5. Consider the partially completed ANOVA summary table below. Source df MS Regression 1 700 Residual Total 8 1100 а. Complete the remaining entries in the table. b. Calculate the sample coefficient of determination. C. Using a=0.05, is there a significant relationship between two variables?
5. Consider the partially completed ANOVA summary table below. Source df MS Regression 1 700 Residual Total 8 1100 а. Complete the remaining entries in the table. b. Calculate the sample coefficient of determination. C. Using a=0.05, is there a significant relationship between two variables?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Question 5: ANOVA Summary Table**
Consider the partially completed ANOVA summary table below.
| Source | df | SS | MS |
|-------------|----|-----|------|
| Regression | 1 | 700 | |
| Residual | — | — | — |
| Total | 8 | 1100| |
a. Complete the remaining entries in the table.
b. Calculate the sample coefficient of determination.
c. Using α = 0.05, is there a significant relationship between two variables?
**Table Explanation:**
- **df (Degrees of Freedom):** A measure used in statistics that describes the number of independent values or quantities which can be assigned to a statistical distribution.
- **SS (Sum of Squares):** A measure that quantifies the total variation in a data set.
- **MS (Mean Square):** This is calculated by dividing the SS by its respective df. It is used to evaluate the variability of a set of data.
**Tasks:**
- **Part a:** Fill in the missing degrees of freedom for the Residual source and calculate the MS for Regression and Residual.
- **Part b:** The sample coefficient of determination (R²) can be calculated using the formula:
\[
R^2 = \frac{SS_{Regression}}{SS_{Total}}
\]
- **Part c:** Determine if the relationship is significant using a significance level of α = 0.05. This can involve calculating the F-statistic and comparing it against a critical value from the F-distribution table.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b594cb1-1c34-4228-b6c7-f688a1b5598b%2Fc014fecb-e0d3-4a06-aeb6-3acb09a307d1%2F7m5892n_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 5: ANOVA Summary Table**
Consider the partially completed ANOVA summary table below.
| Source | df | SS | MS |
|-------------|----|-----|------|
| Regression | 1 | 700 | |
| Residual | — | — | — |
| Total | 8 | 1100| |
a. Complete the remaining entries in the table.
b. Calculate the sample coefficient of determination.
c. Using α = 0.05, is there a significant relationship between two variables?
**Table Explanation:**
- **df (Degrees of Freedom):** A measure used in statistics that describes the number of independent values or quantities which can be assigned to a statistical distribution.
- **SS (Sum of Squares):** A measure that quantifies the total variation in a data set.
- **MS (Mean Square):** This is calculated by dividing the SS by its respective df. It is used to evaluate the variability of a set of data.
**Tasks:**
- **Part a:** Fill in the missing degrees of freedom for the Residual source and calculate the MS for Regression and Residual.
- **Part b:** The sample coefficient of determination (R²) can be calculated using the formula:
\[
R^2 = \frac{SS_{Regression}}{SS_{Total}}
\]
- **Part c:** Determine if the relationship is significant using a significance level of α = 0.05. This can involve calculating the F-statistic and comparing it against a critical value from the F-distribution table.
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