Linear Regression Functions with Neglected Variables

Abstract

This article discusses some properties of the computed Y values obtained by fitting a linear regression function to independent observations by the method of least squares. For the general case where the form of the fitted function may not be correct it is proved that (a) the sampling variance of the computed values and of the residual differences is the same as for the special case where the form of the fitted function is correct, and (b) the mean square bias of the set of computed values is less than, or equal to, that of any other set of linear estimates. These and other properties lead to the suggestion that in minimizing the mean square error, one or more variables be neglected unless Snedecor's F is greater than two.