Question

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

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. $\mathit{y}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}\mathit{x}\mathbf{+}\mathit{\epsilon }$.

Step-by-step solution

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.

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.

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.

Writing the equation for the probabilistic straight-line model

The equation for the probabilistic straight-line model is

$\mathit{y}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}\mathit{x}\mathbf{+}\mathit{\epsilon }$