The following estimated regression equation based on 10 observations was presented. ŷ = 29.1670 + 0.5902x1 + 0.4960x2 Here, SST = 6,734.125, SSR = 6,212.375, sb1 = 0.0816, and sb2 = 0.0569. (a) Compute MSR and MSE. (Round your answers to three decimal places.) MSR=?? MSE=?? (b) Compute F and perform the appropriate F test. Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 = ?2 = 0 Ha: One or more of the parameters is not equal to zero. H0: ?1 > ?2 Ha: ?1 ≤ ?2 H0: ?1 ≠ 0 and ?2 ≠ 0 Ha: One or more of the parameters is equal to zero. H0: ?1 < ?2 Ha: ?1 ≥ ?2 H0: ?1 ≠ 0 and ?2 = 0 Ha: ?1 = 0 and ?2 ≠ 0 Find the value of the test statistic. (Round your answer to two decimal places.) F = ?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is sufficient evidence to conclude that the overall model is significant. -Do not reject H0. There is sufficient evidence to conclude that the overall model is significant. - Reject H0. There is insufficient evidence to conclude that the overall model is significant. -Do not reject H0. There is insufficient evidence to conclude that the overall model is significant. (c) Perform a t test for the significance of ?1.Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 < 0 Ha: ?1 ≥ 0 H0: ?1 > 0 Ha: ?1 ≤ 0 H0: ?1 = 0 Ha: ?1 > 0 H0: ?1 ≠ 0 Ha: ?1 = 0 H0: ?1 = 0 Ha: ?1 ≠ 0 Find the value of the test statistic. (Round your answer to two decimal places.) t = ?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Do not reject H0. There is sufficient evidence to conclude that ?1 is significant.Reject H0. -There is sufficient evidence to conclude that ?1 is significant. Do not reject H0. -There is insufficient evidence to conclude that ?1 is significant.Reject H0. -There is insufficient evidence to conclude that ?1 is significant. (d) Perform a t test for the significance of ?2.Use ? = 0.05. State the null and alternative hypotheses. H0: ?2 ≠ 0 Ha: ?2 = 0 H0: ?2 > 0 Ha: ?2 ≤ 0 H0: ?2 = 0 Ha: ?2 ≠ 0 H0: ?2 = 0 Ha: ?2 > 0 H0: ?2 < 0 Ha: ?2 ≥ 0 Find the value of the test statistic. (Round your answer to two decimal places.) t = ?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Do not reject H0. There is insufficient evidence to conclude that ?2 is significant.Reject H0. -There is insufficient evidence to conclude that ?2 is significant. Do not reject H0. -There is sufficient evidence to conclude that ?2 is significant.Reject H0. -There is sufficient evidence to conclude that ?2 is significant.
The following estimated regression equation based on 10 observations was presented. ŷ = 29.1670 + 0.5902x1 + 0.4960x2 Here, SST = 6,734.125, SSR = 6,212.375, sb1 = 0.0816, and sb2 = 0.0569. (a) Compute MSR and MSE. (Round your answers to three decimal places.) MSR=?? MSE=?? (b) Compute F and perform the appropriate F test. Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 = ?2 = 0 Ha: One or more of the parameters is not equal to zero. H0: ?1 > ?2 Ha: ?1 ≤ ?2 H0: ?1 ≠ 0 and ?2 ≠ 0 Ha: One or more of the parameters is equal to zero. H0: ?1 < ?2 Ha: ?1 ≥ ?2 H0: ?1 ≠ 0 and ?2 = 0 Ha: ?1 = 0 and ?2 ≠ 0 Find the value of the test statistic. (Round your answer to two decimal places.) F = ?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is sufficient evidence to conclude that the overall model is significant. -Do not reject H0. There is sufficient evidence to conclude that the overall model is significant. - Reject H0. There is insufficient evidence to conclude that the overall model is significant. -Do not reject H0. There is insufficient evidence to conclude that the overall model is significant. (c) Perform a t test for the significance of ?1.Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 < 0 Ha: ?1 ≥ 0 H0: ?1 > 0 Ha: ?1 ≤ 0 H0: ?1 = 0 Ha: ?1 > 0 H0: ?1 ≠ 0 Ha: ?1 = 0 H0: ?1 = 0 Ha: ?1 ≠ 0 Find the value of the test statistic. (Round your answer to two decimal places.) t = ?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Do not reject H0. There is sufficient evidence to conclude that ?1 is significant.Reject H0. -There is sufficient evidence to conclude that ?1 is significant. Do not reject H0. -There is insufficient evidence to conclude that ?1 is significant.Reject H0. -There is insufficient evidence to conclude that ?1 is significant. (d) Perform a t test for the significance of ?2.Use ? = 0.05. State the null and alternative hypotheses. H0: ?2 ≠ 0 Ha: ?2 = 0 H0: ?2 > 0 Ha: ?2 ≤ 0 H0: ?2 = 0 Ha: ?2 ≠ 0 H0: ?2 = 0 Ha: ?2 > 0 H0: ?2 < 0 Ha: ?2 ≥ 0 Find the value of the test statistic. (Round your answer to two decimal places.) t = ?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Do not reject H0. There is insufficient evidence to conclude that ?2 is significant.Reject H0. -There is insufficient evidence to conclude that ?2 is significant. Do not reject H0. -There is sufficient evidence to conclude that ?2 is significant.Reject H0. -There is sufficient evidence to conclude that ?2 is significant.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
The following estimated regression equation based on 10 observations was presented.
ŷ = 29.1670 + 0.5902x1 + 0.4960x2
Here, SST = 6,734.125, SSR = 6,212.375,
sb1 = 0.0816,
and
sb2 = 0.0569.
(a)
Compute MSR and MSE. (Round your answers to three decimal places.)
MSR=??
MSE=??
(b)
Compute F and perform the appropriate F test. Use ? = 0.05.
State the null and alternative hypotheses.
| H0: ?1 = ?2 = 0 |
| Ha: One or more of the parameters is not equal to zero. |
| H0: ?1 > ?2 |
| Ha: ?1 ≤ ?2 |
| H0: ?1 ≠ 0 and ?2 ≠ 0 |
| Ha: One or more of the parameters is equal to zero. |
| H0: ?1 < ?2 |
| Ha: ?1 ≥ ?2 |
| H0: ?1 ≠ 0 and ?2 = 0 |
| Ha: ?1 = 0 and ?2 ≠ 0 |
Find the value of the test statistic. (Round your answer to two decimal places.)
F = ??
Find the p-value. (Round your answer to three decimal places.)
p-value = ??
State your conclusion.
-Reject H0. There is sufficient evidence to conclude that the overall model is significant.
-Do not reject H0. There is sufficient evidence to conclude that the overall model is significant.
- Reject H0. There is insufficient evidence to conclude that the overall model is significant.
-Do not reject H0. There is insufficient evidence to conclude that the overall model is significant.
(c)
Perform a t test for the significance of ?1.Use ? = 0.05.
State the null and alternative hypotheses.
| H0: ?1 < 0 |
| Ha: ?1 ≥ 0 |
| H0: ?1 > 0 |
| Ha: ?1 ≤ 0 |
| H0: ?1 = 0 |
| Ha: ?1 > 0 |
| H0: ?1 ≠ 0 |
| Ha: ?1 = 0 |
| H0: ?1 = 0 |
| Ha: ?1 ≠ 0 |
Find the value of the test statistic. (Round your answer to two decimal places.)
t = ??
Find the p-value. (Round your answer to three decimal places.)
p-value = ??
State your conclusion.
-Do not reject H0. There is sufficient evidence to conclude that ?1 is significant.Reject H0.
-There is sufficient evidence to conclude that ?1 is significant. Do not reject H0.
-There is insufficient evidence to conclude that ?1 is significant.Reject H0.
-There is insufficient evidence to conclude that ?1 is significant.
(d)
Perform a t test for the significance of ?2.Use ? = 0.05.
State the null and alternative hypotheses.
| H0: ?2 ≠ 0 |
| Ha: ?2 = 0 |
| H0: ?2 > 0 |
| Ha: ?2 ≤ 0 |
| H0: ?2 = 0 |
| Ha: ?2 ≠ 0 |
| H0: ?2 = 0 |
| Ha: ?2 > 0 |
| H0: ?2 < 0 |
| Ha: ?2 ≥ 0 |
Find the value of the test statistic. (Round your answer to two decimal places.)
t = ??
Find the p-value. (Round your answer to three decimal places.)
p-value = ??
State your conclusion.
-Do not reject H0. There is insufficient evidence to conclude that ?2 is significant.Reject H0.
-There is insufficient evidence to conclude that ?2 is significant. Do not reject H0.
-There is sufficient evidence to conclude that ?2 is significant.Reject H0.
-There is sufficient evidence to conclude that ?2 is significant.
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