In: Math
Some critics of big business argue that CEOs are overpaid and that their compensation is not related the performance of their company. To test this theory, data on executive's total pay and company's performance was collected from a randomly selected set of fifty companies.
A. Identify the independent variable(s) - If any (and define them precisely and indicate whether they are qualitative or quantitative).
B. Identify the dependent variable - if any (and define them precisely and indicate whether they are qualitative or quantitative).
C. Identify the type of analysis that is appropriate (Chi- Square test of independence, ANOVA, Regression, or Correlation)
D. Justify why the analysis you identified in part C is correct.
Solution:
A. Identify the independent variable(s) - If any (and define them precisely and indicate whether they are qualitative or quantitative).
Answer: Company's performance is the independent variable because we want to see if it has any impact on CEO's compensation and the company's performance can be in terms of revenue or stock price of the company. Therefore, the company's performance is a quantitative variable.
B. Identify the dependent variable - if any (and define them precisely and indicate whether they are qualitative or quantitative).
Answer: CEO's compensation is dependent variable because we want to see how it is impacted by the performance of the company. The CEO's compensation is a quantitative variable.
C. Identify the type of analysis that is appropriate (Chi-Square test of independence, ANOVA, Regression, or Correlation)
Answer: The type of analysis that is appropriate is Regression Analysis.
D. Justify why the analysis you identified in part C is correct.
Answer: Since the objective of this analysis is to determine the relationship between the company's performance and CEO's compensation. Regression analysis helps us to describe the relationship between the dependent variable and independent variable. Regression analysis gives us a least squares regression equation, where the coefficients describe the relationship between the independent variable and dependent variable. The regression equation can also be used to make a prediction about the compensation of CEO's based on the performance of the company. Therefore, the regression analysis will be appropriate to use here.