This chapter discusses multivariate regression, multivariate analysis of covariance (MANOCOVA) and the test for additional information. Multivariate regression is the technique used to estimate the regression coefficients and the variance about the regression from a given (n × p) data matrix X containing n independent observations on X. The canonical variates U and V are frequently defined as arising from the problem of maximizing r(U, V) for all a and b, which is equivalent to the problem of maximizing aTS12b, subject to the constraints aTS11a = bTS22b = 1. The chapter reviews the methodology of analysis of covariance for a univariate response and a single covariate. The test for additional information described by C. R. Rao is designed to assess the usefulness of particular components of the response when the aim of the analysis is to test hypotheses on the linear model.