Abstract
The estimation of the regression coefficient of a population, defined byE (y)= γ+βx, incorporating two preliminary tests of significance has been discussed. The experimenter has two random samples of different sizes from two such populations, as defined above, with regression coefficientsβ1 andβ2 respectively, whereβ2 may possibly be equal toβ1. Besides this, it is also conjectured that the common conditional varianceσ2 of the two populations has a specified valueσ 0 2 . The two preliminary tests are used to resolve these two uncertainties.
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