420Hw10ans - STAT 420 (10 points) (due Friday, November 7,...

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STAT 420 Fall 2008 Homework #10 (10 points) (due Friday, November 7, by 3:00 p.m.) 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 ( x 2 ). Company Profit, y CEO Income, x 1 Stock, x 2 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 http://www.stat.uiuc.edu/~stepanov/Hw10_1.csv > Hw10_1.dat = read.table("http://www.stat.uiuc.edu/~stepanov/Hw10_1.csv", sep=",", header=T) > Hw10_1.dat Company y CEO x1 x2 1 Gap 824.5 Drexler 3743 1.71 2 Intel 6068.0 Grove 52598 0.13 3 Gateway 2000 346.4 Waitt 855 43.93 4 HJ Heinz 746.9 O’Reilly 2916 1.63 5 Conseco 630.7 Hilbert 124579 3.64 6 Citicorp 5807.0 Reed 6200 0.22 7 Cisco Systems 1362.3 Chambers 560 0.06 8 General Electric 9296.0 Welch 40626 0.03 9 America Online 254.0 Case 26917 0.54 10 Computer Associates 570.0 Wang 10614 3.79 11 Lockheed Martin 1001.0 Augustine 2533 0.01 12 Bear Stearns 538.6 Cayne 23215 3.44
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a) Fit the interaction model Y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 1 x 2 + ε Give the least squares prediction equation and determine whether the overall model is statistically useful for predicting company profit at α = 0.10. > Hw10_1.dat$x1x2 <- Hw10_1.dat$x1 * Hw10_1.dat$x2 > Hw10_1.dat Company y CEO x1 x2 x1x2 1 Gap 824.5 Drexler 3743 1.71 6400.53 2 Intel 6068.0 Grove 52598 0.13 6837.74 3 Gateway 2000 346.4 Waitt 855 43.93 37560.15 4 HJ Heinz 746.9 O’Reilly 2916 1.63 4753.08 5 Conseco 630.7 Hilbert 124579 3.64 453467.56 6 Citicorp 5807.0 Reed 6200 0.22 1364.00 7 Cisco Systems 1362.3 Chambers 560 0.06 33.60 8 General Electric 9296.0 Welch 40626 0.03 1218.78 9 America Online 254.0 Case 26917 0.54 14535.18 10 Computer Associates 570.0 Wang 10614 3.79 40227.06 11 Lockheed Martin 1001.0 Augustine 2533 0.01 25.33 12 Bear Stearns 538.6 Cayne 23215 3.44 79859.60 > > Hw10_1.fit <-lm(y ~ x1 + x2 + x1x2, data=Hw10_1.dat)
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420Hw10ans - STAT 420 (10 points) (due Friday, November 7,...

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