Exercise 6.7. Consider the regression model Y + + 2X2 + . How can the incremen-

Question

Exercise 6.7. Consider the regression model Y + + 2X2 + . How can the incremen- tal sum-of-squares approach be used to test the hypothesis that the two population slopes are equal to each other, 16: ,-A? [Hint: Under Ho, the model becomes Y= + fix! + fix2+ = Y= d 2.] Under what circumstances would a hypothesis of this form be meaningful? (Hint: Consider the units of measurement ofxi 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? +(X1+X2)+, where 1s the common value of an

Explanation / Answer

First check the overall null hypothesis that finds whether entire model is better than just modelling y with its mean.

H0: the model itself contributes nothing useful and all the slope coefficients are zero.

beta1=beta2=0

H1:at least one of the betaj is not zero.

If the null hypothesis is rejected, then one is supposed to test the null hypothesis for each of the coefficients of the following form.

H0:the jth variable contributes nothing useful after allowing for the other predictors in the model:betaj=0.

H1:the jth variable makes an useful contribution to the model:betaj=/=0

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