Consider the multiple regression results shown in Table 12.5.10, which attempt to explain compensation of the top executives of 11 major energy corporations based on the revenues and the return on equity of the firms.35 For example, the data for Consol Energy, Inc. consist of a compensation number of 13.75 (in millions of dollars) for the CEO J. Brett Harvey, an ROE number of 16.42% (which is the same number as 0.1642), and a revenue number of 4,570 (in millions of dollars).
a. To within approximately how many dollars can you predict the compensation of the CEO of these firms based on revenue and ROE?
b.* Find the predicted compensation and the residual prediction error for the CEO of Consol Energy, Inc., expressing both quantities in dollars.
c. If ROE is interpreted as an indicator of the firm€™s performance, is there a significant link between performance and compensation (adjusting for firm sales)? How do you know?
d. Is there a significant link between revenue and compensation (adjusting for firm ROE)? How do you know?
e. What exactly does the regression coefficient 0.002309 for revenue tell you?

TABLE 12.5.10 Multiple Regression Results for Executive Compensation e regression equation is Compensation 0.908811 +0.002309Revenue 0.116328 ROE S# 4.6101 R 0.5201 F 4.3351 with 2 and 8 degrees of freedonm P 0.0530 Th Effect on Compensation Coeff StdErr 95% Confidence Interval of Coeff StdErr 2.4616 0.0008 1.6268 t statis tic p-Value Variable Constant Revenue ROE From 0 0.908811 0.002309 -0.116328 0.722 0.025 0.945 -4.7675 6.5852 0.0042 3.6351 0.3692 2.7434 -0.0715 0.0004 -3.8677