Question

The given data represent the total compensation for 10 randomly selected CEOs and their companys stock performance in 2009.

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Answer #1

a) Test for correlation coefficeint:

H0: There is no linear relation between Compnsation(X) and Stock Return(Y)

H1: There is linear relation between Compnsation(X) and Stock Return(Y):

Critical value of r is 0.707 at 5% los and 10-2 = 8 df

Since |r| = 0.1787 < Critical value of r so we accept H0

thus we conclude that there is no linear relation between Compnsation(X) and Stock Return(Y)

b) From the given data

S.NO. Compensation(X) Stock Return (Y) X^2 Y^2 XY
1 26.33 6.37 693.2689 40.5769 167.7221
2 12.83 30.56 164.6089 933.9136 392.0848
3 19.57 32.17 382.9849 1034.9089 629.5669
4 13.63 79.58 185.7769 6332.9764 1084.6754
5 12.15 -8.83 147.6225 77.9689 -107.2845
6 11.91 2.33 141.8481 5.4289 27.7503
7 26.03 4.58 677.5609 20.9764 119.2174
8 15.26 10.31 232.8676 106.2961 157.3306
9 17.28 3.67 298.5984 13.4689 63.4176
10 14.72 11.31 216.6784 127.9161 166.4832
Total: 169.71 172.05 3141.8155 8694.4311 2700.9638

Based on the above table, the following is calculated: n 1 X X; 169.71 10 16.971 n n Y = 172.05 10 17.205 n n 72 2 1 SSxx = x

b) The predicted stock return for a company whose CEO made $15 million is

Y-hat = 31.402 - 0.8365(15) = 18.9%

c) The predicted stock return for a company whose CEO made $25 million is

Y-hat = 31.402 - 0.8365(25) = 10.5%

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