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. 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. H0: β1 ≠ 0 Ha: β1 = 0 c. H0: β1 < 0 Ha: β1 ≥ 0 d. H0: β1 = 0 Ha: β1 > 0e. 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. H0: β2 = 0 Ha: β2 ≠ 0 c. H0: β2 > 0 Ha: β2 ≤ 0d. H0: β2 < 0 Ha: β2 ≥ 0e. 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.)
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. 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. H0: β1 ≠ 0 Ha: β1 = 0 c. H0: β1 < 0 Ha: β1 ≥ 0 d. H0: β1 = 0 Ha: β1 > 0e. 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. H0: β2 = 0 Ha: β2 ≠ 0 c. H0: β2 > 0 Ha: β2 ≤ 0d. H0: β2 < 0 Ha: β2 ≥ 0e. 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.)
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Question
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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.
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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