In: Statistics and Probability
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 salary.xlsx. 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%.
Draw a boxplot and a histogram of the salary of CEO. Are there any apparent outliers in the data? Are there high leverage points?
Use your software to estimate the relationship and report your results.
??????? = ?0 + ?1???? + ??
Looking at a plot of the residuals against predicted values and at the normal probability plot of residuals, does the estimated model appear satisfactory?
Use your software to estimate the model, this time by using the database salaryalt.xlsx 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.
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?
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%?
Use your results to calculate a 95% interval to estimate the mean salary of CEOs whose firms have an ROE of 20 per cent.
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 |
26 | 2983 | 19 |
27 | 1160 | 16.1 |
28 | 3844 | 12.1 |
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 |
87 | 4143 | 14.4 |
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 |
108 | 6640 | 10.2 |
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 |
125 | 3142 | 35.7 |
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 |
161 | 3068 | 21.5 |
162 | 730 | 29.5 |
163 | 729 | 22.6 |
164 | 11233 | 22.9 |
165 | 949 | 13 |
166 | 3646 | 7.8 |
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 |
174 | 14822 | 19.4 |
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 |