MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Looking at this output in the photo, we know that the proportion of the variation in mileage is accounted for by the linear relationship with the weight of the car is 43.8 % and that the estimate of the regression standard deviationis is 6.78.
Determine the equation of the Least Squares Regression Line and what the interpretation of the slope for weight of car is? Then performing a T-test, determine what the value of the t stastitic is if we wanted to test if there is a significant straight-line relationship between the weight and the mileage of a car.
Transcribed Image Text:**Regression Analysis Overview**
In this regression summary, we assess the relationship between the dependent variable and an independent variable, WEIGHT. The output provides key statistics necessary to understand the model's effectiveness and significance:
1. **R-Square:** 0.438
- This value, also known as the coefficient of determination, indicates that approximately 43.8% of the variance in the dependent variable can be explained by the model.
2. **Root MSE:** 6.78
- The Root Mean Square Error measures the standard deviation of the residuals, offering insight into how well the model predicts the dependent variable.
**Parameter Estimates Table:**
| Parameter | Estimate | Standard Error | t Value | Pr > |t| |
|------------|----------|----------------|---------|-------|
| Intercept | 40.439 | 6.275 | 6.445 | 0.0000 |
| WEIGHT | -0.521 | 0.164 | -3.182 | 0.0072 |
- **Intercept:**
- Estimate: 40.439
- Standard Error: 6.275
- t Value: 6.445
- Pr > |t|: 0.0000
- The intercept is significant at the 0.0000 level, indicating it is a crucial model component.
- **WEIGHT:**
- Estimate: -0.521
- Standard Error: 0.164
- t Value: -3.182
- Pr > |t|: 0.0072
- The coefficient for WEIGHT is statistically significant (p = 0.0072), suggesting a negative relationship with the dependent variable.
This analysis highlights the statistically significant impact of WEIGHT on the dependent variable, providing a foundation for further exploration of the model and its assumptions.
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