You may need to use the appropriate technology to answer this question. Consider the data. X₁12345 Y₁ 28 5 11 13 (a) Compute the mean square error using equation s² = MSE (Round your answer to two decimal places.) (b) Compute the standard error of the estimate using equations = √✓MSE = (d) Use the t test to test the following hypotheses (a = 0.05): Ho: B₂0 (c) Compute the estimated standard deviation of b, using equation Sb₁√(x,x)2- (Round your answer to three decimal places.) 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= SSE n-2 Source Sum of Variation of Squares State your conclusion. Reject Ho. We cannot conclude that the relationship between x and y is significant. O Do not reject Ho- We cannot conclude that the relationship between x and y is significant. Reject Ho. We conclude that the relationship between x and y is significant. O Do not reject Ho. We conclude that the relationship between x and y is significant. Regression (e) 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 decimal places, and your p-value to three decimal places.) Error Total Degrees of Freedom SSE Vn-2 Mean Square (Round your answer to three decimal places.) F Find the p-value. (Round your answer to three decimal places.) p-value= Find the value of the test statistic. (Round your answer to two decimal places.) p-value State your conclusion. O Do not reject Ho- We cannot conclude that the relationship between x and y is significant. O Do not reject Ho. We conclude that the relationship between x and y is significant.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Consider the data provided in the following table:

| \(X_i\) | 1 | 2 | 3 | 4 | 5 |
|-------|---|---|---|---|---|
| \(Y_i\) | 2 | 5 | 8 | 11 | 13 |

(a) Compute the mean square error using equation \(\sigma^2 = \frac{SSE}{n-2}\). (Round your answer to two decimal places.)

\[\boxed{\text{Answer Input}}\]

(b) Compute the standard error of the estimate using equation \(s = \sqrt{\frac{SSE}{n-2}}\). (Round your answer to three decimal places.)

\[\boxed{\text{Answer Input}}\]

(c) Compute the estimated standard deviation of \(b_1\) using equation \(s_{b_1} = \frac{s}{\sqrt{\sum (X_i - \bar{X})^2}}\). (Round your answer to three decimal places.)

\[\boxed{\text{Answer Input}}\]

(d) Use the t test to test the following hypotheses (\(\alpha = 0.05\)):

\[
H_0: \beta_1 = 0
\]
\[
H_1: \beta_1 \ne 0
\]

Find the value of the test statistic. (Round your answer to three decimal places.)

\[\boxed{\text{Answer Input}}\]

Find the p-value. (Round your answer to four decimal places.)

\[\text{p-value} = \boxed{\text{Answer Input}}\]

State your conclusion.

\(\boxed{\text{Radio Button}} \, \text{Reject } H_0: \text{ We cannot conclude that the relationship between } x \text{ and } y \text{ is significant.}\)

\(\boxed{\text{Radio Button}} \, \text{Do not reject } H_0: \text{ We cannot conclude that the relationship between } x \text{ and } y \text{ is significant.}\)

\(\boxed{\text{Radio Button}} \, \text{Reject } H_0: \text{ We conclude that the relationship between } x \text{ and } y \text{ is significant.}\)

\(\boxed{\text{Radio Button}} \, \text{Do not reject } H_0: \
Transcribed Image Text:Consider the data provided in the following table: | \(X_i\) | 1 | 2 | 3 | 4 | 5 | |-------|---|---|---|---|---| | \(Y_i\) | 2 | 5 | 8 | 11 | 13 | (a) Compute the mean square error using equation \(\sigma^2 = \frac{SSE}{n-2}\). (Round your answer to two decimal places.) \[\boxed{\text{Answer Input}}\] (b) Compute the standard error of the estimate using equation \(s = \sqrt{\frac{SSE}{n-2}}\). (Round your answer to three decimal places.) \[\boxed{\text{Answer Input}}\] (c) Compute the estimated standard deviation of \(b_1\) using equation \(s_{b_1} = \frac{s}{\sqrt{\sum (X_i - \bar{X})^2}}\). (Round your answer to three decimal places.) \[\boxed{\text{Answer Input}}\] (d) Use the t test to test the following hypotheses (\(\alpha = 0.05\)): \[ H_0: \beta_1 = 0 \] \[ H_1: \beta_1 \ne 0 \] Find the value of the test statistic. (Round your answer to three decimal places.) \[\boxed{\text{Answer Input}}\] Find the p-value. (Round your answer to four decimal places.) \[\text{p-value} = \boxed{\text{Answer Input}}\] State your conclusion. \(\boxed{\text{Radio Button}} \, \text{Reject } H_0: \text{ We cannot conclude that the relationship between } x \text{ and } y \text{ is significant.}\) \(\boxed{\text{Radio Button}} \, \text{Do not reject } H_0: \text{ We cannot conclude that the relationship between } x \text{ and } y \text{ is significant.}\) \(\boxed{\text{Radio Button}} \, \text{Reject } H_0: \text{ We conclude that the relationship between } x \text{ and } y \text{ is significant.}\) \(\boxed{\text{Radio Button}} \, \text{Do not reject } H_0: \
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