Consider the regression model Y 1x1 2x2 . How can the incremental sum-of-squares approach be used to test the hypothesis

Consider the regression model Y ¼ α þ β1x1 þ β2x2 þ ε. How can the incremental sum-of-squares approach be used to test the hypothesis that the two population slopes are equal to each other, H0: β1 ¼ β2? [Hint: Under H0, the model becomes Y ¼ αþβx1 þβx2 þε ¼ Y ¼ αþβðx1 þx2Þ þε, where β is the common value of β1 and β2.]

Under what circumstances would a hypothesis of this form be meaningful? (Hint: Consider the units of measurement of x1 and x2.) Now, test the hypothesis that the ‘‘population’’ regression coefficients for education and income in Duncan’s occupational prestige regression are equal to each other. Is this test sensible?