The calculation of partial and multiple coefficients of regression and correlation.

Abstract

is a simple straightforward method which should be particularly valuable to the inexperienced worker. Essentially, it consists of reducing a 2 X 2 determinant over and over, that is, a multiplication using the plus bar followed by a multiplication using the minus bar of a calculating machine. It is possible that when the number of variables is large that the simplicity of the method will be offset by the large number of operations to be performed. J. W. D.It is the purpose of this paper to present a systematic method for calculating partial and multiple coefficients of regression and correlation which has distinct advantages over present methods. There are no recursion formulae to be remembered such as those of Yule 1 nor elaborate determinants to expand as in the method presented by Kelley. 2 Although there is some similarity to the Doolittle method, the one presented here was developed independently as an application of a simplified technique for solving systems of linear equations, 3 and it is simpler and more direct than certain published simplifications of the Doolittle method. 4 I. PARTIAL REGRESSION AND CORRELATIONIn order to demonstrate the technique for calculating partial coefficients of correlation we shall assume a four-variable problem 1

The solution of simultaneous equations

“…A method which does not involve division at all in the forward solution has lately come into prominence. For example, Rider has used it in his recent text (15, p. 36) and Wren has recently described it (4). If we multiply the first equation of (1) by -a~, and the second by a,~ and add, we get A similar elimination involving the first and third equations gives The four equations in four unknowns have thus been reduced, by multiplication and subtraction, to three equations in three link's.owns.…”