The accompanying data represent the total compensation for 12 randomly selected chief executive officers (CEOs) and the company's stock performance. Use the data to complete parts (a) through (d).
3 Click the icon to view the data table.
Data Table of Compensation and Stock Performance
Company Compensation (millions of dollars) StockReturn (%)
A 13.82 71.39
B 3.83 69.37
C 6.16 141.42
D 1.95 37.61
E 1.13 10.34
F 3.71 29.55
G 11.96 0.77
H 6.22 62.48
I 9.31 53.21
J 4.19 52.05
K 20.22 24.31
L 5.55 31.72
(a) Treating compensation as the explanatory variable, x, use technology to determine the estimates of β0 and β1 .
The estimate of β1 is __________(Round to three decimal places as needed.)
The estimate of β0 is ___________(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 = 0.01 level of significance.
What are the null and alternative hypotheses?
A. H0 : β0 ≠ 0
H1 : β0 = 0
B. H0 : β0 = 0
H1 : β0 ≠ 0
C. H0 : β1 ≠ 0
H1 : β1 = 0
D. H0 : β1 = 0
H1 : β1 ≠ 0
Compute the test statistic using technology. ___________(Round to two decimal places as needed.)
Compute the P-value using technology.____________(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. Do not reject H0 . There is 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.
D. Reject H0 . There is not sufficient evidence to conclude that a linear relation exists between compensation and stock return.
(c) Assuming the residuals are normally distributed, construct a 99% confidence interval for the slope of the true least-squares regression line.
Lower bound = ____________ Upper bound =______________
(Round to two 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.
Appplying regression on above data:
a) The estimate of β1 is =-0.555
b) The estimate of β0 is =52.755
D. H0 : β1 = 0
H1 : β1 ≠ 0
test statistic using technology =-0.27
P-value using technology =0.795
C. Do not reject H0 . There is not sufficient evidence to conclude that a linear relation exists between compensation and stock return.
c)
Lower bound =-7.146
Upper bound = 6.037
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.
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