Can a corporation's annual profit be predicted from information about the company's CEO? Forbes (May 1999) presented data (shown in TABLE 2) on company profit (y) in (millions of dollars), CEO's annual income (x1) (in thousands of dollars) and percentage of the company's stock owned by the CEO (x2). Use the data in the TABLE below and answer the following questions.
(a) Fit a multiple regression model of y on x1 and x2. Fit two simple linear regressions: (I) y on x1; (II) y on x2. Compare the results of multiple regression analysis with each of simple linear regressions.
Rank the models in terms of usefulness and briefly comment on their performance. Use all of the tests and measures of usefulness discussed in class.
(b) Do you detect any signs of multicollinearity?
(c) Use the printout to test the following hypotheses using a significance level of 5%: (I) increasing the CEO's annual income (other things constant) will increase the company profit; (II) increasing the percentage of company stock owned by the CEO will increase the company profit.
TABLE: Company profit (y), CEO's annual income (x1), and the company stock owned by the CEO (x2)
|
Company
|
Profit (y)
|
CEO's income (x1)
|
% of the company stock owned by the CEO (x2)
|
|
Gap
|
824.5
|
3743
|
1.71
|
|
Intel
|
6068.0
|
52598
|
.13
|
|
Gateway 2000
|
346.4
|
855
|
43.93
|
|
HJ Heinz
|
746.9
|
2916
|
1.63
|
|
Conseco
|
630.7
|
124579
|
3.64
|
|
Citicorp
|
5807.0
|
6200
|
.22
|
|
Cisco Systems
|
1362.3
|
560
|
.06
|
|
General Electric
|
9296.0
|
40626
|
.03
|
|
America Online
|
254.0
|
26917
|
.54
|
|
Computer Associates
|
570.0
|
10614
|
3.79
|
|
Lockheed Martin
|
1001.0
|
2533
|
.01
|
|
Bear Stearns
|
538.6
|
23215
|
3.44
|