As discussed in the preceding sections, partial least squares depends on selecting factors of the predictors and
of the responses that have maximum covariance, whereas principal components regression effectively ignores
and selects
to have maximum variance, subject to orthogonality constraints. In contrast, reduced rank regression selects
to account for as much variation in the predicted responses as possible, effectively ignoring the predictors for the purposes of factor extraction. In reduced rank regression,
the Y-weights
are the eigenvectors of the covariance matrix
of the responses that are predicted by ordinary least squares regression, and the X-scores are the projections of the Y-scores
onto the X space.