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 r = 0.2114. (a) What would be the predicted stock return for a company whose CEO made $15 million? (b) What would be the predicted stock return for a company whose CEO made $25 million?

Compensation millions) 26.31 5.9 12.95 30.79 19.52 31.68 13.02 79.69 12.17 8.39 11.72 2.89 25.93 53 14.81 11.25 17.08 3.53 14.58 11.73 Stock Return

Explanation / Answer

The regression equation is

y=a+bx

from Excel we have

The fitted model is

y =-0.98 x +33.8

a) when x= 15

y= -.98(15) +33.8=19.1

the predicted value for stock returns is 19.1%

b) when x= 25

y= -.98(25) +33.8=

the predicted value for stock returns is 9.3%

SUMMARY OUTPUT Regression Statistics Multiple R 0.211386 R Square 0.044684 Adjusted R Square -0.07473 Standard Error 26.08492 Observations 10 ANOVA df SS MS F Significance F Regression 1 254.6098 254.6098 0.374193 0.557707 Residual 8 5443.384 680.4231 Total 9 5697.994 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 33.79426 28.09595 1.202816 0.263435 -30.9951 98.58363 -30.9951 98.58363 Comensation -0.97741 1.597821 -0.61171 0.557707 -4.66199 2.707173 -4.66199 2.707173

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