An observation on the variance of a predicted response in regression analysis

Abstract

In studying individual parameters and the predicted response in regression analysis, three important properties are usually distinguished. These are bias, variance and  mean-square error. The choice of a predicted response has to be made on a balance of these properties and computational simplicity. To avoid over fitting, along with the  obvious advantage of having a simpler equation, it is shown that the addition of a  variable to a regression equation does not reduce the variance of a predicted response.

Key words: Linear regression; Partitioned matrix; Predicted response