A simple derivation of the distribution of the multiple correlation coefficient
E.J. Williams · Communication in Statistics- Theory and Methods · 1978
It is shown that the non-null distribution of the multiple correlation coefficient may be derived rather easily if the correlated normal variables are defined in a convenient vay. The invariance of the correlation distribution to linear transformations of the variables makes the results generally applicable. The distribution is derived as the well-known mixture of null distributions, and some generalizations when the variables are not normally distributed are indicated.