Relationships Between Data - Introduction to Linear Regression Simple Regression Notes
If you need guidance in terms of using Excel to run regressions, check pages 1 - 10 of the Excel - Linear Regression Tutorial posted to this folder of BlackBoard.
Do the following problems. Hand in a hard copy of your solutions at the next class session.
1) 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.
|
Odometer Reading
|
Trade-in Value
|
|
Car
|
(1,000 miles)
|
($100s)
|
|
1
|
59
|
37
|
|
2
|
92
|
31
|
|
3
|
61
|
43
|
|
4
|
72
|
39
|
|
5
|
52
|
41
|
|
6
|
67
|
39
|
|
7
|
88
|
37
|
|
8
|
62
|
40
|
|
9
|
95
|
29
|
|
10
|
83
|
33
|
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 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?
2) Consider the Beta Technologies data from last week's assignment. Run a regression using Excel with Annual Salary as the dependent (Y) variable and Beta Experience as the independent (X) variable. Now run a second regression model with Annual Salary as the dependent (Y) variable and Prior Experience as the independent (X) variable.
Which model do you think is better for predicting Annual Salary? Provide as much support for your response as possible. How good is the better model?