On the theory of correlation for any number of variables, treated by a new system of notation

Abstract 1. The systems of notation hitherto used by writers on the theory of correlation are somewhat unsatisfactory when many variables are involved. In the present paper a new notation is proposed which is simple, definite, and quite general, thus very greatly facilitating the treatment of the subject. The majority of the results given in the sequel were, in fact, first suggested by the notation itself. 2. Let x1x2...xn denote deviations in the values of the n variables from their respective arithmetic means. Then the regression equation may be written :— x1 = b12.34...nx2 + b13.24...nx3 + ... + b1n.23...n-1xn