Question

The accompanying data include the total compensation​ (in $millions) for CEOs of 50 companies and the investment return for a recent year.

Company   Compensation ($mil)   Return (%)
Company 1   20.6   17
Company 2   16.3   8
Company 3   27.8   10
Company 4   26.2   0
Company 5   31.2   15
Company 6   23.7   64
Company 7   15.1   54
Company 8   17.9   33
Company 9   11.9   13
Company 10   15.6   6
Company 11   17.9   34
Company 12   14.4   48
Company 13   12.7   21
Company 14   13.6   0
Company 15   14.9   59
Company 16   14.2   20
Company 17   13.4   4
Company 18   43.5   -20
Company 19   16.8   -8
Company 20   21.3   17
Company 21   14.5   3
Company 22   84.6   25
Company 23   24.1   7
Company 24   15.9   5
Company 25   22.9   25
Company 26   14.9   -1
Company 27   31.4   6
Company 28   14.6   27
Company 29   14.8   30
Company 30   60.3   39
Company 31   17.1   31
Company 32   17.9   -17
Company 33   19.2   24
Company 34   67.7   25
Company 35   12.7   33
Company 36   19.3   17
Company 37   18.1   5
Company 38   15.5   -5
Company 39   12.7   -19
Company 40   13.9   24
Company 41   19.4   5
Company 42   16.6   21
Company 43   17.2   0
Company 44   17.8   81
Company 45   61.1   24
Company 46   42.2   48
Company 47   14.9   36
Company 48   22.7   13
Company 49   39.8   -7
Company 50   16.8   -3

A. Compute the correlation coefficient between compensation and the investment return.

B. At the 0.05 level of​ significance, is the correlation between compensation and the investment return statistically​ significant?

- The null and alternative hypotheses

- The test statistic

- The​ p-value

C. Write a short summary of the findings in​ (a) and​ (b). Are the results​ surprising?

Answer 1

A. The correlation coefficient between compensation and the investment return is 0.063.

B. The hypothesis being tested is:

H₀: β₁ = 0

H₁: β₁ ≠ 0

Source	SS	df	MS	F	p-value
Regression	87.0523	1	87.0523	0.19	.6658
Residual	22,121.7677	48	460.8702
Total	22,208.8200	49

The test statistic is 0.19

The p-value is 0.6658.

Since the p-value (0.6658) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the correlation between compensation and the investment return is statistically​ significant.

C. The correlation coefficient between compensation and the investment return is 0.063. Since there is a weak positive relationship between compensation and the investment return, this is not a good model. Also, this model is not statistically​ significant.