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Whereas in PCR the response variable, y, plays no role in identifying the principle component directions, in partial least squares (PLS), y supervises the identification of PLS directions (see pages 237-8 in the textbook for details on how this is done). Other than this key difference, PLS is similar to PCR in that we use cross-validation or test error to perform dimension reduction by selecting the number of PLS directions, and then we fit a multiple linear regression model to just these directions.

After completing the reading for this lesson, please finish the Quiz and R Lab on ANGEL (check the course schedule for due dates).