Question

1095    14.1
1001    10.9
1122    23.5
578     5.9
1368    13.8
1145    20
1078    16.4
1094    16.3
1237    10.5
833     26.3
567     25.9
933     26.8
1339    14.8
937     22.3
2011    56.3
1585    12.6
905     20.4
1058    1.9
922     19.9
1220    15.4
1022    38.7
759     16.4
1414    24.4
1041    15.6
1688    14.4
2983    19
1160    16.1
3844    12.1
476     16.2
1492    18.4
1024    14.2
1593    14.9
427     12.4
829     17.1
797     16.9
577     18.1
1342    10.9
1774    19.3
709     18.3
860     18.4
1336    13.8
516     13.7
931     12.7
815     15.1
1681    16.5
568     10.2
775     19.6
1188    12.8
782     15.9
1170    17.3
1469    8.5
916     16.4
1070    19.5
894     19.2
829     15.9
780     19.9
2327    28.1
717     25
1368    15
2028    12.6
1195    20.3
256     22.7
775     14.8
1407    13.2
543     10.3
874     17.7
1287    10
1248    15.6
875     6.8
925     12.4
798     13.1
760     15.8
600     12.8
991     15.3
1570    0.5
911     16.5
1360    15.1
700     13
741     11.1
1097    8.9
953     17.5
441     15.9
595     14.2
1067    9.3
1298    9.5
1798    15.5
4143    14.4
1336    11.1
1750    15.9
912     16.4
1892    8.6
833     24.6
1142    15.4
1159    16.9
1283    7.2
2109    11.6
1039    26.4
992     21.4
1253    19.2
721     15.1
1351    9
1391    9.4
1245    19
1550    3.5
2150    22.1
1846    10.9
573     15.1
6640    10.2
959     17.3
612     33.3
1820    22.8
1411    11.1
1026    12.4
1287    20.9
800     6.7
1115    7.1
1631    11.8
1910    14
996     10.1
918     6.4
1261    12.4
1053    17.6
1221    15.1
1738    23.6
3142    35.7
1900    23.2
427     12.4
1700    44.4
360     2.1
459     18.4
1340    16.1
729     15.1
223     22.7
2101    23.4
1082    25.7
1781    27
791     19.9
2092    43.7
1573    16.4
1045    11.6
1694    24.8
453     26.2
1130    44.5
1334    22.3
1344    22.3
1585    35.1
1946    13.1
1619    11
1620    19.4
967     28.5
1431    43.9
1231    26.8
770     15.7
1594    15
1568    28.2
995     15.4
1077    20
1161    42.2
1401    19.6
1127    16.2
3068    21.5
730     29.5
729     22.6
11233   22.9
949     13
3646    7.8
1502    48.1
807     18
713     18
1489    21.7
736     21.3
1226    26.9
543     30.5
14822   19.4
890     15.6
1627    19.4
2408    29.1
2248    40.8
787     13.7
474     11.1
439     10.8
465     5.1
594     12.3
688     7.4
607     6.2
634     12.7
532     10.6
441     7.4
694     12.6
520     12.8
757     2.9
668     13.5
803     10.7
500     11.9
552     12.9
412     10.1
1100    7.3
959     14.6
333     13.8
503     8.9
448     14
732     12.9
720     14.5
808     14.7
930     9
525     15.5
658     12.1
555     13.7
626     14.4

Let Y be annual salary (salary) in thousands of dollars, and X be the average return on equity (roe) for the CEO’s firm for the previous three years. Return on equity is defined to be net income as a percentage of common equity. If roe = 5, than the average return on equity is 5%.

a. We are interested in investigating the relationship between roe, a measure of a firm’s performance and CEO compensation. To do this regress salary on roe and present the results of the regression in the form of an equation. State other relevant output that you obtained from running this regression below the equation, and be sure to summarize your results. You should also include the relevant output of the software you used to estimate your regression.

Based on your results in Part A:

b. Is the estimated intercept coefficient significantly different from 0? State the null and alternative hypothesis you are testing and conduct the hypothesis test at the α = 0.01 level. Explain your work.

c. One might hypothesize that the slope should be greater than 0. Set up a null and alternative hypothesis and conduct a hypothesis test with respect to this statement. Use a 5% level of significance. Explain your work.

d. Discuss the meaning of the slope parameter. That is, what does the slope parameter measure, and how is the predicted value of the dependent variable affected by a 1 unit change in the independent variable?

e. Using the Jargue – Bera (JB) test, determine if the error terms (or disturbances) are normally distributed? Be sure to include the test statistic and the p – value in your answer. Explain your work.

f. Suppose the roe = 30. What salary would you predict for the CEO of this firm? (remember that salary is given in 000s)

Answer 1

Answering first four parts:

a) for the relationship between roe and ceo compensation, salary is regressed on roe. It is done using R software.

salary= (alpha) + (beta)roe + error

Intercept coefficient obtained in this case is 963.2

slope coefficient: 18.5

other summaries are:

Residuals:
    Min      1Q  Median      3Q     Max 
-1160.2  -526.0  -254.0   138.8 13499.9 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   963.19     213.24   4.517 1.05e-05 ***
x              18.50      11.12   1.663   0.0978 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1367 on 207 degrees of freedom
Multiple R-squared:  0.01319,   Adjusted R-squared:  0.008421 
F-statistic: 2.767 on 1 and 207 DF,  p-value: 0.09777

b)