Chapter 14, Problem 66CR

Much interest in management circles has focused on how employee compensation is related to various company characteristics. The article “Determinants of R and D Compensation Strategies” (Personnel Psychology [1984]: 635–650) proposed a quantitative scale for y = Base salary for employees of high-tech companies. The following estimated multiple regression equation was then presented:

$\hat{y}=2.60+0.125x_1+0.893x_2+0.057x_3-0.014x_4$

where x₁, = Sales volume (in millions of dollars), x₂ = Stage in product life cycles (1 = growth, 0 = mature), x₃ = Profitability (%), and x₄ = Attrition rate (%).

1. a. There were n = 33 firms in the sample and R² = 0.69. Is the fitted model useful?
2. b. Predict base compensation for a growth stage firm with sales volume $50 million, profitability 8%, and attrition rate 12%.
3. c. The estimated standard deviations for the coefficient estimates were 0.064, 0.141, 0.014, and 0.005 for $b_1,b_2,b_3$, and b₄ respectively. Should any of the predictors be deleted from the model? Explain.
4. d. β₂ is the difference between average base compensation for growth stage and mature stage firms when all other predictors are held fixed. Use the information in Part (c) to calculate a 95% confidence interval for β₂.