Question

I need help with - ​(d) Based on your results to parts​ (b) and​ (c), would you recommend using the​ least-squares regression line to predict the stock return of a company based on the​ CEO's compensation?​ Why? What would be a good estimate of the stock return based on the data in the​ table? - the final part of the problem. Thank you!

The accompanying data represent the total compensation for 12 randomly selected chief executive officers​ (CEOs) and the​ company's stock performance.

Company   Compensation   Return
A   14.62   74.84
B   3.29   60.79
C   6.65   141.68
D   1.92   33.03
E   1.78   11.89
F   2.88   30.99
G   11.37   0.92
H   6.81   64.52
I   8.91   52.12
J   3.17   52.88
K   20.67   23.68
L   6.43   31.83

​(a) Treating compensation as the explanatory​ variable, x, use technology to determine the estimates of β0 and β1.

The estimate of β1 is −0.234.

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

The estimate of β0 is 50.000

​(Round to one decimal place as​ needed.)

b) Assuming that the residuals are normally distributed​, test whether a linear relation exists between compensation and stock return at the α=0.10level of significance. What are the null and alternative​ hypotheses?

A. H0​: β1≠0 H1​: β1=0

B. H0​: β0=0 H1​: β0≠0

C. H0​: β1=0 H1​: β1≠0 Your answer is correct.

D. H0​: β0≠0 H1​: β0=0

Compute the test statistic using technology.

−0.12

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

Compute the​ P-value using technology.

0.907 ​

(Round to three decimal places as​ needed.)

State the appropriate conclusion. Choose the correct answer below.

A. Reject H0. There is sufficient evidence to conclude that a linear relation exists between compensation and stock return.

B. Reject H0. There is not sufficient evidence to conclude that a linear relation exists between compensation and stock return.

C. Do not reject H0. There is not sufficient evidence to conclude that a linear relation exists between compensation and stock return. correct answer

D. Do not reject H0. There is sufficient evidence to conclude that a linear relation exists between compensation and stock return.

​(c) Assuming the residuals are normally​ distributed, construct a 90​% confidence interval for the slope of the true​ least-squares regression line.

Lower bound: -3.89

Upper bound: 3.42

(Round to 2 decimal places as needed)

​(d) Based on your results to parts​ (b) and​ (c), would you recommend using the​ least-squares regression line to predict the stock return of a company based on the​ CEO's compensation?​ Why? What would be a good estimate of the stock return based on the data in the​ table?

A.

Based on the results from parts​ (b), the regression line could be used to predict the stock return.​ However, the results from part​ (b) indicate that the regression line should not be used. The results are not conclusive and further analysis of the data is needed.

B.

The regression line could be used to predict the stock return. The test in part​ (b) and the confidence interval in part​ (c) both confirm that there is a relationship between the variables.

C.

Based on the results from parts​ (b), the regression line should not be used to predict the stock return.​ However, the results from part​ (c) indicate that the regression line should be used. The results are not conclusive and further analysis of the data is needed.

D.

Based on the results from parts​ (b) and​ (c), the regression line should not be used to predict the stock return. The mean stock return would be a good estimate of the stock return based on the data in the table.

Answer 1

Answer d

Using part B and C, it is clear that the p value is 0.907, which is insignificant at 0.05 significance level because it is greater than 0.05 level and the confidence interval range is -3.89 to 3.42, which includes the null value of 0.

So, confidence interval and p value, both suggest that the slope coefficient is no significant enough. Therefore, we can not use the regression for prediction.

option D is correct answer