4.1. Introduction

In the previous chapter, we considered the multivariate linear regression model

In the model, the

  • n by p matrix Y contains the random observations on p dependent variables,

  • k + 1 by p matrix B is the matrix of unknown parameters,

  • n by p matrix ε is the matrix of random errors such that each row of ε is a p variate normal vector with mean vector zero and variance-covariance matrix Σ. The matrix Σ is assumed to be a p by p positive definite matrix.

  • n by k + 1 matrix X was assumed to be of full rank, that is, Rank(X) = k + 1.

There are, however, situations especially those involving the analysis of classical experimental designs ...

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