1. (Supplemental Exercise - Required) XYZ Co. is studying CEO salaries to determine how to set...
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1. (Supplemental Exercise - Required) XYZ Co. is studying CEO salaries to determine how to set theirs. For 26 public companies, they record 2021 Sales (SMil) and CEO Pay ($000). The data is collected in the dataset, CEO Compensation. Open the dataset and use the data to answer the questions below. Compute the correlation between Sales and CEO Pay. a. b. Create two new variables, Log Sales and Log CEO Pay by taking the logarithms base 10 of the original variables. Compute the correlation between Log Sales and Log CEO Pay. c. We have learned that the correlation coefficient is unit-free. But the correlations in a and b are not equal. Briefly explain why. d. Fit the regression models, CEO Pay vs Sales and Log CEO Pay vs Log Sales, including the Normal Probability Plots of the Residuals and the Residuals plots. What do these plots tell you about the two models? e. XYZ had 2021 sales of $5 billion. They wish to set their CEO Pay based on the one of the regression models above. For each model, calculate the projected CEO Pay based on sales of $5 billion. f. More specifically, XYZ wants their CEO Pay to be within the 95% confidence interval for average CEO Pay for public companies with $5 billion in sales. Given this, which of the models should they use to set the CEO Pay. (Consider the residual plots and the prediction output on the following page.) Briefly explain your answer. CEO COMPENSATION.MWX Prediction for CEO Pay ($000) Regression Equation CEO Pay ($000) = 853 +0.06882 Sales ($Mil.) Settings Variable Setting Sales ($Mil.) 5000 Prediction Fit SE Fit 95% CI 95% PI 1196.93 182.845 (819.561, 1574.31) (-700.640, 3094.51) CEO COMPENSATION.MWX Prediction for LogCEOPay Regression Equation LogCEOPay = 1.657 +0.4140 LogSales Settings Variable Setting LogSales 3.699 Prediction Fit SE Fit 95% CI 95% PI 3.18820 0.0333053 (3.11946, 3.25694) (2.86640, 3.51000) CEO COMPENSATION.MWX Prediction for CEO Pay ($000) Regression Equation CEO Pay ($000) = 853 +0.06882 Sales ($Mil.) Settings Variable Setting Sales ($Mil.) 5000 Prediction Fit SE Fit 95% CI 95% PI 1196.93 182.845 (819.561, 1574.31) (-700.640, 3094.51) CEO COMPENSATION.MWX Prediction for LogCEOPay Regression Equation LogCEOPay = 1.657 +0.4140 LogSales Settings Variable Setting LogSales 3.699 Prediction Fit SE Fit 95% CI 95% PI 3.18820 0.0333053 (3.11946, 3.25694) (2.86640, 3.51000) 1. (Supplemental Exercise - Required) XYZ Co. is studying CEO salaries to determine how to set theirs. For 26 public companies, they record 2021 Sales (SMil) and CEO Pay ($000). The data is collected in the dataset, CEO Compensation. Open the dataset and use the data to answer the questions below. Compute the correlation between Sales and CEO Pay. a. b. Create two new variables, Log Sales and Log CEO Pay by taking the logarithms base 10 of the original variables. Compute the correlation between Log Sales and Log CEO Pay. c. We have learned that the correlation coefficient is unit-free. But the correlations in a and b are not equal. Briefly explain why. d. Fit the regression models, CEO Pay vs Sales and Log CEO Pay vs Log Sales, including the Normal Probability Plots of the Residuals and the Residuals plots. What do these plots tell you about the two models? e. XYZ had 2021 sales of $5 billion. They wish to set their CEO Pay based on the one of the regression models above. For each model, calculate the projected CEO Pay based on sales of $5 billion. f. More specifically, XYZ wants their CEO Pay to be within the 95% confidence interval for average CEO Pay for public companies with $5 billion in sales. Given this, which of the models should they use to set the CEO Pay. (Consider the residual plots and the prediction output on the following page.) Briefly explain your answer. CEO COMPENSATION.MWX Prediction for CEO Pay ($000) Regression Equation CEO Pay ($000) = 853 +0.06882 Sales ($Mil.) Settings Variable Setting Sales ($Mil.) 5000 Prediction Fit SE Fit 95% CI 95% PI 1196.93 182.845 (819.561, 1574.31) (-700.640, 3094.51) CEO COMPENSATION.MWX Prediction for LogCEOPay Regression Equation LogCEOPay = 1.657 +0.4140 LogSales Settings Variable Setting LogSales 3.699 Prediction Fit SE Fit 95% CI 95% PI 3.18820 0.0333053 (3.11946, 3.25694) (2.86640, 3.51000) CEO COMPENSATION.MWX Prediction for CEO Pay ($000) Regression Equation CEO Pay ($000) = 853 +0.06882 Sales ($Mil.) Settings Variable Setting Sales ($Mil.) 5000 Prediction Fit SE Fit 95% CI 95% PI 1196.93 182.845 (819.561, 1574.31) (-700.640, 3094.51) CEO COMPENSATION.MWX Prediction for LogCEOPay Regression Equation LogCEOPay = 1.657 +0.4140 LogSales Settings Variable Setting LogSales 3.699 Prediction Fit SE Fit 95% CI 95% PI 3.18820 0.0333053 (3.11946, 3.25694) (2.86640, 3.51000)
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Related Book For 
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
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