The given data represent the total compensation for 10 randomly selected CEOs an
ID: 3179234 • Letter: T
Question
The given data represent the total compensation for 10 randomly selected CEOs and their company's stock performance in 2009. Analysis of this data reveals a correlation coefficient of
r= -0.1838
Critical Values for Correlation Coefficient
n
3 0.997
4 0.950
5 0.878
6 0.811
7 0.754
8 0.707
9 0.666
10 0.632
11 0.602
12 0.576
13 0.553
14 0.532
15 0.514
16 0.497
17 0.482
18 0.468
19 0.456
20 0.444
21 0.433
22 0.423
23 0.413
24 0.404
25 0.396
26 0.388
27 0.381
28 0.374
29 0.367
30 0.361
n
What would be the predicted stock return for a company whose CEO made $15 million? What would be the predicted stock return for a company whose CEO made $25 million?
Stock Compensation millions of dollars) Return 26.82 5.45 30.56 12.01 19.07 31.48 79.73 13.81 12.05 8.73 11.73 2.27 26.54 4.97 15.08 10.55 3.81 17.25 14.13 11.99Explanation / Answer
from above
hence b1=Sxy/Sxx =-0.8156
and Bo=Ybar-Xbar*b1 = 17.21-16.85*(-0.8156)=30.9506
hence least square equation y=-0.8156x+30.9506
predicted value for x=15; =-0.8156*15+30.9506 =18.7161
predicted value for x=25; =-0.8156*25+30.9506 =10.5598
x y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi' (Y-Yi')^2 26.82 5.45 99.42 138.25 -113.02 9.07534 13.1430905 12.01 30.56 23.42 178.28 -69.40 21.15484 88.4570349 19.07 31.48 4.93 203.69 26.57 15.39648 258.679525 13.81 79.73 9.24 3909.00 -212.45 19.6867 3605.19744 12.05 -8.73 23.03 672.78 133.79 21.12221 891.154724 11.73 2.27 26.20 223.14 81.83 21.38322 365.315055 26.54 4.97 93.92 149.77 -114.21 9.303717 18.7811015 15.08 10.55 3.13 44.33 14.17 18.65085 65.6238001 17.25 3.81 0.16 179.51 -0.56 16.88093 170.849259 14.13 11.99 7.39 27.23 16.06 19.4257 55.2896579 Total 168.49 172.08 290.84 5725.97 -237.22 5532.49069 mean 16.85 17.21 SSx Ssy SxyRelated Questions
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