On the computation of the distribution of the square of the sample multiple correlation coefficient

Abstract

Two computationally simple methods are proposed to evaluate the distribution function and the density of the square of the sample multiple correlation coefficient. No auxiliary routine is required. The accuracy of recursive computations can be effectively controlled. The distribution function and the density can be evaluated concurrently because their computing formulas are closely related. This property can enhance efficiency of Newton's method for computing the quantiles of the distribution. The corresponding algorithms are provided in a step-by-step form.