## Computational Methods

The REG procedure first composes a crossproducts matrix.
The matrix can be calculated from input data, reformed from
an input correlation matrix, or read in from an SSCP data set.
For each model, the procedure selects the
appropriate crossproducts from the main matrix.
The normal equations formed from the crossproducts
are solved using a sweep algorithm (Goodnight 1979).
The method is accurate for data that are
reasonably scaled and not too collinear.
The mechanism that PROC REG uses to check for singularity
involves the diagonal (pivot) elements of
**X**'**X** as it is being swept.
If a pivot is less than SINGULAR*CSS, then a singularity
is declared and the pivot is not swept (where CSS is the
corrected sum of squares for the regressor and SINGULAR
is machine dependent but is approximately 1E-7 on most machines
or reset in the PROC statement).

The sweep algorithm is also used in
many places in the model-selection methods.
The RSQUARE method uses the leaps and bounds
algorithm by Furnival and Wilson (1974).

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.