The ANOVA summary table to the right is for a multiple regression model with six independent variables. Complete parts (a) through (e). d. Compute the coefficient of multiple determination, r², and interpret its meaning. 2 = (Round to four decimal places as needed.) Interpret the meaning of the coefficient of multiple determination. The coefficient of multiple determination indicates that% of the variation in the variables. (Round to two decimal places as needed.) e. Compute the adjusted r². (Round to four decimal places as needed.) Source Regression Error Total Degrees of Sum of Freedom Squares 240 190 430 6 26 32 variable can be explained by the variation in the
The ANOVA summary table to the right is for a multiple regression model with six independent variables. Complete parts (a) through (e). d. Compute the coefficient of multiple determination, r², and interpret its meaning. 2 = (Round to four decimal places as needed.) Interpret the meaning of the coefficient of multiple determination. The coefficient of multiple determination indicates that% of the variation in the variables. (Round to two decimal places as needed.) e. Compute the adjusted r². (Round to four decimal places as needed.) Source Regression Error Total Degrees of Sum of Freedom Squares 240 190 430 6 26 32 variable can be explained by the variation in the
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Transcribed Image Text:The ANOVA summary table on the right is for a multiple regression model with six independent variables. Complete parts (a) through (e).
| Source | Degrees of Freedom | Sum of Squares |
|-------------|--------------------|----------------|
| Regression | 6 | 240 |
| Error | 26 | 190 |
| Total | 32 | 430 |
---
**Draw a conclusion. Choose the correct answer below.**
- **A.** There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is less than the critical value.
- **B.** There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the p-value is less than the level of significance.
- **C.** There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the level of significance.
- **D.** There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the critical value.
![**ANOVA Summary Table and Calculation of Coefficient of Determination**
The ANOVA summary table provided is for a multiple regression model with six independent variables. Here are the parts requiring completion:
**ANOVA Summary Table:**
- **Source:**
- Regression
- Error
- Total
- **Degrees of Freedom:**
- Regression: 6
- Error: 26
- Total: 32
- **Sum of Squares:**
- Regression: 240
- Error: 190
- Total: 430
**Task (d): Compute the coefficient of multiple determination, \( r^2 \), and interpret its meaning.**
- Formula to compute \( r^2 \):
\[
r^2 = \frac{\text{Sum of Squares for Regression}}{\text{Total Sum of Squares}}
\]
- Interpretation:
- The coefficient of multiple determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variables.
- Boxes to complete:
- \( r^2 = \text{[ ] (Round to four decimal places as needed.)} \)
- The coefficient of multiple determination indicates that [ ]% of the variation in the [dependent variable] can be explained by the variation in the [independent variables].
- (Round to two decimal places as needed.)
**Task (e): Compute the adjusted \( r^2 \).**
- Adjusted \( r^2 \) formula takes into account the number of predictors in the model and the number of data points:
\[
r^2_{adj} = 1 - \left(\frac{(1 - r^2)(\text{Total Degrees of Freedom})}{\text{Total Degrees of Freedom} - \text{Number of Predictors} - 1}\right)
\]
- Box to complete:
- \( r^2_{adj} = \text{[ ] (Round to four decimal places as needed.)} \)
Understanding and computing \( r^2 \) and adjusted \( r^2 \) provides insight into the effectiveness of the regression model in explaining the variability of the response data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc91d435c-8a20-4fa9-b80f-5aaeb9e13244%2Fd4d710b9-56b4-4212-87fd-2352072725e6%2F7lcmy8o_processed.png&w=3840&q=75)
Transcribed Image Text:**ANOVA Summary Table and Calculation of Coefficient of Determination**
The ANOVA summary table provided is for a multiple regression model with six independent variables. Here are the parts requiring completion:
**ANOVA Summary Table:**
- **Source:**
- Regression
- Error
- Total
- **Degrees of Freedom:**
- Regression: 6
- Error: 26
- Total: 32
- **Sum of Squares:**
- Regression: 240
- Error: 190
- Total: 430
**Task (d): Compute the coefficient of multiple determination, \( r^2 \), and interpret its meaning.**
- Formula to compute \( r^2 \):
\[
r^2 = \frac{\text{Sum of Squares for Regression}}{\text{Total Sum of Squares}}
\]
- Interpretation:
- The coefficient of multiple determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variables.
- Boxes to complete:
- \( r^2 = \text{[ ] (Round to four decimal places as needed.)} \)
- The coefficient of multiple determination indicates that [ ]% of the variation in the [dependent variable] can be explained by the variation in the [independent variables].
- (Round to two decimal places as needed.)
**Task (e): Compute the adjusted \( r^2 \).**
- Adjusted \( r^2 \) formula takes into account the number of predictors in the model and the number of data points:
\[
r^2_{adj} = 1 - \left(\frac{(1 - r^2)(\text{Total Degrees of Freedom})}{\text{Total Degrees of Freedom} - \text{Number of Predictors} - 1}\right)
\]
- Box to complete:
- \( r^2_{adj} = \text{[ ] (Round to four decimal places as needed.)} \)
Understanding and computing \( r^2 \) and adjusted \( r^2 \) provides insight into the effectiveness of the regression model in explaining the variability of the response data.
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