Estimating coefficients in linear models: It don't make no nevermind.

Abstract

It is proved that under very general circumstances coefficients in multiple regression models can be replaced with equal weights with almost no loss in accuracy on the original data sample. It is then shown that these equal weights will have greater robustness than least squares regression coefficients. The implications for problems of prediction are discussed. In the two decades since Meehl's (1954) book on the respective accuracy of clinical versus clerical prediction, little practical consequence has been observed. Diagnoses are still made by clinicians, not by clerks; college admissions are still done by committee, not by computer. This is true despite the considerable strength of Meehl's argument that humans are very poor at combining information optimally and that regression models evidently combine information rather well. These points were underlined in some recent work by Dawes and Corrigan (1974), in which they found again that human predictors do poorly when compared with regression models. Strikingly, they found that for some reason, linear models with random regression weights also do better than do humans. Even more striking, when all regression weights were set equal to one another they found still higher correlation with criterion on a validating sample. The obvious question here is Why? Is it because humans are so terrible at combining information that almost any rule works better, or is it some artifact of linear regression?

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