Homework answers / question archive / Case Study: What Determines the Re-sale Value of a Car? [1]     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? [1]     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? [1]

 

 

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. 

The due dates for each part of the case are given in the syllabus. You may work with other students in determining how to approach a question or solve Excel problems

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 II: BIVARIATE STATISTICAL ANALYSIS - (2 page memorandum in Word)

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

3. Certified BMW thinks that price may at least partially be explained by the quantitative variables.
   1. What is the strength of the linear relationship between price and the age of the car?

            Explain how you made this determination and interpret the appropriate statistic.

b. Which quantitative variable has the strongest linear relationship with price?  Justify your answer based on the appropriate statistic.

    

4. Provide Certified BMW with a simple regression model to estimate price using the quantitative variable from 3(b).

a. Show graphically the linear relationship between price and the quantitative variable from 3(b).

b. Estimate the regression equation based on the graph in 4(a).

2. State the estimated equation (in the appendix) and interpret each of the coefficients (in the memorandum).
3. What percentage of the variation in price has been explained by your model?
4. Use this model to predict the price for the first observation in the data set.
5. Suppose Certified BMW has a new observation with identical values as in the first observation, except that price is now $36,000. Based on the results of the linear model, would you view this amount as reasonable or unreasonable?  Why or why not?

 

5. Certified BMW thinks the following variables should be included when explaining price: (1) age, (2) mileage, (3) transmission type, (4) model type, and (5) whether the car is a convertible or not.

a.  Based on theory or your intuition, what type of relationship do you expect between the dependent variable and each of the independent variables?

b.  Using Excel, estimate the multiple regression equation for price based on these 5 independent variables.  (You do NOT need to put the equation in the memorandum.)

c. Do the signs of the coefficients in the estimated equation match your expectation in 5(a)?  Please explain.

d. Interpret each of the regression coefficients for Certified BMW.

6. Certified BMW is concerned about making business decisions based on sample data. They would like to know whether it is reasonable to estimate price based on this sample data.  Please respond to their concern and explain briefly an appropriate sampling procedure.