SummaryIt is shown that the least squares estimators ofBand Σ in the multivariate linear model {EYi=X1B,D(Yi) =Σ, 1 ≤i≤n,Y1Ynuncorrelated} subject to the constraintsYiM=XiNare just the usual least squares estimatorsB̂= (X'X)‐1X'Yand ΣC = 1/n(Y‐XB̂)(Y‐XB̂) in the unconstrained model where Σ has full rank. Tests of hypotheses concerningBare discussed for situations in which eachYihas a multivariate normal distribution, and examples of the applicability of th