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Consider an equation to explain salaries of CEOS in terms of annual firm sales, return on equity (roe, in percentage points, so 0-100), and return on the firm's stock (ros, in percentage points, so 0-100) log(salary) = Bo + Bilog(sales) + B2roe + Bzros + u. 1. In terms of the model parameters, state the null hypothesis that, after controlling for sales and ros, roe has no effect on CEO salary. State the alternative that return on equity affects CEO salary. 2. Using relevant data, the following equation was obtained by OLS: log(salary) =4.32 + .280log(sales) + .0174roe + .00024ros

Consider an equation to explain salaries of CEOS in terms of annual firm sales, return on equity (roe, in percentage points, so 0-100), and return on the firm's stock (ros, in percentage points, so 0-100) log(salary) = Bo + Bilog(sales) + B2roe + Bzros + u. 1. In terms of the model parameters, state the null hypothesis that, after controlling for sales and ros, roe has no effect on CEO salary. State the alternative that return on equity affects CEO salary. 2. Using relevant data, the following equation was obtained by OLS: log(salary) =4.32 + .280log(sales) + .0174roe + .00024ros

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider an equation to explain salaries of CEOS in terms of annual firm sales, return on equity (roe, in percentage points, so 0-100), and return on the firm's stock (ros, in percentage points, so 0-100) log(salary) Bo + Bilog(sales) + Baroe + B3ros + u. 1. In terms of the model parameters, state the null hypothesis that, after controlling for sales and ros, roe has no effect on CEO salary. State the alternative that return on equity affects CEO salary. 2. Using relevant data, the following equation was obtained by OLS: log(salary) =4.32 + .280log(sales) + .0174roe + .00024ros (.32) (.035) (.0041) (.00010) n = 209 R2 = .283 By what percentage is salary predicted to increase if roe increases by 10 percentage points? Is the effect of roe on CEO salary economically meaningful? 3. Test the null hypothesis that roe has no effect on salary against the alternative that roe has an effect. Carry out the test at a 5% significance level. 4. Would you include roe in a final model explaining CEO compensation in terms of firm performance? Explain. 5. Construct a 95% confidence interval for B3. Do you reject the null hypothesis that ros has no effect on CEO salary at the 5% significance level?
Transcribed Image Text:Consider an equation to explain salaries of CEOS in terms of annual firm sales, return on equity (roe, in percentage points, so 0-100), and return on the firm's stock (ros, in percentage points, so 0-100) log(salary) Bo + Bilog(sales) + Baroe + B3ros + u. 1. In terms of the model parameters, state the null hypothesis that, after controlling for sales and ros, roe has no effect on CEO salary. State the alternative that return on equity affects CEO salary. 2. Using relevant data, the following equation was obtained by OLS: log(salary) =4.32 + .280log(sales) + .0174roe + .00024ros (.32) (.035) (.0041) (.00010) n = 209 R2 = .283 By what percentage is salary predicted to increase if roe increases by 10 percentage points? Is the effect of roe on CEO salary economically meaningful? 3. Test the null hypothesis that roe has no effect on salary against the alternative that roe has an effect. Carry out the test at a 5% significance level. 4. Would you include roe in a final model explaining CEO compensation in terms of firm performance? Explain. 5. Construct a 95% confidence interval for B3. Do you reject the null hypothesis that ros has no effect on CEO salary at the 5% significance level?
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