## Computational Method

Let **X** represent the *n* ×*p* design matrix and
**Y** the *n* ×1 vector of dependent variables.
(See the section "Parameterization of PROC GLM Models" for information on how **X** is
formed from your model specification.)
The normal equations are solved using a modified sweep routine that produces a
generalized (g2) inverse (**X'X**)^{-} and a
solution **b** = (**X'X**)^{-}**X'y**
(Pringle and Raynor 1971).

For each effect in the model, a matrix **L** is
computed such that the rows of **L** are estimable.
Tests of the hypothesis are then made by first computing

and then computing the associated *F*
value using the mean squared error.

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