To encourage performance, loyalty, and continuing education, the human resources department at a large company wants to develop a regression-based compensation model for mid-level managers based on three variables: (1) business unitprofitability, (2) years with company, and (3) graduate degree in relevant field. The accompanying table shows a portion of data collected for 36 managers.

a. Estimate the following model for compensation: y = β0 + β1 Profit + β2 Years + β3 Grad + β4 Profit × Years + β5 Profit × Grad + β6 Years × Grad + ε.
b. At the 5% significance level, is the overall regression model significant?
c. Which predictor variables and interaction terms are significant at α = 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.

Business-Unit Profit Graduate Years with Degree? Compensation S/year) (000/year) Company (1-yes, 0-no) 118,100 4,500 5,400 0,00 5 85,000 4,200 29