Parameter

Estimate

Standard Error

t Statistic

​P-value

Intercept

45.6448945.64489

2.66062.6606

17.1617.16

less than<0.0001

Slope​ (Weight)

negative 0.00522−0.00522

0.00060.0006

negative 8.13−8.13

less than<0.0001


The data provided appears to be the output of a linear regression analysis, where the dependent variable (likely mileage, MPG) is predicted based on the independent variable (weight of the vehicles).

Here's what each parameter represents:

1. **Intercept (45.64489):** This is the estimated value of the dependent variable (mileage) when the independent variable (weight) is 0. Since a weight of 0 is not realistic for vehicles, this value is more of a baseline in the context of the regression model.

2. **Standard Error (2.6606 for Intercept, 0.0006 for Slope):** This measures the accuracy of the coefficient estimates. A smaller standard error indicates that the estimate is more reliable.

3. **t Statistic (17.16 for Intercept, -8.13 for Slope):** This is the coefficient divided by its standard error. It tells us how many standard deviations the coefficient is away from 0. A high absolute value of the t statistic suggests that the coefficient is significantly different from 0.

4. **P-value (<0.0001 for both Intercept and Slope):** This indicates the probability that the observed relationship is due to chance. A P-value of less than 0.05 (or <0.0001 in this case) suggests that the relationship is statistically significant.

5. **Slope (-0.00522):** This value indicates the change in the dependent variable (mileage) for a one-unit increase in the independent variable (weight). A negative slope of -0.00522 suggests that for every additional pound in vehicle weight, the mileage decreases by 0.00522 miles per gallon.

### Interpretation
The regression analysis shows that there is a statistically significant negative relationship between vehicle weight and mileage. Heavier vehicles tend to have lower mileage.

### Relative Questions
1. What is the significance of the intercept in a linear regression model?
2. How can you interpret the negative slope in terms of vehicle weight and mileage?
3. Why is the standard error important when evaluating the reliability of the regression coefficients?
4. What does a high t statistic indicate about a regression coefficient?
5. How would you interpret the P-value in the context of this regression analysis?
6. What could be potential reasons for a negative relationship between weight and mileage?
7. How does this regression model help in predicting the fuel efficiency of other vehicles based on their weight?
8. What could be the implications of this analysis for vehicle manufacturers?

**Tip:** When analyzing regression results, always check the significance of the coefficients (P-values) to ensure that the relationships identified by the model are not due to random chance.

Explore the results of a linear regression analysis including parameters like Intercept, Slope, Standard Error, t Statistic, and P-value. Learn how to interpret these findings and their significance in statistical modeling.

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