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Data Analytics with Business Applications

BUSAN205-22A

Problem Set

This problem requires you to try to estimate what factors help determine the compensation (C) in thousands of dollars (includes salary and other payments such as bonuses) that is paid to Chief Executives (CEO’s) of large companies. You are given the information that is available on 30 highly paid CEO’s in the file labeled CEO.xlsx.  The file contains data on compensation for the CEOs (C, in thousands of dollars).  the most recent sales revenue (R) in millions of dollars, numbers of employees (E), and the capital investment (KI) in millions of dollars for their companies

(a) Outline the key statistics for each of the variables, by using the descriptive statistics function in Data Analysis in Excel. Briefly describe each variable by referring to 3 or 4 of the statistics presented in the table. (Hint: Present the table showing all the statistics identified in the 1^st column and then paste in the relevant information for each variable).                                                                                             (10 marks)

(b) Briefly explain whether you expect that there will be a negative or positive relationship between a CEO’s compensation and each of the other variables (You should base your answers on Economic/Management Theory, not on the actual given data)                                      (3 marks)

(c) Use Excel to draw a scatter-plot of the CEO compensation and sales revenue variables. The CEO compensation should be on the y-axis. Show the trend line and the regression equation on the graph. What is the likely relationship between the two variables and does this confirm your expectations in (b)?  (5 marks)

(d) Estimate the simple regression equation showing how a CEO’s compensation is determined by the sales revenue of the company. Interpret this equation and comment on its significance. Make sure to paste your Excel outputs below.                                                       ( 6 marks)                                                                                                              

(e) Next, we would like to see how our results might change if we use multiple regression model. Estimate C (CEO compensation) as function of all independent variables and summarize the results both from the simple regression that you estimated in (d) and multiple regression models in the table below. Include the p-value underneath each coefficient.                                                                                                      (4 marks)

(f) In Model (2), CEO compensation was estimated as a function of sales revenue, number of employees and capital investment. Interpret this equation and comment on the significance of each coefficient. Also comment on the overall significance of the equation. Does each coefficient have the sign that you anticipated in (b)? If not, why not?                                                                                                   (6 marks)

(g) Re-estimate the multiple regression equation using the natural logs of each variable using the same variables as in f). Paste your Excel Output Below.                                                 (6 marks)

(i) Comment on the significance of this equation and interpret the coefficients.

(ii) Explain what would be expected to happen to the CEO compensation if there was a ten percent increase in each of the independent variables.                                                                      

(h) Suggest two other quantitative variables that could be included in the regression. How could they improve the estimation of CEO compensation and what impact would you expect them to have on previously estimated coefficients?                          (4 marks)                                                          

(i) Provide a short summary brief to explain to a non-economist or non-statistician the key factors that influence all forms of compensation for CEOs based on this sample.                  ( 6 marks)