Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
6th Edition
ISBN: 9781337115186
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
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Textbook Question
Chapter 14.5, Problem 23E
The data from exercise 1 follow.
- a. Compute the mean square error using equation (14.15).
- b. Compute the standard error of the estimate using equation (14.16).
- c. Compute the estimated standard deviation of b1 using equation (14.18).
- d. Use the t test to test the following hypotheses (α = .05):
- e. Use the F test to test the hypotheses in part (d) at a .05 level of significance. Present the results in the analysis of variance table format.
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From the data below;
x1
1
2
3
4
5
y1
3
7
5
11
14
a) Compute the mean square error
b) Compute the standard error of the estimate
c) Compute the estimated standard deviation of b1
d) Use the t-test to test the following hypothesis (α= .05)
Ho: β1 = 0
Ha: β1 ≠ 0
e) Use the F-test to test the hypotheses in part (d) at a 0.5 level of significance. Present in the analysis of variance format.
Consider the data.
xi
3
12
6
20
14
yi
60
40
65
5
15
(a)
Compute the mean square error using equation
s2 = MSE =
SSE
n − 2
.
(Round your answer to two decimal places.)
(b)
Compute the standard error of the estimate using equation
s =
MSE
=
SSE
n − 2
.
(Round your answer to three decimal places.)
(c)
Compute the estimated standard deviation of
b1
using equation
sb1 =
s
Σ(xi − x)2
.
(Round your answer to three decimal places.)
(d)
Use the t test to test the following hypotheses (? = 0.05):
H0:
β1
=
0
Ha:
β1
≠
0
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format.
Set up the ANOVA table. (Round your values for MSE and F to two…
Consider the data.
xi
1
2
3
4
5
yi
3
7
5
11
14
(a)
Compute the mean square error using equation
s2 = MSE =
SSE
n − 2
.
(Round your answer to two decimal places.)
(b)
Compute the standard error of the estimate using equation
s =
MSE
=
SSE
n − 2
.
(Round your answer to three decimal places.)
(c) Compute the estimated standard deviation of
b1
using equation
sb1 =
s
Σ(xi − x)2
.
(Round your answer to three decimal places.)
(d)
Use the t test to test the following hypotheses (? = 0.05):
H0:
β1
=
0
Ha:
β1
≠
0
Find the value of the test statistic. (Round your answer to three decimal places.) =____
Find the p-value. (Round your answer to four decimal places.)
p-value = _____
State your conclusion.
(A) Reject H0. We cannot conclude that the relationship between x and y is significant.(B) Do not reject H0. We cannot conclude that the relationship between x and y is…
Chapter 14 Solutions
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
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Compute the mean...Ch. 14.5 - The data from exercise 2 follow.
Compute the mean...Ch. 14.5 - The data from exercise 3 follow.
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- Consider the data. xi 1 2 3 4 5 yi 3 8 5 10 14 (a) Compute the mean square error using equation s2 = MSE= SSE n − 2 . (Round your answer to two decimal places.) (b) Compute the standard error of the estimate using equation s = MSE = SSE n − 2 . (Round your answer to three decimal places.) (c) Compute the estimated standard deviation of b1 using equation sb1 = s Σ(xi − x)2 . (Round your answer to three decimal places.) (d) Use the t test to test the following hypotheses (? = 0.05): H0: ?1 = 0 Ha: ?1 ≠ 0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Do not reject H0. We cannot conclude that the relationship between x and y is significant. Reject H0. We cannot conclude that the relationship between x and y is significant. Do not reject H0.…arrow_forwardGiven are five observations for two variables, x and y. xi 2 7 15 18 20 yi 60 51 42 12 14 Use the estimated regression equation: y^=68.5866-2.6441 . a. Compute the mean square error using equation. (to 4 decimals) b. Compute the standard error of the estimate using equation. (to 4 decimals) c. Compute the estimated standard deviation of b1 using equation. (to 4 decimals) d. Use the t-test to test the following hypotheses (a=0.05): Compute the value of the t-test statistic (Enter negative values as negative numbers). (to 3 decimals) What is the p-value? Use Table 2 from Appendix B. p-value is What is your conclusion? We (do not reject, reject). e. Use the F-test to test the hypotheses in part (d) at a 0.05 level of significance. Complete the F table below using Excel. Calculate the Sum of Squares (to 1 decimal), the Mean Squares (to 1 decimal), and the F ratio (to 2 decimals) and the p-value (to 4 decimals). Sourceof Variation Degreesof Freedom Sum ofSquares MeanSquare F…arrow_forwardThe following is part of the computer output from a regression of monthly returns on Waterworks stock against the S&P 500 Index. A hedge fund manager believes that Waterworks is underpriced, with an alpha of 2% over the coming month. Beta R-square Standard Deviationof Residuals 0.75 0.65 0.06 (i.e., 6% monthly) Now suppose that the manager misestimates the beta of Waterworks stock, believing it to be 0.50 instead of 0.75. The standard deviation of the monthly market rate of return is 5%. Required: a. If he holds a $6 million portfolio of Waterworks stock and wishes to hedge market exposure for the next month using one-month maturity S&P 500 futures contracts, what is the standard deviation of the (now improperly) hedged portfolio? The S&P 500 currently is at 3,000 and the contract multiplier is $50. (Do not round intermediate calculations. Round your percentage answer to 2 decimal places.) b. What is the probability of incurring a loss over the next month…arrow_forward
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