4-13: Students in a management science class have just recd their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follows:

Student 1 2 3 4 5 6 7 8 9

1st test grade 98 77 88 80 96 61 66 95 69

Final avg. 93 78 84 73 84 64 64 95 76

a). develop a regression model that could be used to predict the final average in the course based on the first test grade.

b). predict the final avg. of a student who made an 83 on the first test

c). give the values of r and r(squared) for this model. Interpret the value of r (squared) in the context of this problem.

4-15: Using computer software, find the least squares regression line for the data in problem 4-13. Based on the F test, is there a statistically significant relationship between the first test grade and the final average in the course?

4-17: Accountants at the firm Walker and Walker believed that several traveling executives submit unusually high travel vouchers when they return from business trips. The accountants took a sample of 200 vouchers submitted from the past year; then they developed the following multiple regression equation relating expected travel cost (Y) to number of days on the road (X 1) and distance traveled (X 2) in miles:

^Y= $90.00 + $48.50X 1 + $0.40X 2

4-27: A sample of 20 automobiles was taken, and the miles per gallon (MPG), horsepower, and total weights were recorded. Develop a linear regression model to predict MPG, using horsepower as the only independent variable. Develop another model with weight as the independent variable. Which of these two models is better? Explain.

MPG Horsepower Weight

44 67 1,844

44 50 1,998

40 62 1,752

37 69 1,980

37 66 1,797

34 63 2,199

35 90 2,404

32 99 2,611

30 63 3,236

28 91 2,606

26 94 2,580

26 88 2,507

4-28: Use the data in problem 4-27 to develop a multiple linear regression model. How does this compare with each of the models in problem 4-27?