Question

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). beta 0β0 and beta 1β1. The estimate of beta 1β1 is? ​(Round to three decimal places as​ needed.) Data Table of Compensation and Stock Performance Company Compensation ​(millions of​ dollars) Stock Return​ (%) A 15.98 77.34 B 4.17 67.65 C 6.18 140.24 D 1.16 32.11 E 1.85 10.43 F 2.24 29.52 G 11.24 0.65 H 7.09 66.46 I 8.91 59.09 J 3.15 54.84 K 20.97 22.89 L 6.15 31.77 ​(a) Treating compensation as the explanatory​ variable, x, use technology to determine the estimates of beta 0β0 and beta 1β1. The estimate of beta 1β1 is ​(Round to three decimal places as​ needed.) The estimate of beta 0β0 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 alphaαequals= level of significance. What are the null and alternative​ hypotheses? A. Upper H 0H0​: beta 1β1equals=0 Upper H 1H1​: beta 1β1not equals≠0 B. Upper H 0H0​: beta 0β0not equals≠0 Upper H 1H1​: beta 0β0equals=0 C. Upper H 0H0​: beta 0β0equals=0 Upper H 1H1​: beta 0β0not equals≠0 D. Upper H 0H0​: beta 1β1not equals≠0 Upper H 1H1​: beta 1β1equals=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.Do not reject Upper H 0H0. There is sufficient evidence to conclude that a linear relation exists between compensation and stock return. B.Reject Upper H 0H0. There is not sufficient evidence to conclude that a linear relation exists between compensation and stock return. C.Reject Upper H 0H0. There is sufficient evidence to conclude that a linear relation exists between compensation and stock return. D.Do not reject Upper H 0H0. There is not sufficient evidence to conclude that a linear relation exists between compensation and stock return.Your answer is correct.​(c) Assuming the residuals are normally​ distributed, construct a 95% confidence interval for the slope of the true​ least-squares regression line. Lower bound equals= Upper bound equals= ​ (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) 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. 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. C. 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. D. 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.

Answer 1

A)The estimate of $\beta _1 =$ -.104

The estimate of $\beta _0=$ 50.19

B) Hypotheses are $H_0:\beta _1=0$ (vs) $H_0:\beta _1\neq0$ (A)

Test statistic is t = -.053

p value is .959

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

C)The 95% confidence interval is given as

Lower bound = -4.46

Upper bound = 4.25

D)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. (C)