Abstract
For testing problems of the coefficient vectors of p-variate linear functional and structural relationships, the statistic which is based on the multiple correlation coefficient between the null variate and the uncorrelated (p-1) variates is considered. The asymptotic distributions of the test statistic under null hypothesis, where the estimators are substituted for other unknown parameters, are obtained for the functional and the structural relationship respectively. The testing procedures considered in this article are shown to be the same either for the functional or the structural relationship. The computations are illustrated with an example.
