Compensation. To encourage performance, loyalty, and continuing education, the human resources department at a large company wants to develop a regression-based compensation model (Comp in $ per year) for midlevel managers based on three variables: (1) business-unit profitability (Profit in $1000s per year), (2) years with the company (Years), and (3) whether or not the manager has a graduate degree (Grad equals 1 if graduate degree, 0 otherwise). The accompanying table shows a portion of data collected for 36 managers

a. Estimate the following model for compensation: Comp = 0 + 1Profit + 2Years + 3Grad + 4(Profit Grad) + 5(Years Grad) + .

b. At the 5% significance level, is the overall regression model significant?

c. Which predictor variables and interaction terms are significant at = 0.05?

d. Use the (full) model to determine compensation for a manager having 15 years with the company, a graduate degree, and a business-unit profit of $4,800(000) last year

Grad 1 1 0 1 1 0 1 1 0 1 Comp 118100 90800 79000 115700 97100 51600 88400 107600 75100 60500 69800 69300 127400 82200 123300 50800 60500 71100 50100 87600 68300 90700 81600 68200 80600 69500 97200 193600 75900 78500 88100 99500 87700 63000 93200 85000 1 0 1 Profit 4500 5400 3600 5800 4200 3500 2200 3500 4500 2500 2200 3000 5200 5600 4700 4100 2200 4500 2300 4400 2600 5700 5600 3800 4900 2600 5800 5200 2400 3100 2100 4900 5000 3400 4600 4200 Years 37 5 28 3 11 10 27 22 23 4 5 8 33 14 19 7 33 23 20 20 9 18 26 22 24 3 30 32 11 0 ||0|1|11 0 0 0 0 1 1 0 28 17 31 12 23 20 29 ||0|1|11|11|110 0 0