The following estimated regression equation based on 10 observations was presented ŷ = 25.1270 + 0.5309x1 + 0.4920x2 Here, SST = 6,738.125, SSR = 6,221.375, sb1 = 0.0818, and sb2 = 0.0563. Compute MSR and MSE. (Round your answers to three decimal places.) Compute F and perform the appropriate F test. Use α = 0.05. State the null and alternative hypotheses. a. H0: β1 ≠ 0 and β2 ≠ 0 Ha: One or more of the parameters is equal to zero. b. H0: β1 = β2 = 0 Ha: One or more of the parameters is not equal to zero. c. H0: β1 > β2 Ha: β1 ≤ β2 H0: β1 < β2 Ha: β1 ≥ β2d. H0: β1 ≠ 0 and β2 = 0 Ha: β1 = 0 and β2 ≠ 0 2. Find the value of the test statistic. (Round your answer to two decimal places.) 3. Find the p-value. (Round your answer to three decimal places.) p-value = 4. State your conclusion. a. Reject H0. There is sufficient evidence to conclude that the overall model is significant. b. Do not reject H0. There is sufficient evidence to conclude that the overall model is significant. c. Reject H0. There is insufficient evidence to conclude that the overall model is significant. d. Do not reject H0. There is insufficient evidence to conclude that the overall model is significant.
The following estimated regression equation based on 10 observations was presented ŷ = 25.1270 + 0.5309x1 + 0.4920x2 Here, SST = 6,738.125, SSR = 6,221.375, sb1 = 0.0818, and sb2 = 0.0563. Compute MSR and MSE. (Round your answers to three decimal places.) Compute F and perform the appropriate F test. Use α = 0.05. State the null and alternative hypotheses. a. H0: β1 ≠ 0 and β2 ≠ 0 Ha: One or more of the parameters is equal to zero. b. H0: β1 = β2 = 0 Ha: One or more of the parameters is not equal to zero. c. H0: β1 > β2 Ha: β1 ≤ β2 H0: β1 < β2 Ha: β1 ≥ β2d. H0: β1 ≠ 0 and β2 = 0 Ha: β1 = 0 and β2 ≠ 0 2. Find the value of the test statistic. (Round your answer to two decimal places.) 3. Find the p-value. (Round your answer to three decimal places.) p-value = 4. State your conclusion. a. Reject H0. There is sufficient evidence to conclude that the overall model is significant. b. Do not reject H0. There is sufficient evidence to conclude that the overall model is significant. c. Reject H0. There is insufficient evidence to conclude that the overall model is significant. d. Do not reject H0. There is insufficient evidence to conclude that the overall model is significant.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section: Chapter Questions
Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
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The following estimated regression equation based on 10 observations was presented
ŷ = 25.1270 + 0.5309x1 + 0.4920x2
Here, SST = 6,738.125, SSR = 6,221.375,
sb1 = 0.0818,
and
sb2 = 0.0563.
Compute MSR and MSE. (Round your answers to three decimal places.)
Compute F and perform the appropriate F test. Use α = 0.05.
State the null and alternative hypotheses.
a.
| H0: β1 ≠ 0 and β2 ≠ 0 |
| Ha: One or more of the parameters is equal to zero. |
b.
c.
| H0: β1 = β2 = 0 |
| Ha: One or more of the parameters is not equal to zero. |
| H0: β1 > β2 |
| Ha: β1 ≤ β2 |
| H0: β1 < β2 |
| Ha: β1 ≥ β2 |
| H0: β1 ≠ 0 and β2 = 0 |
| Ha: β1 = 0 and β2 ≠ 0 |
2. Find the value of the test statistic. (Round your answer to two decimal places.)
3. Find the p-value. (Round your answer to three decimal places.)
p-value =
4. State your conclusion.
a. Reject H0. There is sufficient evidence to conclude that the overall model is significant.
b. Do not reject H0. There is sufficient evidence to conclude that the overall model is significant.
c. Reject H0. There is insufficient evidence to conclude that the overall model is significant.
d. Do not reject H0. There is insufficient evidence to conclude that the overall model is significant.
4. Perform a t test for the significance of
β1.
Use α = 0.05.State the null and alternative hypotheses.
a.
| H0: β1 > 0 |
| Ha: β1 ≤ 0 |
b.
c.
| H0: β1 ≠ 0 |
| Ha: β1 = 0 |
| H0: β1 < 0 |
| Ha: β1 ≥ 0 |
d.
e.
| H0: β1 = 0 |
| Ha: β1 > 0 |
| H0: β1 = 0 |
| Ha: β1 ≠ 0 |
5. Find the value of the test statistic. (Round your answer to two decimal places.)
6. Find the p-value. (Round your answer to three decimal places.)
p-value =
7. State your conclusion.
a. Do not reject H0. There is sufficient evidence to conclude that β1 is significant.
b. Reject H0. There is insufficient evidence to conclude that β1 is significant.
c. Reject H0. There is sufficient evidence to conclude that β1 is significant.
d. Do not reject H0. There is insufficient evidence to conclude that β1 is significant.
8. Perform a t test for the significance of
β2.
Use α = 0.05.State the null and alternative hypotheses.
a.
| H0: β2 ≠ 0 |
| Ha: β2 = 0 |
b.
c.
| H0: β2 = 0 |
| Ha: β2 ≠ 0 |
| H0: β2 > 0 |
| Ha: β2 ≤ 0 |
| H0: β2 < 0 |
| Ha: β2 ≥ 0 |
| H0: β2 = 0 |
| Ha: β2 > 0 |
9. Find the value of the test statistic. (Round your answer to two decimal places.)
10. Find the p-value. (Round your answer to three decimal places.)
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