Consider an equation to explain salaries of CEOs in terms of annual firm sales, return onequity (roe, in percentage form), and return on the firm's stock (ros, in percentage form):log(salary) 5 b0 1 b1log(sales) 1 b2roe 1 b3ros 1 u.(i) In terms of the model parameters, state the null hypothesis that, after controlling forsales and roe, ros has no effect on CEO salary. State the alternative that better stockmarket performance increases a CEO's salary.
(ii) Using the data in CEOSAL1.RAW, the following equation was obtained by OLS:l? og(salary ) 5 4.32 1 .280 log(sales) 1 .0174 roe 1 .00024 ros(.32) (.035) (.0041) (.00054)n 5 209, R2 5 .283.B y what percentage is salary predicted to increase if ros increases by 50 points?Does ros have a practically large effect on salary?
(iii) Test the null hypothesis that ros has no effect on salary against the alternative thatros has a positive effect. Carry out the test at the 10% significance level.
(iv) Would you include ros in a final model explaining CEO compensation in terms offirm performance? Explain