Partial least squares regression

Partial least squares (PLS) regression is a statistical method that bears some relation to principal components regression and is a reduced rank regression; instead of finding hyperplanes of maximum variance between the response and independent variables, it finds a linear regression model by projecting the predicted variables and the observable variables to a new space of maximum covariance (see below). Because both the X and Y data are projected to new spaces, the PLS family of methods are known as bilinear factor models.

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