Forbes (May 1999) presented data on Company profit (y; in million dollars), Chief executive officer's (CEO) annual income (x1; in thousand dollars), and Percentage of the company's stock owned by the CEO (x2). For 12 major companies, we wish to build a regression model that will allow us to predict the company profit from the remaining two variables. Note that the CEO's annual income and the percentage of the company's stock owned by the CEO will not be "independent". We need to build a model that contains an interaction term of these two variables.
Obs
Company Gap Intel Gateway 2000 HJ Heinz Conseco Citicorp Cisco Systems General Electric America Online Computer Associate Lockheed Martin Bear Stearns
824.5 6068.0 346.4 746.9 630.7 5807.0 1362.3 9296.0 254.0 570.0 1001.0 538.6
3743 52598 855 2916 124579 6200 560 40626 26917 10614 2533 23215
1.71 0.13 43.93 1.63 3.64 0.22 0.06 0.03 0.54 3.79 0.01 3.44
a) What does it mean to say that CEO's annual income and percentage of company's stock owned by the CEO interact?
b) Propose an appropriate interaction model that will allow us to predict the company profit:
c) With an alpha level of .05, is the contribution of the interaction term significant in the model? Explain.
d) Predict the profit for a company whose CEO earns $10,000,000 and owns 2% of the company's stock:
e) Predict the profit for a company whose CEO earns $10,000,000 and owns x% of the company's stock: How does this compare to part (d)?
Find the residual value for America Online.