Question

Student: Rayza Virgen
Date: 05/24/20   Instructor: Jennifer Aguayo
Course: Math 232 / 83 Spring 2020   Assignment: Homework 15: Section 14.1
3.
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).
1 Click the icon to view the data table.
​(a) Treating compensation as the explanatory​ variable, x, use technology to determine the estimates of beta 0 and beta 1.
The estimate of beta 1 is
nothing.
​(Round to three decimal places as​ needed.)
The estimate of beta 0 is
nothing.
​(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 alphaequals0.01 level of significance.
What are the null and alternative​ hypotheses?
A.
Upper H 0​: beta 0equals0
Upper H 1​: beta 0not equals0
B.
Upper H 0​: beta 1equals0
Upper H 1​: beta 1not equals0
C.
Upper H 0​: beta 0not equals0
Upper H 1​: beta 0equals0
D.
Upper H 0​: beta 1not equals0
Upper H 1​: beta 1equals0
Compute the test statistic using technology.
nothing ​(Round to two decimal places as​ needed.)
Compute the​ P-value using technology.
nothing ​(Round to three decimal places as​ needed.)
State the appropriate conclusion. Choose the correct answer below.
A.
Reject Upper H 0. There is not sufficient evidence to conclude that a linear relation exists between compensation and stock return.
B.
Do not reject Upper H 0. There is sufficient evidence to conclude that a linear relation exists between compensation and stock return.
C.
Reject Upper H 0. There is sufficient evidence to conclude that a linear relation exists between compensation and stock return.
D.
Do not reject Upper H 0. 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
equals
nothing
Upper bound
equals
nothing
​ (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.
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), 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.
1: Data Table of Compensation and Stock Performance
Company
Compensation
​(millions of​ dollars)
Stock
Return​ (%)

A
15.69
77.47
B
3.68
67.96
C
6.29
145.06
D
1.49
34.75
E
1.69
11.64
F
3.26
29.56
G
11.75
0.57
H
7.52
67.65
I
9.04
51.85
J
3.73
52.34
K
20.29
20.91
L
5.11
31.85