# 420Hw07ans - STAT 420(10 points(due Friday October 19 by...

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STAT 420 Fall 2007 Homework #7 (10 points) (due Friday, October 19, 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/Hw7_1.csv 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. b) Is there evidence to indicate that CEO income x 1 and stock percentage x 2 interact? Use α = 0.05. c) Based on the least squares estimates of the β 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.

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> Hw7_1.dat <- read.table("http://www.stat.uiuc.edu/~stepanov/Hw7_1.csv", sep=",", header=T) > Hw7_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 > > > Hw7_1.dat\$x1x2 <- Hw7_1.dat\$x1 * Hw7_1.dat\$x2 > Hw7_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
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## This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.

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420Hw07ans - STAT 420(10 points(due Friday October 19 by...

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