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Introduction to
Regression Procedures |

The PLS procedure fits models using any one of a number of linear
predictive methods, including *partial least squares* (PLS).
Ordinary least-squares regression, as implemented in SAS/STAT
procedures such as PROC GLM and PROC REG, has the single goal of
minimizing sample response prediction error, seeking linear functions
of the predictors that explain as much variation in each response as
possible. The techniques implemented in the PLS procedure have the
additional goal of accounting for variation in the predictors, under
the assumption that directions in the predictor space that are well
sampled should provide better prediction for *new* observations
when the predictors are highly correlated. All of the techniques
implemented in the PLS procedure work by extracting successive linear
combinations of the predictors, called *factors* (also called *
components* or *latent vectors*), which optimally address one or
both of these two goals -explaining response variation and
explaining predictor variation. In particular, the method of partial
least squares balances the two objectives, seeking for factors that
explain both response and predictor variation.

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