submatrix
of particular interest. Also, it is fairly usual to operate instead on
the matrix of product-moment correlations to obtain standardized
regression slopes, which are then multiplied by the ratio of standard
deviations (SD.y/SD.x) to obtain the "raw" regression slopes.)
-- Don.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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