Summary: Goodman [1963] generalized the real normal multivariate model to the complex case. Goodman [1963], and Khatri 119651 derived the sampling distribution theory underlying this model. The present paper generalizes the complex multivariate normal theory to the hypercomplex case. The hypercomplex case studied here includes Hamilton's quaternions, biquaternions, octonions, and bioctonions. It is shown that the complex case results straightforwardly generalize to the hypercomplex case.

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4] have given some results for the st,epwise estimation of the parameters of a univariate regremion model. We give here similar results for a multivariate linear regression model.