The board of directors at a large corporation wants to base their division managers' pay raises on the profit performance of their respective divisions. They have asked you to evaluate the performance and raises at other companies and propose a formula for calculating the percentage increase in base pay based on the percentage change in the division's profit.You collected information from 50 divisions at similar companies and performed a linear regression on the percentage change in the division profits vs. the percentage change in the manager's salary.

Increase in profits

(%)

Increase in Manager's Salary (%)

Increase in profits

(%)

Increase in Manager's Salary (%) 1 -1.572 0.62 26 1.061 2.90 2 -0.557 1.82 27 1.076 3.22 3 0.066 2.11 28 1.478 2.96 4 0.367 2.40 29 1.874 4.50 5 0.458 1.85 30 2.845 4.37 6 0.832 3.72 31 2.878 5.13 7 2.011 4.77 32 3.041 5.52 8 2.102 3.79 33 3.340 6.22 9 2.400 4.21 34 4.395 6.17 10 2.486 3.70 35 4.645 6.83 11 2.851 5.63 36 4.887 6.50 12 2.880 5.41 37 5.102 7.48 13 3.086 4.62 38 -2.668 0.35 14 3.162 5.15 39 -2.668 -0.38 15 3.594 6.70 40 -1.863 -0.56 16 4.645 6.83 41 -0.557 2.79 17 -2.014 0.35 42 0.053 1.66 18 -2.014 1.32 43 0.066 2.90 19 -1.252 0.62 44 0.079 2.41 20 -1.195 1.66 45 1.061 3.46 21 -0.560 1.48 46 2.486 4.21 22 -0.557 1.15 47 2.775 4.50 23 0.148 3.22 48 2.845 5.13 24 0.832 3.58 49 2.883 5.41 25 0.991 3.07 50 2.883 4.93

What is the regression equation from the Summary Output? Is this a useful model? How do you know?

Are the assumptions of regression satisfied? How did you verify them?

Does change in division profit appear to be a good predictor for the manager's pay raise? Why do you think that?

One of your company's divisions had a -0.51 percent change in profits last year, while another had a 20 percent increase. What is the predicted percentage change in salary for these two division managers?