In statistics question 1 of attached image, is the ANOVA table values correct, and does it show model insignificant?
In statistics question 1 of attached image, is the ANOVA table values correct, and does it show model insignificant?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
In statistics question 1 of attached image, is the ANOVA table values correct, and does it show model insignificant?

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
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Step 1: Solution:
1) Given information:
n= 18 observation
k= 4 independent variables
Step by step
Solved in 3 steps with 9 images
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