Log out Go to App
Go to App

Learning Materials

Features

Discover

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

Expert verified

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Impact of race on football card values. University of Colorado sociologists investigated the impact of race on the value of professional football players’ “rookie” cards (Electronic Journal of Sociology, 2007). The sample consisted of 148 rookie cards of National Football League (NFL) players who were inducted into the Football Hall of Fame. The price of the card (in dollars) was modeled as a function of several qualitative independent variables: race of player (black or white), card availability (high or low), and player position (quarterback, running back, wide receiver, tight end, defensive lineman, linebacker, defensive back, or offensive lineman).

  1. Create the appropriate dummy variables for each of the qualitative independent variables.
  2. Write a model for price (y) as a function of race. Interpret theβ’s in the model.
  3. Write a model for price (y) as a function of card availability. Interpret theβ’s in the model.
  4. Write a model for price (y) as a function of position. Interpret theβ’s in the model.

Question: Women in top management. Refer to the Journal of Organizational Culture, Communications and Conflict (July 2007) study on women in upper management positions at U.S. firms, Exercise 11.73 (p. 679). Monthly data (n = 252 months) were collected for several variables in an attempt to model the number of females in managerial positions (y). The independent variables included the number of females with a college degree (x1), the number of female high school graduates with no college degree (x2), the number of males in managerial positions (x3), the number of males with a college degree (x4), and the number of male high school graduates with no college degree (x5). The correlations provided in Exercise 11.67 are given in each part. Determine which of the correlations results in a potential multicollinearity problem for the regression analysis.

  1. The correlation relating number of females in managerial positions and number of females with a college degree: r =0.983.

  2. The correlation relating number of females in managerial positions and number of female high school graduates with no college degree: r =0.074.

  3. The correlation relating number of males in managerial positions and number of males with a college degree: r =0.722.

  4. The correlation relating number of males in managerial positions and number of male high school graduates with no college degree: r =0.528.

The Minitab printout below was obtained from fitting the modely=β0+β1x1+β2x2+β3x1x2+εto n = 15 data points.

a) What is the prediction equation?

b) Give an estimate of the slope of the line relating y to x1 when x2 =10 .

c) Plot the prediction equation for the case when x2 =1 . Do this twice more on the same graph for the cases when x2 =3 and x2 =5 .

d) Explain what it means to say that x1and x2interact. Explain why your graph of part c suggests that x1and x2interact.

e) Specify the null and alternative hypotheses you would use to test whetherx1andx2interact.

f)Conduct the hypothesis test of part e using α=0.01.

Suppose you used Minitab to fit the model y=β0+β1x1+β2x2+ε

to n = 15 data points and obtained the printout shown below.

  1. What is the least squares prediction equation?

  2. Find R2and interpret its value.

  3. Is there sufficient evidence to indicate that the model is useful for predicting y? Conduct an F-test using α = .05.

  4. Test the null hypothesis H0: β1= 0 against the alternative hypothesis Ha: β1≠ 0. Test using α = .05. Draw the appropriate conclusions.

  5. Find the standard deviation of the regression model and interpret it.

Assertiveness and leadership. Management professors at Columbia University examined the relationship between assertiveness and leadership (Journal of Personality and Social Psychology, February 2007). The sample represented 388 people enrolled in a full-time MBA program. Based on answers to a questionnaire, the researchers measured two variables for each subject: assertiveness score (x) and leadership ability score (y). A quadratic regression model was fit to the data, with the following results:

a. Conduct a test of overall model utility. Useα=0.05 .

b. The researchers hypothesized that leadership ability increases at a decreasing rate with assertiveness. Set up the null and alternative hypotheses to test this theory.

  1. Use the reported results to conduct the test, part b. Give your conclusion(atα=0.05 )in the words of the problem.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free