19 Refer To Car Purchase Problem 14 13 Assume That The Fitted Model Is Appropriate And That Large Sample Inferences Ar 1 (102.85 KiB) Viewed 37 times
19. Refer to Car purchase Problem 14.13. Assume that the fitted model is appropriate and that large-sample inferences are applicable. a. Obtain joint confidence intervals for the family income odds ratio exp(20β1) for families whose incomes differ by 20 thousand dollars and for the age of the oldest family automobile odds ratio exp(2β2) for families whose oldest automobiles differ in age by 2 years, with family confidence coefficient of approximately .90. Interpret your intervals. b. Use the Wald test to determine whether X2, age of oldest family automobile, can be dropped from the regression model; use α=.05. State the alternatives, decision rule, and conclusion. What is the approximate P-value of the test? c. Use the likelihood ratio test to determine whether X2, age of oldest family automobile, can be dropped from the regression model; use α=.05. State the full and reduced models, decision rule, and conclusion. What is the approximate P-value of the test? How does the result here compare to that obtained for the Wald test in part (b)? d. Use the likelihood ratio test to determine whether the following three second-order terms, the square of annual family income, the square of age of oldest automobile, and the twofactor interaction effect between annual family income and age of oldest automobile, should be added simultaneously to the regression model containing family income and age of oldest automobile as first-order terms; use α=.05. State the full and reduced models, decision rule, and conclusion. What is the approximate P-value of the test?
13. Car purchase. A marketing research firm was engaged by an automobile manufacturer to conduct a pilot study to examine the feasibility of using logistic regression for ascertaining the likelihood that a family will purchase a new car during the next year. A random sample of 33 suburban families was selected. Data on annual family income ( X1, in thousand dollars) and the current age of the oldest family automobile ( X2, in years) were obtained. A followup interview conducted 12 months later was used to determine whether the family actually purchased a new car (Y=1) or did not purchase a new car (Y=0) during the year. Multiple logistic regression model (14.41) with two predictor variables in first-order terms is assumed to be appropriate. a. Find the maximum likelihood estimates of β0,β1, and β2. State the fitted response function. b. Obtain exp(b1) and exp(b2) and interpret these numbers. c. What is the estimated probability that a family with annual income of $50 thousand and an oldest car of 3 years will purchase a new car next year?
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