By means of factor analysis (FA) or principal components analysis (PCA) a matrix Y with the elements is approximated by the model . Here the parameters express the systematic part of the data yik, "signal," and the residuals ik express the "random" part, "noise." When applying FA or PCA to a matrix of real data obtained, for example, by characterizing N chemical mixtures by M measured variables, one major problem is the estimation of the rank A of the matrix Y, i. e. the estimation of how much of the data is "signal" and how much is "noise." Cross validation can be used to approach this problem. The matrix Y is partitioned and the rank A is determined so as to maximize the predictive properties of model (1) when the parameters are estimated on one part of the matrix Y and the prediction tested on another part of the matrix Y