Refer to the ANOVA table below. Source Regression Error Total d.f 4 45 49 SS 259,412 224,539 483,951 MS 64,853 4,990

MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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  1. State the degrees of freedom for the F test for the overall significance.
  2. Use Appendix F to look up the critical value of F for a = .05.
  3. Calculate the F statistic.  Is the regression significant overall?
The table below is an ANOVA (Analysis of Variance) table used to analyze the differences among group means in a sample.

| **Source**    | **d.f** | **SS**  | **MS**  |
|---------------|---------|---------|---------|
| Regression    | 4       | 259,412 | 64,853  |
| Error         | 45      | 224,539 | 4,990   |
| Total         | 49      | 483,951 |         |

### Explanation:

- **Source:** This column indicates the sources of variability. The sources listed are "Regression," "Error," and "Total."

- **d.f (degrees of freedom):** This column represents the degrees of freedom associated with each source. For regression, the degrees of freedom are 4, for error it is 45, and the total degrees of freedom is 49.

- **SS (Sum of Squares):** This column shows the sum of squares for each source. It measures the total variability. The sum of squares for regression is 259,412, for error it is 224,539, and the total sum of squares is 483,951.

- **MS (Mean Square):** This column provides the mean square for each source, which is calculated by dividing the sum of squares by the corresponding degrees of freedom. The mean square for regression is 64,853 and for error is 4,990. The mean square for the total is not calculated in this table.

This table helps in identifying how much of the total variability can be explained by the model (regression) versus what cannot be explained (error).
Transcribed Image Text:The table below is an ANOVA (Analysis of Variance) table used to analyze the differences among group means in a sample. | **Source** | **d.f** | **SS** | **MS** | |---------------|---------|---------|---------| | Regression | 4 | 259,412 | 64,853 | | Error | 45 | 224,539 | 4,990 | | Total | 49 | 483,951 | | ### Explanation: - **Source:** This column indicates the sources of variability. The sources listed are "Regression," "Error," and "Total." - **d.f (degrees of freedom):** This column represents the degrees of freedom associated with each source. For regression, the degrees of freedom are 4, for error it is 45, and the total degrees of freedom is 49. - **SS (Sum of Squares):** This column shows the sum of squares for each source. It measures the total variability. The sum of squares for regression is 259,412, for error it is 224,539, and the total sum of squares is 483,951. - **MS (Mean Square):** This column provides the mean square for each source, which is calculated by dividing the sum of squares by the corresponding degrees of freedom. The mean square for regression is 64,853 and for error is 4,990. The mean square for the total is not calculated in this table. This table helps in identifying how much of the total variability can be explained by the model (regression) versus what cannot be explained (error).
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