1. (Supplemental Exercise Required) XYZ Co. is studying CEO salaries to determine how to set theirs. For 26 public companies, they record 2021 Sales ($Mil) 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. a. Compute the correlation between Sales and CEO Pay. 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 (SMil.) 5000 Prediction Fit SE Fit 95% CI 95% PI 1196.93 182.845 (819.561, 157431) (-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) A B WN 9 1 Sales ($Mil.) CEO Pay ($000) 2 150 320 3 150 500 4 170 210 5 200 300 6 200 600 7 250 400 8 300 500 400 700 10 500 500 11 800 1000 12 900 800 13 1000 600 14 1000 1300 15 2000 800 16 2000 1200 17 3000 1400 18 5000 1000 19 7000 2800 20 8000 2000 21 10000 1200 22 10000 3300 23 15000 2000 20000 2400 25 40000 2100 26 50000 7000 27 80000 5000 28 24 1. (Supplemental Exercise Required) XYZ Co. is studying CEO salaries to determine how to set theirs. For 26 public companies, they record 2021 Sales ($Mil) 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. a. Compute the correlation between Sales and CEO Pay. 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 (SMil.) 5000 Prediction Fit SE Fit 95% CI 95% PI 1196.93 182.845 (819.561, 157431) (-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) A B WN 9 1 Sales ($Mil.) CEO Pay ($000) 2 150 320 3 150 500 4 170 210 5 200 300 6 200 600 7 250 400 8 300 500 400 700 10 500 500 11 800 1000 12 900 800 13 1000 600 14 1000 1300 15 2000 800 16 2000 1200 17 3000 1400 18 5000 1000 19 7000 2800 20 8000 2000 21 10000 1200 22 10000 3300 23 15000 2000 20000 2400 25 40000 2100 26 50000 7000 27 80000 5000 28 24