This paper is concerned with the role played by the standardized regression
coefficients in linear regression analysis. The linear regression model is
reparameterized to explicitly contain standardized regression coefficients.
Several estimators of these coefficients are considered. It is shown that the
usual beta coefficient is a good estimator of the coefficients in the linear
regression model with random predictor variables. However, in the linear
regression model with nonstochastic predictors, alternative estimators are
better than the usual beta coefficient. A sociological application is included in
order to display the empirical behavior of the various estimators.
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