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.
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.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.2: Polynomial Functions
Problem 96E: What is the purpose of the Intermediate Value Theorem?
Related questions
Question
![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: \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F928f3826-faea-4936-b5b6-4aab28469498%2F923fa2a3-bda5-4cb9-8596-3dd107e73369%2F8ttv5u_processed.png&w=3840&q=75)
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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Step 1: Write the given information.
VIEWStep 2: Perform the regression analysis for the given data.
VIEWStep 3: Determine the MSE using the regression equation.
VIEWStep 4: Determine the standard error of estimate and estimated standard deviation.
VIEWStep 5: Perform the t test for slope significance.
VIEWStep 6: Perform F test for testing the significance of slope.
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