Regression Lines and the Linear Functional Relationship

Abstract The first half of this paper solves the following problem : if there is a linear multiple regression between n variates, under what conditions will the regression continue to be linear when the variates are influenced by error? The new regression coefficients are obtained in terms of the original coefficients. This leads in the second half to a discussion of the use of regression lines and functional relationships in statistical methodology. In the case of normal distributions the problem of estimation is discussed at some length. Since the classical work has used least squares methods a section relating to this work is included and some criticisms offered.