Forbes magazine's "Executive Compensation Scoreboard." Forbes (April 13, 2011) determined which CEOs are worth their pay based on a comparison of the firm's stock performance and the CEO's annual salary. Data for 175 of the top performers are saved in the file. Some of the variables measured for each CEO include pay-for-performance efficiency rating (x1), value of shares owned (x2), age (x3), and the CEO's average salary over the past 5 years (y). (Recall that the lower the efficiency rating, the more the CEO is worth his/her pay.) Consider the first-order model E(y) = β0 + β1x1 + β2x2 + β3x3.
a. Fit the model to the data and give the least squares prediction equation.
b. Conduct a test of overall model adequacy using α = .05.
c. Predict, with 95% confidence, the 5-year pay of a CEO with x1 = 173, x2 = $102.9 million, and x3 = 59 years.