Robustness of the multiple correlation coefficient when sampling from a mixture of two multivariate normal populations

The density of the multiple correlation coefficient is derived by direct integration when the sample covariance matrix has a linear non-central distribution. Using the density, we deduce the null and non-null distribution of the multiple correlation coefficient when sampling from a mixture of two multivariate normal populations with the same covariance matrix. We also compute actual significance levels of the test of the hypothesis Ho: P1.2.p-0 versus Ha:P1.2…p> 0, given the mixture model.