A Note on Residual Heterovariance and Estimation Efficiency in Regression

Abstract

The object of this note is to present a table showing the effect of a particular kind *of residual variance heterogeneity on the efficiency of estimation of coefficients in least square regression, and to consider what, if anything, is to be done about it. The theory of the problem is well-known (see, for example, [2], pages 19-20 and 67-70) ; the almost invariable practice is to ignore the problem, apparently on the assumption that such heterogeneity does not matter, at any rate in comparison with the other problems in regression with which analysts are so ruefully aware. A convenient model in simple regression for our purpose is