Properties of some currently used reduced-rank regression procedures are investigated. Difficulties associated with the selection of a predictor subset on the basis of the calibration sample are discussed. It is shown that the largest principal components regression procedure of Horst (1941) and Burket (1964) may be regarded as a means for obtaining estimates of regression weights under the assumption of the formal factor analysis model. The use of alternative weighting procedures in principal components regression is discussed. It is pointed out that a factor analysis regression procedure suggested by Horst (1941) may be used in conjunction with the maximum likelihood factor analytic solution to provide maximum likelihood estimates of the regression weights under the assumption of the formal factor analysis model. A superficially different procedure proposed by Scott (1966) is shown to be equivalent to this factor analysis regression procedure. Some properties of factor analysis regression using a maximum likelihood solution are given. A description is given of a series of artificial experiments which was carried out to throw light on some properties of the reduced-rank regression procedures. Implications of the results are discussed.