Testing the stability of regression parameters when some additional data sets are available (Q1321868)

Summary: We consider the problem of testing the stability of regression parameters in regression lines of different populations when some additional, but unidentified, data sets from those populations are available. The standard test \((T_ 0)\) discards the additional data and tests the stability of the regression parameters using only the data sets from identified populations. We propose two test procedures (\(T_ 1\) and \(T_ 2\)) utilizing all the available data, because the additional data may contain information about the parameters of the regression lines which are tested for stability. A power comparison among the tests is also presented. It is shown that \(T_ 1\) always has larger power than \(T_ 0\). In certain situations \(T_ 2\) has the largest power.