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.

Company   Compensation ($mil)   Stock Return (%)
Company A   14.54   75.47
Company B   4.09   64.03
Company C   7.08   142.05
Company D   1.09   32.73
Company E   1.93   10.65
Company F   3.77   30.63
Company G   12.01   0.77
Company H   7.63   69.37
Company I   8.42   58.72
Company J   4.08   55.97
Company K   20.93   24.26
Company L   6.67   32.19

​(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.

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

r=__?__

​(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,

1,

0,

so

▼

a negative

no

a positive

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

▼

no

a positive

a negative

role in determining the compensation of a CEO.

Answer 1

a) The explanatory variable is - Stock return

b) The scatter diagram of the data is :

c) The linear correlation coefficient between compensation and stock return r =  -0.029

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