Question: Car dealers across North America use the “Red Book” to help them determine the value of used cars that their customers trade in when purchasing new cars. The book, which is published monthly, lists average trade-in values for all basic models of North American, Japanese and European cars. These averages are determined on the basis of the amounts paid at recent used-car auctions. The book indicates alternative values of each car model according to its condition and optional features, but it does not inform dealers how the odometer reading affects the trade in value.

In an experiment to determine whether the odometer reading should be included in the Red Book, an interested buyer of used cars randomly selects ten 3-year-old cars of the same make, condition, and optional features. The trade-in value and mileage for each car are shown in the accompanying table.

Run the appropriate regression model using Excel with Trade-in Value as the dependent variable (Y) and Odometer Reading as the independent variable (X). (Note you can copy and paste this table of data into Excel.)

Answer the following questions:

a. According to the regression equation, what’s the incremental change in automobile trade-in value for an increase of 1000 miles on the odometer?

b. Can we conclude that the coefficient \[{{\beta }_{1}}\] is significant – that is, different than zero?

c. Predict with 95% confidence the trade-in value of such a car that has been driven 60,000 miles.

d. What percentage of the variation in trade-in value is “explained” by the odometer reading?