1) Interpret the multiple coefficient of determination R-square. 2) Compare the R-square of the simple linear regression and the R-square of the multiple regression, what does the differences in R-squares tell us? 3) What does F-test for significance tell us? ### Summary Output#### Regression Statistics- **Multiple R:** 0.925203031- **R Square:** 0.856000649- **Adjusted R Square:** 0.829000771- **Standard Error:** 6.141529119- **Observations:** 20#### ANOVA| Source | df | SS | MS | F | Significance F ||---------------|----|-------------|------------|---------|-----------------|| Regression | 3 | 3587.455921 | 1195.819 | 31.70387| 5.76336E-07 || Residual | 16 | 603.4940788 | 37.71838 | | || Total | 19 | 4190.95 | | | |#### Coefficients| Predictor | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% ||------------------|--------------|----------------|----------|---------|-------------|-------------|| Intercept | -107.5365038 | 14.71362875 | -7.30863 | 1.76E-06| -138.728003 | -76.34500423|| Age | 1.222244407 | 0.159044683 | 7.68491 | 9.3E-07 | 0.885084402 | 1.559403737 || Pressure | 0.298352084 | 0.045048505 | 6.570401 | 6.44E-06| 0.202090353 | 0.394613815 || Smoker (Yes=1) | 6.826351851 | 2.908212167 | 2.347267 | 0.032109| 0.661217468 | 12.99148623 |### Explanation of DataThis table displays the results of a multiple regression analysis. - **Regression Statistics** provide a measure of how well the regression model fits the data. - **Multiple R** is the correlation coefficient showing the strength of the relationship. - **R Square** indicates the proportion of variance explained by the

We are provided with summary output of regression as given in the question.

1) Interpret the multiple coefficient of determination R-square. 2) Compare the R-square of the simple linear regression and the R-square of the multiple regression, what does the differences in R-squares tell us? 3) What does F-test for significance tell us?

1) Interpret the multiple coefficient of determination R-square. 2) Compare the R-square of the simple linear regression and the R-square of the multiple regression, what does the differences in R-squares tell us? 3) What does F-test for significance tell us?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

1) Interpret the multiple coefficient of determination R-square.

2) Compare the R-square of the simple linear regression and the R-square of the multiple regression, what does the differences in R-squares tell us?

3) What does F-test for significance tell us?

### Summary Output

#### Regression Statistics
- **Multiple R:** 0.925203031
- **R Square:** 0.856000649
- **Adjusted R Square:** 0.829000771
- **Standard Error:** 6.141529119
- **Observations:** 20

#### ANOVA
| Source | df | SS | MS | F | Significance F |
|---------------|----|-------------|------------|---------|-----------------|
| Regression | 3 | 3587.455921 | 1195.819 | 31.70387| 5.76336E-07 |
| Residual | 16 | 603.4940788 | 37.71838 | | |
| Total | 19 | 4190.95 | | | |

#### Coefficients
| Predictor | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% |
|------------------|--------------|----------------|----------|---------|-------------|-------------|
| Intercept | -107.5365038 | 14.71362875 | -7.30863 | 1.76E-06| -138.728003 | -76.34500423|
| Age | 1.222244407 | 0.159044683 | 7.68491 | 9.3E-07 | 0.885084402 | 1.559403737 |
| Pressure | 0.298352084 | 0.045048505 | 6.570401 | 6.44E-06| 0.202090353 | 0.394613815 |
| Smoker (Yes=1) | 6.826351851 | 2.908212167 | 2.347267 | 0.032109| 0.661217468 | 12.99148623 |

### Explanation of Data

This table displays the results of a multiple regression analysis.

- **Regression Statistics** provide a measure of how well the regression model fits the data.
- **Multiple R** is the correlation coefficient showing the strength of the relationship.
- **R Square** indicates the proportion of variance explained by the

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