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Chapter 12: Q156SE (page 810)

Question: A CEO’s impact on corporate profits. Can a corporation’s annual profit be predicted from information about the company’s CEO? Each year Forbes publishes data on company profit (in \( millions), CEO’s annual income (in \) thousands), and percentage of the company’s 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 “CEO income x1 and stock percentage x2 interact to affect company profit y.”

Short Answer

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Answer

The company profit can be modelled using the CEO’s annual income and stock percentage. Higher the CEO’s annual income, higher the company’s profit. Also, the interaction between the stock percentage of the CEO and his/her annual income denotes higher profit for the company. The CEO’s 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’s annual income and stock percentage. The higher the CEO’s annual income, the higher the company’s profit. Also, the interaction betweenthe stock percentage of the CEO and his/her annual income denotes higher profit for the company. The CEO’s 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=β0+β1x1+β2x2+β3x1x2

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

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Most popular questions from this chapter

Service workers and customer relations. A study in Industrial Marketing Management (February 2016) investigated the impact of service workers’ (e.g., waiters and waitresses) personal resources on the quality of the firm’s relationship with customers. The study focused on four types of personal resources: flexibility in dealing with customers(x1), service worker reputation(x2), empathy for the customer(x3), and service worker’s task alignment(x4). A multiple regression model was employed used to relate these four independent variables to relationship quality (y). Data were collected for n = 220 customers who had recent dealings with a service worker. (All variables were measured on a quantitative scale, based on responses to a questionnaire.)

a) Write a first-order model for E(y) as a function of the four independent variables. Refer to part

Which β coefficient measures the effect of flexibility(x1)on relationship quality (y), independently of the other

b) independent variables in the model?

c) Repeat part b for reputation(x2), empathy(x3), and task alignment(x4).

d) The researchers theorize that task alignment(x4)“moderates” the effect of each of the other x’s on relationship quality (y) — that is, the impact of eachx, x1,x2, orx3on y depends on(x4). Write an interaction model for E(y) that matches the researchers’ theory.

e) Refer to part d. What null hypothesis would you test to determine if the effect of flexibility(x1)on relationship quality (y) depends on task alignment(x4)?

f) Repeat part e for the effect of reputation(x2)and the effect of empathy(x3).

g) None of the t-tests for interaction were found to be “statistically significant”. Given these results, the researchers concluded that their theory was not supported. Do you agree?

Question: Glass as a waste encapsulant. Because glass is not subject to radiation damage, encapsulation of waste in glass is considered to be one of the most promising solutions to the problem of low-level nuclear waste in the environment. However, chemical reactions may weaken the glass. This concern led to a study undertaken jointly by the Department of Materials Science and Engineering at the University of Florida and the U.S. Department of Energy to assess the utility of glass as a waste encapsulant. Corrosive chemical solutions (called corrosion baths) were prepared and applied directly to glass samples containing one of three types of waste (TDS-3A, FE, and AL); the chemical reactions were observed over time. A few of the key variables measured were

y = Amount of silicon (in parts per million) found in solution at end of experiment. (This is both a measure of the degree of breakdown in the glass and a proxy for the amount of radioactive species released into the environment.)

x1 = Temperature (°C) of the corrosion bath

x2 = 1 if waste type TDS-3A, 0 if not

x3 = 1 if waste type FE, 0 if not

(Waste type AL is the base level.) Suppose we want to model amount y of silicon as a function of temperature (x1) and type of waste (x2, x3).

a. Write a model that proposes parallel straight-line relationships between amount of silicon and temperature, one line for each of the three waste types.

b. Add terms for the interaction between temperature and waste type to the model of part a.

c. Refer to the model of part b. For each waste type, give the slope of the line relating amount of silicon to temperature.

e. Explain how you could test for the presence of temperature–waste type interaction.

Question: Bordeaux wine sold at auction. The uncertainty of the weather during the growing season, the phenomenon that wine tastes better with age, and the fact that some vineyards produce better wines than others encourage speculation concerning the value of a case of wine produced by a certain vineyard during a certain year (or vintage). The publishers of a newsletter titled Liquid Assets: The International Guide to Fine Wine discussed a multiple regression approach to predicting the London auction price of red Bordeaux wine. The natural logarithm of the price y (in dollars) of a case containing a dozen bottles of red wine was modelled as a function of weather during growing season and age of vintage. Consider the multiple regression results for hypothetical data collected for 30 vintages (years) shown below.

  1. Conduct a t-test (atα=0.05 ) for each of the βparameters in the model. Interpret the results.
  2. When the natural log of y is used as a dependent variable, the antilogarithm of a b coefficient minus 1—that is ebi - 1—represents the percentage change in y for every 1-unit increase in the associated x-value. Use this information to interpret each of the b estimates.
  3. Interpret the values of R2and s. Do you recommend using the model for predicting Bordeaux wine prices? Explain

Consider relating E(y) to two quantitative independent variables x1 and x2.

  1. Write a first-order model for E(y).

  2. Write a complete second-order model for E(y).

Question: Tilting in online poker. In poker, making bad decisions due to negative emotions is known as tilting. A study in the Journal of Gambling Studies (March, 2014) investigated the factors that affect the severity of tilting for online poker players. A survey of 214 online poker players produced data on the dependent variable, severity of tilting (y), measured on a 30-point scale (where higher values indicate a higher severity of tilting). Two independent variables measured were poker experience (x1, measured on a 30-point scale) and perceived effect of experience on tilting (x2, measured on a 28-point scale). The researchers fit the interaction model, . The results are shown below (p-values in parentheses).

  1. Evaluate the overall adequacy of the model using α = .01.

b. The researchers hypothesize that the rate of change of severity of tilting (y) with perceived effect of experience on tilting (x2) depends on poker experience (x1). Do you agree? Test using α = .01.
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