1. Can a corporation's annual profit be predicted from information about the company's chief executive officer (CEO)? Forbes (May, 1999) presented data on company profit (y ), (in $ millions), CEO's annual income (x 1 ) (in $ thousands), and percentage of the company's stock owned by the CEO (x2). Company Profit, y CEO Income, X 1 Stock, X2 Gap 824.5 Drexler 3,743 1.71% Intel 6,068.0 Grove 52,598 13 Gateway 2000 346.4 Waitt 855 43.93 HJ Heinz 746.9 O'Reilly 2,916 1.63 Conseco 630.7 Hilbert 124,579 3.64 Citicorp 5,807.0 Reed 6,200 22 Cisco Systems 1,362.3 Chambers 560 .06 General Electric 9,296.0 Welch 40,626 .03 America Online 254.0 Case 26,917 54 Computer Associates 570.0 Wang 10,614 3.79 Lockheed Martin 1,001.0 Augustine 2,533 .01 Bear Stearns 538.6 Cayne 23,215 3.44 Source: "Compensation Fit for a King," Forbes, May 1999. The data are stored in https:/etfiles.uiuc.edu/stepanov/www/Hw09_1.csv a) Fit the interaction model Y = Bo + B1 x1 + B2x2+ B3X 1 X2+ & Give the least squares prediction equation and determine whether the overall model is statistically useful for predicting company profit at a = 0.10. b) Is there evidence to indicate that CEO income x ] and stock percentage X2 interact? Use a = 0.05. C) Based on the least squares estimates of the P parameters, give the estimate of the change in profit for every one thousand dollar increase in a CEO's income when CEO owns 2% of the company's stock