Question

We are interested in the relationship between the compensation of Chief Executive Officers (CEO) of firms and the return on equity of their respective firm, using the dataset below. The variable salary shows the annual salary of a CEO in thousands of dollars, so that y = 150 indicates a salary of $150,000. Similarly, the variable ROE represents the average return on equity (ROE)for the CEO’s firm for the previous three years. A ROE of 20 indicates an average return of 20%.

d) Use your software to estimate the model, this time by using the database below which excludes all the data points for which the salary of the CEO appears extraordinarily large considering the ROE of their firm. Report your results.

obs salary roe

1 1095 14.1

2 1001 10.9

3 1122 23.5

4 578 5.9

5 1368 13.8

6 1145 20

7 1078 16.4

8 1094 16.3

9 1237 10.5

10 833 26.3

11 567 25.9

12 933 26.8

13 1339 14.8

14 937 22.3

15 2011 56.3

16 1585 12.6

17 905 20.4

18 1058 1.9

19 922 19.9

20 1220 15.4

21 1022 38.7

22 759 16.4

23 1414 24.4

24 1041 15.6

25 1688 14.4

27 1160 16.1

29 476 16.2

30 1492 18.4

31 1024 14.2

32 1593 14.9

33 427 12.4

34 829 17.1

35 797 16.9

36 577 18.1

37 1342 10.9

38 1774 19.3

39 709 18.3

40 860 18.4

41 1336 13.8

42 516 13.7

43 931 12.7

44 815 15.1

45 1681 16.5

46 568 10.2

47 775 19.6

48 1188 12.8

49 782 15.9

50 1170 17.3

51 1469 8.5

52 916 16.4

53 1070 19.5

54 894 19.2

55 829 15.9

56 780 19.9

57 2327 28.1

58 717 25

59 1368 15

60 2028 12.6

61 1195 20.3

62 256 22.7

63 775 14.8

64 1407 13.2

65 543 10.3

66 874 17.7

67 1287 10

68 1248 15.6

69 875 6.8

70 925 12.4

71 798 13.1

72 760 15.8

73 600 12.8

74 991 15.3

75 1570 0.5

76 911 16.5

77 1360 15.1

78 700 13

79 741 11.1

80 1097 8.9

81 953 17.5

82 441 15.9

83 595 14.2

84 1067 9.3

85 1298 9.5

86 1798 15.5

88 1336 11.1

89 1750 15.9

90 912 16.4

91 1892 8.6

92 833 24.6

93 1142 15.4

94 1159 16.9

95 1283 7.2

96 2109 11.6

97 1039 26.4

98 992 21.4

99 1253 19.2

100 721 15.1

101 1351 9

102 1391 9.4

103 1245 19

104 1550 3.5

105 2150 22.1

106 1846 10.9

107 573 15.1

109 959 17.3

110 612 33.3

111 1820 22.8

112 1411 11.1

113 1026 12.4

114 1287 20.9

115 800 6.7

116 1115 7.1

117 1631 11.8

118 1910 14

119 996 10.1

120 918 6.4

121 1261 12.4

122 1053 17.6

123 1221 15.1

124 1738 23.6

126 1900 23.2

127 427 12.4

128 1700 44.4

129 360 2.1

130 459 18.4

131 1340 16.1

132 729 15.1

133 223 22.7

134 2101 23.4

135 1082 25.7

136 1781 27

137 791 19.9

138 2092 43.7

139 1573 16.4

140 1045 11.6

141 1694 24.8

142 453 26.2

143 1130 44.5

144 1334 22.3

145 1344 22.3

146 1585 35.1

147 1946 13.1

148 1619 11

149 1620 19.4

150 967 28.5

151 1431 43.9

152 1231 26.8

153 770 15.7

154 1594 15

155 1568 28.2

156 995 15.4

157 1077 20

158 1161 42.2

159 1401 19.6

160 1127 16.2

162 730 29.5

163 729 22.6

165 949 13

167 1502 48.1

168 807 18

169 713 18

170 1489 21.7

171 736 21.3

172 1226 26.9

173 543 30.5

175 890 15.6

176 1627 19.4

177 2408 29.1

178 2248 40.8

179 787 13.7

180 474 11.1

181 439 10.8

182 465 5.1

183 594 12.3

184 688 7.4

185 607 6.2

186 634 12.7

187 532 10.6

188 441 7.4

189 694 12.6

190 520 12.8

191 757 2.9

192 668 13.5

193 803 10.7

194 500 11.9

195 552 12.9

196 412 10.1

197 1100 7.3

198 959 14.6

199 333 13.8

200 503 8.9

201 448 14

202 732 12.9

203 720 14.5

204 808 14.7

205 930 9

206 525 15.5

207 658 12.1

208 555 13.7

209 626 14.4

e) Produce a histogram and a normal probability plot of the residuals of this regression. Does this regression appear to meet the conditions of absence of outliers and near normality?

f) What are the units of the slope coefficient b1 in this equation? What is the impact on the salary of the CEO of firm i if the ROE increases by 1%?

g) Use your results to calculate a 95% interval to estimate the mean salary of CEOs whose firms have an ROE of 20 per cent.

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.289704038
R Square	0.08392843
Adjusted R Square	0.079301806
Standard Error	440291.5705
Observations	200
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3.51662E+12	3.51662E+12	18.14031743	3.16947E-05
Residual	198	3.83836E+13	1.93857E+11
Total	199	4.19002E+13
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	804388.3293	69946.9583	11.49997582	8.97587E-24	666451.705	942324.9536
roe	15562.29667	3653.854497	4.259145153	3.16947E-05	8356.831741	22767.7616

Salary 804388.33 15562.3(ROE)

Salary 50 45 40 35 30 25 20 15 10 1033,1303] (1573, 1843] (2113, 2383 (1303, 1573] 1843, 2113] 493, 763 1223, 493] 2383, 2653]

ROE 80 70 60 50 40 30 20 10

roe Residual Plot 0 30.40 50 60 roe

Normal Probability Plot 0 0 20 40 60 80 100 120 Sample Percentile

Does this regression appear to meet the conditions of absence of outliers and near normality?

Yes, the regression seems to meet conditions. We have a little heavy right tail but, it will work.

f) What are the units of the slope coefficient b1 in this equation? What is the impact on the salary of the CEO of firm i if the ROE increases by 1%?

Salary 804388.33 15562.3(ROE)

For each 1% increase in ROE, salary will increase by $15562.3

g) Use your results to calculate a 95% interval to estimate the mean salary of CEOs whose firms have an ROE of 20 per cent.

Salary = (804.388 15.56 (20)) . 1000 = 1115588 つ,つ

summary(mod) Call: 1m(formulasalary2 - roe, datadata) Residuals: -934652 -325828 -54032 307430 1150749 Coefficients: (Intercept) 804388 Min 1Q Median 3Q Max Estimate std. Error t value Pr(ltI) 69947 11. 500 <2e-16 ** 3654 4.259 3.17e-05** roe 15562 signif. codes : 0 , 0.001 **, 0.01 *, 0.05 ", 0.1 , 1 Residual standard error: 440300 on 198 degrees of freedom Multiple R-squared: 0.08393, Adjusted R-squared 0.0793 F-statistic: 18.14 on 1 and 198 DF, p-value: 3.169e-05 > set<-data. frame( + roe-c (20) > predict(mod,newdata = set, interval = "confidence", level = 0.95) 1 1115634 1050878 1180390 fit 1wr upr

95% Confidence interval =(1050878,1180390)