Homework answers / question archive / Case Study: What Determines the Re-sale Value of a Car?    When car dealers lease a car, how do they decide what to charge?  One answer, if you’ve got a lot of unpopular cars to move, is to charge whatever it takes to get the cars off the lot

Case Study: What Determines the Re-sale Value of a Car?    When car dealers lease a car, how do they decide what to charge?  One answer, if you’ve got a lot of unpopular cars to move, is to charge whatever it takes to get the cars off the lot

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Case Study: What Determines the Re-sale Value of a Car? 

 

When car dealers lease a car, how do they decide what to charge?  One answer, if you’ve got a lot of unpopular cars to move, is to charge whatever it takes to get the cars off the lot.  Another answer considers the so-called residual value of a car at the end of the lease.  The residual value of a leased car is the value of this car in the used-car market, or re-sale value.

Certified BMW would like you to help them estimate the re-sale value of a car, and they have provided you with a sample of 202 BMWs that have been sold by BMW dealers within a 50 mile radius of Philadelphia.  They are limiting their attention to two particular models, the BMW 325 and 330 models. 

What else determines the re-sale value?  Certified BMW is providing you with the following variables:

• Model: The two BMW models are the 325 (coded = 0) and the 330 (coded = 1) series
• Age:  Age of the car in years (0 indicates a new car)
• Mileage:  Number of miles on the odometer when it is on the resale market
• Price: Resale price in dollars
• Style: Convertible or not a convertible
• Transmission Type:  Whether the car has a manual (stick shift) or automatic transmission
• Color: Color of the car (Alpine White, Electric Red, Black Metallic/Jet, Blue Metallic, Silver/Gray Metallic)

 

This dataset is found on Moodle in the posted Excel file.  To successfully fulfill your contract you need to provide them with detailed statistical analysis and communicate your results clearly in the form of written reports.  For the latter, you need to be able to address potential clients who are not statisticians. 

 

 

PLEASE READ THE INSTRUCTIONS CAREFULLY BEFORE YOU BEGIN.

Written reports are required for all parts of the case.  Please use a typical memorandum format.  Please start each memorandum with an appropriate introduction and end with a brief conclusion. I suggest you answer each question (including its sub-parts) in separate paragraphs with the appropriate Excel output as appendices. The memos need to be more detailed than a typical executive summary.  Please use bullets sparingly! 

You may use single spacing, but please provide ample margins for my comments, and use either 11 or 12 pt. font.

Please DO NOT mention the numbering I have used below in your memo.  The numbering is only provided so that we can easily converse about a question you might have.

 

PART III: INFERENTIAL STATISTICS (2-3 page memorandum in Word)

For each of the following questions, please append your graphs/charts/results from Excel to your third memorandum.  Please remember to provide context for this part of the case with an introduction and conclusion.

3. a. Certified BMW thinks that the average price of all Model 330 cars is greater than $32,000. 

Based on the sample data, is there evidence at the 5% level of significance that the average price of all Model 330 cars is greater than $32,000?  Please do not use the terminology of the “null hypothesis” in your memorandum.  Explain your test in words for management.

2. Clarify to Certified BMW which type of error (Type I or Type II) you might have made in your answer to 7(a).  Please do not use the term “Type I” or “Type II” in your memo.  Rather, explain in plain English what type of error you might have made without using jargon.
3. Moving beyond the concept of a point estimate, please provide an improved estimate of the average price of the Model 330 cars and explain why it is preferable to a point estimate. Here again, you need not use the term “point estimate” in your memo. 

 

4. Certified BMW would like you to further analyze your results from #5.
   1. Set up and test the hypothesis of whether the multiple regression model as a whole is significant. What is your conclusion at the 0.05 level of significance?
   2. Test at the .05 level of significance to determine if there is an inverse relationship between price and mileage.
   3. Test to determine if price is significantly different for the two types of BMW models. What is your conclusion at the 5% level of significance? 
   4. Are convertibles priced significantly higher than other cars?  What is your conclusion at the 5% level of significance?
   5. Do BMWs with manual transmissions (stick shift) sell for more or less than other cars?  What is your conclusion at the 5% level of significance?
   6. Use the regression equation to predict price for the first observation in the data set and calculate the residual.
   7. Do you think that this regression model does a good job of predicting price? Why or why not?     
   8. Should Certified BMW be concerned about multicollinearity in this equation?  Why or why not? If multicollinearity is a problem, how would you address it in this estimation?

 

5. a. Which estimate do you recommend Certified BMW use in estimating price in the future: the one in question 1, the simple regression model’s estimate in question 4, or the estimate based on the multiple regression in question 5?  Justify your answer using the statistical results. 

b.   Certified BMW thinks you can get a better estimate by adding additional independent variables to the equation.  What criteria (not specific variables) would you suggest that they use to determine if a variable should be included?  Propose at least one additional variable for this model that meets these criteria.

3. What statistical concern(s), if any, would you have in implementing your recommendation in this analysis?  Please explain your concern(s).