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The ORTHOREG Procedure |

The ORTHOREG procedure
fits general linear models by the method of least squares. Other
SAS/STAT software procedures, such as GLM or REG, fit the same types
of models, but PROC ORTHOREG
can produce more accurate estimates than
other regression procedures when your data are ill conditioned.
Instead of collecting crossproducts, PROC ORTHOREG uses
Gentleman-Givens transformations to update and
compute the upper triangular matrix **R** of the
QR decomposition of the data matrix, with special
care for scaling (Gentleman 1972; 1973).
This method has the advantage over other orthogonalization
methods (for example, Householder transformations) of
not requiring the data matrix to be stored in memory.

The standard SAS regression procedures (REG and GLM) are very accurate for most problems. However, if you have very ill-conditioned data, these procedures can produce estimates that yield an error sum of squares very close to the minimum but still different from the exact least-squares estimates. Normally, this coincides with estimates that have very high standard errors. In other words, the numerical error is much smaller than the statistical standard error.

Note that PROC ORTHOREG fits models by the method of linear least
squares, minimizing the sum of the squared residuals for predicting
the responses. It does *not* perform the modeling method known
as "orthogonal regression," which minimizes a different criterion
(the distance between the X/Y points taken together and the regression
line.)

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