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Chapter 12: Q156SE (page 810)

Question: A CEO鈥檚 impact on corporate profits. Can a corporation鈥檚 annual profit be predicted from information about the company鈥檚 CEO? Each year Forbes publishes data on company profit (in \( millions), CEO鈥檚 annual income (in \) thousands), and percentage of the company鈥檚 stock owned by the CEO. Consider a model relating company profit (y) to CEO income (x1) and stock percentage (x2). Explain what it means to say that 鈥淐EO income x1 and stock percentage x2 interact to affect company profit y.鈥�

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Answer

The company profit can be modelled using the CEO鈥檚 annual income and stock percentage. Higher the CEO鈥檚 annual income, higher the company鈥檚 profit. Also, the interaction between the stock percentage of the CEO and his/her annual income denotes higher profit for the company. The CEO鈥檚 annual income is determined by the percentage of stocks in his possession. To evaluate the value, the variables, interact in the model.

Step by step solution

01

Model for company profit

The company profit can be modelled using the CEO鈥檚 annual income and stock percentage. The higher the CEO鈥檚 annual income, the higher the company鈥檚 profit. Also, the interaction betweenthe stock percentage of the CEO and his/her annual income denotes higher profit for the company. The CEO鈥檚 annual income is determined by the percentage of stocks in his possession. To evaluate the value, the variables, interact in the model.

02

Mathematical equation 

Mathematically, the equation for company profit (y) can be written as

Ey=尾0+尾1x1+尾2x2+尾3x1x2

Where, x1 = CEO income and x2 = stock percentage.

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Ey=尾0+尾1x1+尾2x2+尾3x3+尾4x4+尾5x5

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e) One theory posits that blond solicitors will achieve the highest mean contribution level, but that there will be no difference between the mean contribution levels attained by brunette Caucasian and minority females. If this theory is true, give the expected signs of the鈥檚 in the model.

f) The researcher found the b estimate for the dummy variable for blond Caucasian to be positive and significantly different from 0 (p-value < 0.01). The尾estimate for the dummy variable for brunette Caucasian was also positive, but not significantly different from 0 (p-value < 0.10). Do these results support the theory, part e?
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