The ORTHOREG Procedure

Overview

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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