Computation of variance accounted for in multiple correlation.

summation of all of the terms of the form 2?oi?oj rij which appear in formula [1]. Then, according to Engelhart's procedure, the shared variance is divided among each of the independent variables in the same proportions as the direct variance. The total amount of variance associated with the ith variable, then, would be the ith beta squared, plus a proportional amount of the total shared variance. Since Engelhart's procedure for partitioning the shared variance is admittedly arbitrary, the purpose of this paper is to present an alternate procedure, which, it is believed, is somewhat less arbitrary in its method of apportioning shared variance, since here the basis for partitioning the shared variance is found in mathematical manip ulations. As a necessary part of this presentation a sec ond technique (2:409-10) for computing the vari ance in the criterion associated with any given in dependent v a r iable must be noted. Such a tech nique is provided in the formula: R ?oiroi + ?o2ro2 + ?o3ro3 + '?onron [2]