From a sample of 209 firms, a researcher obtained the following regression resul

Question

From a sample of 209 firms, a researcher obtained the following regression results: log (salary) = 4.32 + 0.280 log (sales) + 0.0174 (ROE) + 0.0002 (ROS) (0.32) (0.035) (0.0041) (0.00054) Where salary = Salary of CEO Sales = Annual firm sales ROE = Return on equity in percent ROS = Return on firm's stock And where figures in the parentheses are the estimated standard errors. (a) Interpret the above taking regression taking into account any prior expectations that you may have about the signs of the various coefficients. (b) Which of the coefficients are individually statistically significant at 5 percent level? (c) What is the overall significance of the regression? Which test do you use? (d) Critically discuss whether it is possible to interpret the coefficients of ROE and ROS as elasticity coefficients?

Explanation / Answer

Intercept: 4.32: even if firms sales, return on stock & equity are 0, average salary of CEO is expected to be e^4.32 i.e. 75.19 units

Sales: for unit increase in log of sales gives 1.29 units increase in salary of CEOs

ROE: 1% increase in ROE raises salary of CEO by 1.02 units

ROS: 1% increase in ROS raises salary of CEO by 1 (I.E. e^0.0024) units

T_critical =0.032 (=TINV(0.975,208))

Sales: t=.26/.035 > t-critical so it is significant

ROE: t=.0174/.004 > t-critical so it is significant

ROS: t= 0.00024/0.00054 > t-critical so it is significant

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