Bias in Regression Estimates, and Expected Values of Mean Squares and Sums of Squares

Abstract

This chapter explores what can be said in situations where we fit one model (e.g., a straight line) but we fear that this model may be somewhat inadequate (e.g., there in fact may be a little quadratic curvature). First, it discusses possible biases in the estimates of the parameters of a possibly inadequate model and then sees how the consequences of this go through to the analysis of variance table, via the expected values of the various mean squares. The chapter provides details of how to compute the expected values of mean squares and sums of squares. It summarizes the effect bias has on the usual least squares analysis.