Question

In: Statistics and Probability

Use the data in CEOSAL for this exercise. Consider an equation to explain salaries of CEOs...

  1. Use the data in CEOSAL for this exercise. Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity (roe, in percentage form), and return on the firm’s stock (ros, in percentage form). Answer questions after estimating the equation

log(salary)=β0+β1log(sales)+β2roe+β3ros+u.

  1. (3 points) By what percentage is salary predicted to increase if ros increases by 50 points? Does ros have a practically large effect on salary?
  2. (3 points) Test the null hypothesis that ros has no effect on salary against the alternative that ros has a positive effect. Carry out the test at the 10% significance level.
  3. (2 points) Would you include ros in a final model explaining CEO compensation in terms of firm performance? Explain.
salary sales roe ros
1095 27595 14.1 191
1001 9958 10.9 13
1122 6125.9 23.5 14
578 16246 5.9 -21
1368 21783.2 13.8 56
1145 6021.4 20 55
1078 2266.7 16.4 62
1094 2966.8 16.3 44
1237 4570.2 10.5 37
833 2830 26.3 37
567 596.8 25.9 109
933 19773 26.8 -10
1339 40047 14.8 41
937 2513.8 22.3 44
2011 1580.6 56.3 63
1585 6754 12.6 17
905 1066.3 20.4 141
1058 3199.9 1.9 -15
922 1452.7 19.9 56
1220 8995 15.4 28
1022 1212.3 38.7 83
759 2824.2 16.4 21
1414 7621 24.4 -10
1041 4418.3 15.6 74
1688 12343 14.4 15

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