MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Suppose the number of seconds required to accelerate to 60 mph depends on both a car’s weight, its horsepower, and an interaction term between the two variables.

Describe why an interaction term could be appropriate for the variables in this model and construct three linear relationships between acceleration time and weight, each for a different assumed value of horsepower.

 

### Summary Output

#### Regression Statistics
- **Multiple R:** 0.856730669
- **R Square:** 0.733987439
- **Adjusted R Square:** 0.687044045
- **Standard Error:** 2.967605917
- **Observations:** 21

#### Analysis of Variance (ANOVA)

|          | df | SS         | MS         | F          | Significance F      |
|----------|----|------------|------------|------------|---------------------|
| Regression | 3  | 413.0930237 | 137.6976746 | 15.63558552 | 3.87427E-05         |
| Residual   | 17 | 149.7136429 | 8.806688479 |            |                     |
| Total      | 20 | 562.8066667 |            |            |                     |

#### Coefficients

|              | Coefficients   | Standard Error | t Stat      | P-value       |
|--------------|----------------|----------------|-------------|---------------|
| Intercept    | 25.41936066    | 4.338034616    | 5.859649107 | 1.89327E-05   |
| hp           | -0.161091493   | 0.035506341    | -4.536978136 | 0.000291759  |
| curbwt       | -0.000302296   | 0.002232767    | -0.135390557 | 0.893893295  |
| hp*curbwt    | 2.8177E-05     | 9.4596E-06     | 2.978662513 | 0.008429352  |

### Explanation

This output is from a multiple regression analysis, indicating the relationship between a dependent variable and several independent variables. 

- **Multiple R** and **R Square** indicate the strength and proportion of variance explained by the model.
- **Adjusted R Square** accounts for the number of predictors in the model.
- **ANOVA** table shows the breakdown of variances, with a significant F-statistic suggesting the model is a good fit.
- **Coefficients** table provides the estimated impact of each predictor, with associated statistical tests. Lower p-values suggest significant contributions to the model.
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Transcribed Image Text:### Summary Output #### Regression Statistics - **Multiple R:** 0.856730669 - **R Square:** 0.733987439 - **Adjusted R Square:** 0.687044045 - **Standard Error:** 2.967605917 - **Observations:** 21 #### Analysis of Variance (ANOVA) | | df | SS | MS | F | Significance F | |----------|----|------------|------------|------------|---------------------| | Regression | 3 | 413.0930237 | 137.6976746 | 15.63558552 | 3.87427E-05 | | Residual | 17 | 149.7136429 | 8.806688479 | | | | Total | 20 | 562.8066667 | | | | #### Coefficients | | Coefficients | Standard Error | t Stat | P-value | |--------------|----------------|----------------|-------------|---------------| | Intercept | 25.41936066 | 4.338034616 | 5.859649107 | 1.89327E-05 | | hp | -0.161091493 | 0.035506341 | -4.536978136 | 0.000291759 | | curbwt | -0.000302296 | 0.002232767 | -0.135390557 | 0.893893295 | | hp*curbwt | 2.8177E-05 | 9.4596E-06 | 2.978662513 | 0.008429352 | ### Explanation This output is from a multiple regression analysis, indicating the relationship between a dependent variable and several independent variables. - **Multiple R** and **R Square** indicate the strength and proportion of variance explained by the model. - **Adjusted R Square** accounts for the number of predictors in the model. - **ANOVA** table shows the breakdown of variances, with a significant F-statistic suggesting the model is a good fit. - **Coefficients** table provides the estimated impact of each predictor, with associated statistical tests. Lower p-values suggest significant contributions to the model.
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