The given data represent the total compensation for 10 randomly selected CEOs an

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

requals=0.2200.

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 millio

Compensation (millions of dollars) 26.57,12.89.19.81,12.89,11.94,12.18, 26.65,14.95,17.32,14.55

Stock Return (%) 6.03,30.85,31.81,80.25,-8.55,2.91,4.48,10.65,3.78,11.86

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?%

Explanation / Answer

Let y denote performance of the share and x denote the compensation

Then the regression equation to predict the return for a company based on compensation is

Y = a + bx

b = [N* xy - x* y] / N *x2 – (x)2

a = (y – b*x)/N

Where N = 10

Hence, b = (28515 .05- 29548.38)/ 2855.248 = -0.36191

And a =( 174.07--0.36191*169.25)/ 10 = 23.54897

Therefore y = 23.54897 -0.36191*x

Hence,

The predicted stock return for a company

whose CEO made $15 million = 23.54897 -0.36191*15 = 18.12 %

The predicted stock return for a company

whose CEO made $25 million = 23.54897 -0.36191*25 = 14.5012 %

x y xy x2 y2 26.57 6.03 160.2171 705.9649 36.3609 12.89 30.85 397.6565 166.1521 951.7225 19.81 31.81 630.1561 392.4361 1011.876 12.89 80.25 1034.423 166.1521 6440.063 11.94 -8.55 -102.087 142.5636 73.1025 12.18 2.91 35.4438 148.3524 8.4681 26.65 4.48 119.392 710.2225 20.0704 14.95 10.65 159.2175 223.5025 113.4225 17.32 3.78 65.4696 299.9824 14.2884 14.55 11.86 172.563 211.7025 140.6596 Total 169.75 174.07 2672.451 3167.031 8810.034

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