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 = Year's 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

Classification Table Predicted did buyer purchase extended warranty Percentage Observed No Yes Correct Step 1 did buyer purchase No 479 38 92.6 extended warranty Yes 110 73 39.9 Overall Percentage 78.9 a. The cut value is .500Model Summary -2 Log Cox & Snell R Nagelkerke R Step likelihood Square Square 616.263" 236 .345 a. Estimation terminated at iteration number 6 because parameter estimates changed by less than .001,Omnibus Tests of Model Coefficients Chi-square df Sig. Step 1 Step 188.101 000 Block 188.101 000 Model 188.101 000Variables in the Equation B S.E. Wald Sig Exp(B) Step 1" buyer_age 019 016 1.398 .237 1.020 buyer_education -.058 .117 .245 .621 .944 years_address -.086 021 17 001 000 .918 buyer_income -.003 005 -405 525 .997 car_value 000 000 69.004 000 .999 cred_score .019 002 78.027 000 1.019 Constant -9.104 1.263 51.953 .000 .000 a. Variable (s) entered on step 1: buyer_age, buyer_education, years_address, buyer_income, car_value, cred_score