Principal Component Analysis is a method for reducing the dimensionality of datasets while also limiting information loss. It accomplishes this by producing uncorrelated variables that maximize variance one after other. The accepted criterion evaluating Component’s (PC) performance λ_j/tr(S) where tr(S) denotes trace covariance matrix S. standard procedure to determine how many PCs should be ma...

Multiple regression with correlated predictor variables is relevant to a broad range of problems in the physical, chemical, and engineering sciences. Chemometricians, in particular, have made heavy use of principal components regression and related procedures for predicting a response variable from a large number of highly correlated predictors. In this paper we develop a general theory that gu...