Abstract: | Consider the two linear regression models of Yij on Xij, namely Yij = βio + βij, Xij + Eij = 1, 2,…, ni, i = 1, 2, where Eij are assumed to be normally distributed with zero mean and common unknown variance σ2. The problem of estimating the conditional mean of Y1 for a given value of X1 is considered when it is a priori suspected that β10 = β20 and β11 = β21. The preliminary test estimator is proposed. The exact expressions for the bias and the mean square error of the estimator are derived. The relative efficiency of the new estimator to the usual least square estimator based on the first regression alone is computed and is used to determine the appropriate value of the significance level of the preliminary test β10 = β20 and β11 = β21. |