A car dealer believes there is a strong relationship between a trade-in vehicle’

Question

A car dealer believes there is a strong relationship between a trade-in vehicle’s mileage (or at least its odometer reading) and the price it brings at auction. That is, the predicted auction price (Pi) for car i = Pi = A + B x miles(i). The table below is an example of the kind of information the dealer has collected about several recent transactions. Suppose the dealer can access N such transactions. Formulate a model that estimates the values of parameters A and B that minimizes the sum of the absolute deviations between the predicted and the actual auction price for the vehicles (you need not solve the problem.)

Odometer (miles) for vehicle i

Auction price Pi

43,890

$12,500

37,750

13,350

27,300

14,600

15,500

15,750

8,900

17,500

A. Please define the decision variables you will need for your model. Feel free to use indices or subscripts “j” or a specific vehicle or transaction.

B. Please furnish an algebraic statement of the objective function for your model in terms of the variables defined in part A.

C. Please write out a prototype each category of constraints needed for your model, using your defined variables. Be sure to state the purpose of each constraint.

Odometer (miles) for vehicle i

Auction price Pi

43,890

$12,500

37,750

13,350

27,300

14,600

15,500

15,750

8,900

17,500

Explanation / Answer

A) decision variable are

dependent variable - Action price Pi

indeopendent variable - Odemeter for vehicle i

B) Using Excel we find out regression model .

Pi = 18286.16 - 0.13297 (miles)

Action price Pi = 18286.16 - 0.13297*Odemeter for vehicle i

This is the model for this data set .

Comment - As Odemeter for vehicle i increses 1 unit then Action price will decreses 0.13297 unit .

C)

R-squre = 0.974616

Correlation = -0.98723

Using this we conclus that the model is very good because the R -Square is very Strong.

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Best of luck :)

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