The relationship between canonical correlation analysis and multivariate multiple regression

The similarities between multivariate multiple regression and canonical correlation analysis have been inconsistently acknowledged in the literature. The present article shows that, although the stated objectives of these two analyses seem different, aspects of the analyses themselves are mathematically equivalent. A multivariate multiple regression analysis that incorporates discriminant analysis as part of its post hoc investigation will produce identically the same results as a canonical correlation analysis in terms of omnibus significance testing, variable weighting schemes, and dimension reduction analysis. A numerical example is provided.