One aspect of multiple regression--the shrinkage of the multiple correlation coefficient on cross-validation is reviewed. The paper consists of four sections. In section one, the distinction between a fixed and a random multiple regression model is made explicit. In section two, the cross-validation paradigm and an explanation for the occurrence of shrinkage are presented. In section three, research on shrinkage by Burket (1964) and by Brown (1969) is covered. Finally, in section four, shrinkage literature is considered with respect to theoretical-methodological advances and the development of better computer programs. (Author/RC)