15.3. In studying the purchase of durable goods Y (Y= 1 if purchased, Y = 0 if no purchase) as a function of several variables for a total of 762 households, Janet A. Fisher* obtained the following LPM results: Explanatory Variable Constant 1957 disposable income, X (Disposable income = X), X Checking accounts, X3 Savings accounts, X4 U.S. savings bonds, X5 Housing status: rent, X6 Housing status: own, X7 Monthly rent, Xg Monthly mortgage payments, X9 Personal noninstallment debt, X10 Age, X11 Age squared, X12 Coefficient 0.1411 0.0251 -0.0004 -0.0051 0.0013 -0.0079 -0.0469 Notes: All financial variables are in thousands of dollars. Housing status: Rent (1 if rents: 0 otherwise). Housing status: Own (1 if owns; 0 otherwise). 0.0136 -0.7540 -0.9809 -0.0367 0.0046 -0.0001 0.1760 0.0398 Marital status, X13 (1 = married) Number of children, X14 (Number of children = X14), X15 -0.0036 Purchase plans, X16 (1= planned; 0 otherwise) 0.1760 R = 0.1336 Standard Error 0.0118 0.0004 0.0108 0.0047 0.0067 0.0937 0.0712 1.0983 0.5162 0.0326 0.0084 0.0001 0.0501 0.0358 0.0072 0.0384 Source: Janet A. Fisher, "An Analysis of Consumer Goods Expenditure." The Review of Economics and Statistics, vol. 64. no. 1, Table 1, 1962, p. 67. a. Comment generally on the fit of the equation. b. How would you interpret the coefficient of -0.0051 attached to the checking ac- counts variable? How would you rationalize the negative sign for this variable? c. What is the rationale behind introducing the age-squared and number of children- squared variables? Why is the sign negative in both cases? *"An Analysis of Consumer Goods Expenditure," The Review of Economics and Statistics, vol. 64, no. 1, 1962, pp. 64-71. Chapter 15 Qualitative Response Regression Models 583 d. Assuming values of zero for all but the income variable, find out the conditional probability of a household whose income is $20,000 purchasing a durable good. e. Estimate the conditional probability of owning durable good(s), given: X = $15,000, X3 = $3,000, X = $5,000, X6= 0, X7= 1, Xs = $500, X = $300, X100, X1135, X13= 1, X14 = 2, X16 = 0.