Given the following ANOVA table: Mean Degrees Source of of Variance Freedom Sum of Sum of F-stat Squares Squares Regression 5.4 Residual 48 2.507 Total What is the value of MSR? Please report your answer in 3 decimal places.

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### ANOVA Table

Given the following ANOVA table:

| Source of Variance | Degrees of Freedom | Sum of Squares | Mean Sum of Squares | F-stat |
|--------------------|--------------------|----------------|---------------------|--------|
| Regression         |                    |                |                     | 5.4    |
| Residual           | 48                 | 2.507          |                     |        |
| Total              |                    |                |                     |        |

**Question:**
What is the value of MSR? Please report your answer in 3 decimal places.

This table is used to perform an Analysis of Variance (ANOVA), which helps to find the significance of one or more categorical independent variables on a continuous dependent variable. The table shows the breakdown of variance into different components: Regression and Residual (also known as Error).

- **Degrees of Freedom (DF):** This indicates the number of independent values or quantities that can vary in the analysis.
- **Sum of Squares (SS):** This is a measure of variance; it quantifies how much the data points differ from the mean.
- **Mean Sum of Squares (MS):** This is obtained by dividing the Sum of Squares by the corresponding Degrees of Freedom.
- **F-statistic (F-stat):** This is used to determine if the variance between the means of the groups is significantly different.

To calculate **MSR (Mean Sum of Squares for Regression)**, you need:
- Degrees of Freedom for Regression (DFR)
- Sum of Squares for Regression (SSR)

MSR is calculated as:
\[ \text{MSR} = \frac{\text{SSR}}{\text{DFR}} \]

However, since neither the DFR nor the SSR are given, some of this necessary information would need to be inferred or provided to solve entirely.
Transcribed Image Text:### ANOVA Table Given the following ANOVA table: | Source of Variance | Degrees of Freedom | Sum of Squares | Mean Sum of Squares | F-stat | |--------------------|--------------------|----------------|---------------------|--------| | Regression | | | | 5.4 | | Residual | 48 | 2.507 | | | | Total | | | | | **Question:** What is the value of MSR? Please report your answer in 3 decimal places. This table is used to perform an Analysis of Variance (ANOVA), which helps to find the significance of one or more categorical independent variables on a continuous dependent variable. The table shows the breakdown of variance into different components: Regression and Residual (also known as Error). - **Degrees of Freedom (DF):** This indicates the number of independent values or quantities that can vary in the analysis. - **Sum of Squares (SS):** This is a measure of variance; it quantifies how much the data points differ from the mean. - **Mean Sum of Squares (MS):** This is obtained by dividing the Sum of Squares by the corresponding Degrees of Freedom. - **F-statistic (F-stat):** This is used to determine if the variance between the means of the groups is significantly different. To calculate **MSR (Mean Sum of Squares for Regression)**, you need: - Degrees of Freedom for Regression (DFR) - Sum of Squares for Regression (SSR) MSR is calculated as: \[ \text{MSR} = \frac{\text{SSR}}{\text{DFR}} \] However, since neither the DFR nor the SSR are given, some of this necessary information would need to be inferred or provided to solve entirely.
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