In statistics question 1 of attached image, is the ANOVA table values correct, and does it show model insignificant?

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In statistics question 1 of attached image, is the ANOVA table values correct, and does it show model insignificant?
# Regression Analysis Exercise

This exercise involves a regression analysis with 18 observations and four independent variables. The following details were obtained:

- **Multiple R**: 0.6000
- **R Square**: 0.3600
- **Standard Error**: 4.8000

Based on the above information, the following ANOVA (Analysis of Variance) table needs to be completed and analyzed:

## ANOVA Table

| Source      | df   | SS     | MS      | F      |
|-------------|------|--------|---------|--------|
| Regression  | 4    | 168.48 | 42.12   | 1.828  |
| Error       | 13   | 299.52 | 23.04   |        |
| Total       | 17   | 468    |         |        |

- **df (Degrees of Freedom)**: Calculated as follows:
  - Regression: k = 4
  - Error: n - k - 1 = 13
  - Total: n - 1 = 17

- **SS (Sum of Squares)**:
  - Regression: 168.48
  - Error: 299.52
  - Total: 468

- **MS (Mean Square)**:
  - Regression: MSR = SSR/df = 168.48/4 = 42.12
  - Error: MSE = SSE/df = 299.52/13 = 23.04

- **F Ratio**:
  - F = MSR/MSE = 42.12/23.04 = 1.828

- **F Critical Value**: 3.179 (from F-distribution table with degree of freedom (4, 13) at α = 0.05)

- **Significance**: The model is not significant because the F statistic (1.828) < F critical value (3.179).

### Further Calculations

1. **Multiple Regression Analysis** with 31 observations and the regression analysis output is as follows:

| Coefficients | Standard Error |
|--------------|----------------|
| Intercept    | 18.00          | 8.00           |
| X1           | 6.40           | 2.35           |
| X2           | 0.60           | 1.00           |
|
Transcribed Image Text:# Regression Analysis Exercise This exercise involves a regression analysis with 18 observations and four independent variables. The following details were obtained: - **Multiple R**: 0.6000 - **R Square**: 0.3600 - **Standard Error**: 4.8000 Based on the above information, the following ANOVA (Analysis of Variance) table needs to be completed and analyzed: ## ANOVA Table | Source | df | SS | MS | F | |-------------|------|--------|---------|--------| | Regression | 4 | 168.48 | 42.12 | 1.828 | | Error | 13 | 299.52 | 23.04 | | | Total | 17 | 468 | | | - **df (Degrees of Freedom)**: Calculated as follows: - Regression: k = 4 - Error: n - k - 1 = 13 - Total: n - 1 = 17 - **SS (Sum of Squares)**: - Regression: 168.48 - Error: 299.52 - Total: 468 - **MS (Mean Square)**: - Regression: MSR = SSR/df = 168.48/4 = 42.12 - Error: MSE = SSE/df = 299.52/13 = 23.04 - **F Ratio**: - F = MSR/MSE = 42.12/23.04 = 1.828 - **F Critical Value**: 3.179 (from F-distribution table with degree of freedom (4, 13) at α = 0.05) - **Significance**: The model is not significant because the F statistic (1.828) < F critical value (3.179). ### Further Calculations 1. **Multiple Regression Analysis** with 31 observations and the regression analysis output is as follows: | Coefficients | Standard Error | |--------------|----------------| | Intercept | 18.00 | 8.00 | | X1 | 6.40 | 2.35 | | X2 | 0.60 | 1.00 | |
Expert Solution
Step 1: Solution:

1) Given information:

n= 18 observation 

k= 4 independent variables 

R squared equals 0.3600
s tan d a r d space e r r o r space equals s equals 4.8000

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