Question

The accompanying data represent the total compensation for 12randomly selected chief executive officers​ (CEO) and the​ company's stock performance in a recent year. Complete parts​ (a)through​ (d) below.

Company	Compensation​ ($mil)	Stock Return​ (%)
Company A	14.51		75.47
Company B	4.09		63.96
Company C	7.06		142.07
Company D	1.01		32.66
Company E	1.96		10.63
Company F	3.77		30.69
Company G	12.03		0.71
Company H	7.63		69.35
Company I	8.47		58.74
Company J	4.07		55.97
Company K	20.91		24.27
Company L	6.65		32.17

1. One would think that a higher stock return would lead to a higher compensation. Based on​ this, what would likely be the explanatory​ variable?

*Compensation

*Stock return

Draw a scatter diagram of the data. Use the result from part​ (a) to determine the explanatory variable.

c) Determine the linear correlation coefficient between compensation and stock return.

r equals=

​(Round to three decimal places as​ needed.)

The linear correlation coefficient is close to ______so ________linear relation exists between compensation and stock return. It appears that stock performance plays _____role in determining the compensation of a CEO.

Answer 1

a) explanatory​ variable = Stock return

c)

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	14.51	75.47	46.6489	662.8479	175.8440
2	4.09	63.96	12.8881	202.6590	-51.1066
3	7.06	142.07	0.3844	8527.7529	-57.2544
4	1.01	32.66	44.4889	291.1858	113.8180
5	1.96	10.63	32.7184	1528.3539	223.6186
6	3.77	30.69	15.2881	362.2995	74.4236
7	12.03	0.71	18.9225	2402.3885	-213.2116
8	7.63	69.35	0.0025	385.1733	-0.9813
9	8.47	58.74	0.6241	81.2853	7.1225
10	4.07	55.97	13.0321	39.0104	-22.5475
11	20.91	24.27	175.0329	647.9146	-336.7586
12	6.65	32.17	1.0609	308.1488	18.0808
Total	92.16	596.69	361.0918	15439.0199	-68.9525
Mean	7.680	49.724	SSX	SSY	SXY

correlation coefficient r=

Sxy/(√Sxx*Syy) =

-0.029

The linear correlation coefficient is close to 0 so it appear there is no linear relation exists between compensation and stock return. It appears that stock performance plays no role in determining the compensation of a CEO.