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= -0.1787. 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? Click the icon to view the compensation and stock performance data Click the icon to view a table of critical values for the correlation coefficient. What would be the predicted stock return for a company whose CEO made $15 million? % (Type an integer or decimal rounded to one decimal place as needed.)

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 - (ΣΧ; = 3141.8155 – 169.712/10 = 261.66709 n i=1 i=1 2 72 1 SSyy = y;? Y; 8694.4311 - 172.052/10 = 5734.31085 n i=1 i=1 72 SSXY ΣΧΥ; ** (Ex) (x) 2700.9638 – 169.71 x 172.05/10 = -218.8967 i=1 i=1 Therefore, based on the above calculations, the regression coefficients (the slope m, and the y- intercept n) are obtained as follows: m = SSXY SSxx -218.89675 261.66709 -0.8365 n=Y - X:n . m = = 17.205 – 16.971 x (-0.8365) = 31.402 Therefore, we find that the regression equation is: Y = 31.402 - 0.8365X

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%