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Chapter 11: Q11E (page 649)

Best-paid CEOs. Refer to Glassdoor Economic Research firm’s 2015 ranking of the 40 best-paid CEOs in Table 2.1 (p. 65). Recall that data were collected on a CEO’s age and ratio of salary to a typical worker’s pay at the firm. One objective is to predict the ratio of salary to worker pay based on the CEO’s age.

a. In this study, identify the dependent and independent variables.

b. Explain why a probabilistic model is more appropriate than a deterministic model.

c. Write the equation of the straight-line, probabilistic model.

Short Answer

Expert verified
  1. The dependent variable is the ratio of the CEO’s salary, and the independent variable is the CEO’s age.
  2. There might be some unexpected variances in the dependent variable owing to factors other than the independent variable.
  3. y=β0+β1x+ε.

Step by step solution

01

Introduction

The variable that is tested and quantified in an experiment is called the dependent variable. It depends on the independent variable.

The independent variable is the one that the researcher manipulates or modifies. This variable is supposed to have a direct influence on the dependent variable.

02

Determining which variables are dependent and which are independent

The variable of interest to the researcher is the dependent variable. Therefore, the dependent variable is the ratio of the CEO’s salary.

The independent variable is one that is thought to influence the dependent variable.Therefore; an independent variable is the CEO’s age.

03

Explaining why a probabilistic rather than a deterministic model is more appropriate 

The theory of probability, or the concept that randomness plays a role in forecasting future occurrences, is the foundation of a probabilistic technique or model. A deterministic model, on the other hand, is the polar opposite of a random model. It indicates that something can be anticipated precisely without the addition of randomness.

There are no random components in a deterministic model. The same results are received every time the model is used with identical beginning circumstances. Randomness is present in a probabilistic model. Even with identical beginning circumstances, the model is likely to provide different outcomes each time it is run. A probabilistic model is one that integrates random variation in some way.

We conduct a risk analysis as the CEO's age and salary ratio are unknown. Quantifying that uncertainty with a range of potential values and associated probabilities (i.e., with probability distributions) makes the risks more understandable to everyone. Therefore, there might be some unexpected variance in the dependent variable owing to factors other than the independent variable.

04

Writing the equation for the probabilistic straight-line model

The equation for the probabilistic straight-line model is

y=β0+β1x+ε

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Most popular questions from this chapter

Time in bankruptcy. Financially distressed firms can gain protection from their creditors while they restructure by filing for protection under U.S. Bankruptcy Codes. In a prepackaged bankruptcy, a firm negotiates a reorganization plan with its creditors prior to filing for bankruptcy. This can result in a much quicker exit from bankruptcy than traditional bankruptcy filings. A study of 49 prepackaged bankruptcies was published in Financial Management (Spring 1995). For each firm, information was collected on the time (in months) in bankruptcy as well as the results of the board of directors’ vote on the type of reorganization plan. Three types of plans were studied: “Joint”—a joint exchange offer with prepackaged bankruptcy solicitation; “Prepack”—prepackaged bankruptcy solicitation only; and “None”—no pre-filing vote held. The data for the 49 firms is provided in the accompanying table

a. Construct a stem-and-leaf display for the length of time in bankruptcy for all 49 companies.

b. Summarize the information reflected in the stem-and-leaf display from part a. Make a general statement about the length of time in bankruptcy for firms using “prepacks.”

c. Select a graphical method that will permit a comparison of the time-in-bankruptcy distributions for the three types or reorganization plans.

d. Firms that were reorganized through a leveraged buyout are identified by an asterisk in the table. Mark these firms on the stem-and-leaf display, part a, by circling their bankruptcy times. Do you observe any pattern in the graph? Explain

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Generation Y’s entitlement mentality. The current workforce is dominated by “Generation Y”—people born between 1982 and 1999. These workers have a reputation as having an entitlement mentality (e.g., they believe they have a right to a high-paying job, without the work ethic). The reasons behind this phenomenon were investigated in Proceedings of the Academy of Educational Leadership (Vol. 16, 2011). A sample of 272 undergraduate business students was administered a questionnaire designed to capture the behaviors that lead to an entitlement mentality. The responses were used to measure the following two quantitative variables for each student: entitlement score (y)—where higher scores indicate a greater level of entitlement, and “helicopter parents” score (x)—where higher scores indicate that the student’s parents had a higher level of involvement in his or her everyday experiences and problems.

a. Give the equation of a simple linear regression model relating y to x.

b. The researchers theorize that helicopter parents lead to an entitlement mentality. Based on this theory, would you expect β0 to be positive or negative (or are you unsure)? Would you expect β1 to be positive or negative (or are you unsure)? Explain.

c. The p-value for testing H0: β0 = 0 versus Ha: β1> 0 was reported as .002. Use this result to test the researchers’ entitlement theory at α = .01.

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a. Calculate the estimated standard error for the regression model.

b. Interpret the estimation value calculated in part a.

Congress voting on women’s issues. The American Economic Review (March 2008) published research on how the gender mix of a U.S. legislator’s children can influence the legislator’s votes in Congress. The American Association of University Women (AAUW) uses voting records of each member of Congress to compute an AAUW score, where higher scores indicate more favorable voting for women’s rights. The researcher wants to use the number of daughters a legislator has to predict the legislator’s AAUW score.

a. In this study, identify the dependent and independent variables.

b. Explain why a probabilistic model is more appropriate than a deterministic model.

c. Write the equation of the straight-line, probabilistic model.
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