Estimation of standardized regression coefficients

Often in reporting the results of a regression analysis, researchers, particularly in the social sciences, choose to standardize the estimators of the regression coefficients into what are called “beta coefficients.” Most studies in which beta coefficients are reported involve linear models which contain stochastic predictor variables. However, in dealing with regression models in which thep redictor variables are nonstochastic, standardized regression coefficients can be defined which are analogous to those found in the models with stochastic predictor variables. We consider the problem of estimating these parameters. Several estimators are introduced and their properties are discussed. Two data examples are included to demonstrate the empirical behavior of the various estimators.