In Chapter 5.7 we used the data in file pizza4.dat to estimate the model PIZZA b1 b2AGE b3INCOME b4AGE INCOME

In Chapter 5.7 we used the data in file pizza4.dat to estimate the model PIZZA ¼ b1 þ b2AGE þ b3INCOME þ b4ðAGE  INCOMEÞ þ e

(a) Test the hypothesis that age does not affect pizza expenditure—that is, test the joint hypothesis H0:b2 ¼ 0, b4 ¼ 0. What do you conclude?

(b) Construct point estimates and 95% interval estimates of the marginal propensity to spend on pizza for individuals of ages 20, 30, 40, 50, and 55. Comment on these estimates.

(c) Modify the equation to permit a ‘‘life-cycle’’ effect in which the marginal effect of income on pizza expenditure increases with age, up to a point, and then falls.

Do so by adding the term (AGE2  INC) to the model. What sign do you anticipate on this term? Estimate the model and test the significance of the coefficient for this variable. Did the estimate have the expected sign?

(d) Using the model in (c), construct point estimates and 95% interval estimates of the marginal propensity to spend on pizza for individuals of ages 20, 30, 40, 50 and 55. Comment on these estimates. In light of these values, and of the range of age in the sample data, what can you say about the quadratic function of age that describes the marginal propensity to spend on pizza?

(e) Forthemodelinpart (c),areeachofthecoefficientestimates forAGE, (AGEINC)

and (AGE2

INC) significantlydifferent fromzeroata 5%significancelevel?Carry out a joint test for the significance of these variables. Comment on your results.

(f) Check the model used in part

(c) for collinearity. Add the term (AGE3  INC) to the model in

(c) and check the resulting model for collinearity.