Question

The accompanying data represent the total compensation for

12

randomly selected chief executive officers​ (CEO) and the​ company's stock performance in a recent year. Complete parts​ (a) through​ (d) below.

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Click the icon to view the CEO data.

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

Stock return

Compensation

​(b) Draw a scatter diagram of the data. Use the result from part​ (a) to determine the explanatory variable. Choose the correct graph below.

A.

0160025Stock ReturnCompensation

A scatter diagram has a horizontal axis labeled "Stock Return" from 0 to 160 in increments of 20 and a vertical axis labeled "Compensation" from 0 to 25 in increments of 5. The following 12 approximate points are plotted, listed here from left to right: (0, 14.5); (10, 4); (24, 7); (30, 1); (32, 2); (32, 4); (56, 12); (58, 7.5); (64, 8.5); (70, 4); (76, 21); (142, 6.5).

B.

0160025Stock ReturnCompensation

A scatter diagram has a horizontal axis labeled “Stock Return” from 0 to 160 in increments of 20 and a vertical axis labeled “Compensation” from 0 to 25 in increments of 5. The following 12 approximate points are plotted, listed here from left to right: (0, 12); (10, 2); (24, 21); (30, 4); (32, 1); (32, 6.5); (56, 4); (58, 8.5); (64, 4); (70, 7.5); (76, 14.5); (142, 7).

C.

0250160CompensationStock Return

A scatter diagram has a horizontal axis labeled "Compensation" from 0 to 25 in increments of 5 and a vertical axis labeled "Stock Return" from 0 to 160 in increments of 20. The following 12 approximate points are plotted, listed here from left to right: (1, 32); (2, 10); (4, 30); (4, 56); (4, 64); (6.5, 32); (7, 142); (7.5, 70); (8.5, 58); (12, 0); (14.5, 76); (21, 24).

D.

0250160CompensationStock Return

A scatter diagram has a horizontal axis labeled "Compensation" from 0 to 25 in increments of 5 and a vertical axis labeled "Stock Return" from 0 to 160 in increments of 20. The following 12 approximate points are plotted, listed here from left to right: (1, 76); (2, 64); (4, 10); (4, 32); (4, 142); (6.5, 30); (7, 0); (7.5, 70); (8.5, 58); (12, 56); (14.5, 24); (21, 32).

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

requals=nothing

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

​(d) Does a linear relation exist between compensation and stock​ return? Does stock performance appear to play a role in determining the compensation of a​ CEO?

The linear correlation coefficient is close to

▼

1 comma1,

0 comma0,

negative 1 comma−1,

so

▼

no

a positive

a negative

linear relation exists between compensation and stock return. It appears that stock performance plays

▼

no

a negative

a positive

role in determining the compensation of a CEO.

Data Company   Compensation ($mil)   Stock Return (%)
Company A   14.55   75.44
Company B   4.08   63.96
Company C   7.11   142.05
Company D   1.05   32.68
Company E   1.99   10.67
Company F   3.78   30.67
Company G   12.02   0.77
Company H   7.65   69.41
company I   8.45   58.69
Company J   4.08   55.95
Company K   20.92   24.28
Company L   6.65   32.15

Answer 1

The data is as follows:

Stock Return (%)	Compensation ($mil)
75.44	14.55
63.96	4.08
142.05	7.11
32.68	1.05
10.67	1.99
30.67	3.78
0.77	12.02
69.41	7.65
58.69	8.45
55.95	4.08
24.28	20.92
32.15	6.65

​(a) One would think that a higher stock return would lead to a higher compensation. Based on​ this, Stock return should be the explanatory variable as it explains the variation in higher compensation.

b) Let's make the scatterplot in Excel. Select the data -> Go to Insert-> Scatterplot. The output is:

Stock Return is on the x-axis. From the graph above, we can see that some of the points are (0, 12); (10, 2); (24, 21); (30, 4); (32, 1);

Hence, B) is the correct option.

C) Linear correlation coefficient = R = √0.0008 =  0.028

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