Q 28

Question 28

Instructions: Read the problem and examine the SPSS output. Then answer the question briefly but completely.

3. Automobile dealers stand to profit handsomely from extended warranties offered on the used vehicles they sell. Extended warranties may offer ten years or 100,000 miles on all automobile systems. For purposes of pricing and warranty design, a warranty company wanted to see what variables predicted whether car buyers purchased an extended warranty. They estimated a logistic regression model on late model used cars with less than 50,000 miles based on the following buyer information:

Y = Did the car purchaser also buy an extended warranty?

X1 = Age of the car buyer

X2 = Education level of the buyer

X3 = Years buyer lived at current address

X4 = Buyer annual income

X5 = Selling price of the car

X6 = Buyer credit score

The results of the initial logistic regression model estimation follow. Based on this output, answer the following questions.

A) Summarize the results of the analysis. How well did the model perform? What predictors proved to be statistically significant? Which ones best predict the odds of purchasing an extended warranty?

B) Explain the odds ratios for the statistically significant variables. How would a one unit increase in the value of these variables change the odds of purchasing a warranty? Do odds ratios so close to 1.0 mean the model is ineffective?

C) From a marketing perspective, what would you propose that the warranty company do to better market its product? What options should the company consider? Refer to specific features of the output to make your recommendations.

D) What other information would like to see included in the model if you had the information at your disposal? Why?

Omnibus Tests of Model Coefficients df Step 1 Step Block Model Chi-square 188.101 188.101 188.101 6 6 6 Sig. .000 .000 .000 Model Summary -2 Log Cox & Snell R Nagelkerke R Step likelihood Square Square 1 616.263 .236 .345 a. Estimation terminated at iteration number 6 because parameter estimates changed by less than 001. Classification Table Predicted did buyer purchase extended warranty No Yes Observed Step 1 did buyer purchase extended warranty Overall Percentage a. The cut value is 500 No Yes 479 110 38 73 Percentage Correct 92.6 39.9 78.9 Variables in the Equation B S.E. Wald dr Sig Exp(8) Step 1 buyer_age .019 .016 1.398 1 .237 1.020 buyer_education -.058 .117 .245 1 .621 .944 years_address - 086 .021 17.001 1 .000 918 buyer_income -.003 .005 .405 1 .525 .997 car_value .000 .000 69.004 1 .000 .999 cred_score ,019 .002 78.027 1 ,000 1.019 Constant -9.104 1.263 51.953 1 .000 .000 a. Variable(s) entered on step 1: buyer_age, buyer_education, years_address, buyer_income, car_value, cred_score Omnibus Tests of Model Coefficients df Step 1 Step Block Model Chi-square 188.101 188.101 188.101 6 6 6 Sig. .000 .000 .000 Model Summary -2 Log Cox & Snell R Nagelkerke R Step likelihood Square Square 1 616.263 .236 .345 a. Estimation terminated at iteration number 6 because parameter estimates changed by less than 001. Classification Table Predicted did buyer purchase extended warranty No Yes Observed Step 1 did buyer purchase extended warranty Overall Percentage a. The cut value is 500 No Yes 479 110 38 73 Percentage Correct 92.6 39.9 78.9 Variables in the Equation B S.E. Wald dr Sig Exp(8) Step 1 buyer_age .019 .016 1.398 1 .237 1.020 buyer_education -.058 .117 .245 1 .621 .944 years_address - 086 .021 17.001 1 .000 918 buyer_income -.003 .005 .405 1 .525 .997 car_value .000 .000 69.004 1 .000 .999 cred_score ,019 .002 78.027 1 ,000 1.019 Constant -9.104 1.263 51.953 1 .000 .000 a. Variable(s) entered on step 1: buyer_age, buyer_education, years_address, buyer_income, car_value, cred_score