Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Further aspects of the theory of multiple regression

Mr M. S. Bartletta1

a1 Queens' College

This paper may be regarded as a sequel to a previous papers(1) in these Proceedings. The vector and matrix notation of that paper used for a statistical sample is systematized somewhat further, so that while a sample S refers as before to the matrix of nm values (a sample of m observations in one variate only being a row vector), we write

S0305004100019897_eqn001

for the linear regression formula between the dependent and independent variates into which a sample is supposed partitioned (in place of equation (12) of (1)). More generally, a third submatrix S0 is partitioned off, and its effect eliminated (corresponding to equation (13) of (1)), but without loss of generality we assume that S2 in equation (1) above can always stand for S2.0 if necessary.

(Received August 10 1937)

(Accepted November 22 1937)