Chapter 3: Describing Relationships

1. Q: What does an association between groups indicate in a distribution?
A: Differences in distribution indicate an association.

2. Q: How do you display two quantitative variables graphically?
A: Use a scatter plot, with the explanatory variable on the x-axis and the response variable on the y-axis, labeling the axes with units.

3. Q: What is correlation?
A: Correlation quantifies the strength and direction of a linear relationship, ranging from -1 (strong negative) to 1 (strong positive).

4. Q: What does a residual represent?
A: The difference between the actual response value and the predicted value from the model.

5. Q: How can residuals indicate model fit?
A: A residual plot with no pattern suggests the linear model is a good fit; a pattern suggests it is not.

6. Q: What is the Least Squares Regression Line (LSRL)?
A: A linear model minimizing the sum of squared residuals, ensuring the smallest possible error.

7. Q: What point does the LSRL always pass through?
A: (xˉ,yˉ)(\bar{x}, \bar{y})(xˉ,yˉ​), where xˉ\bar{x}xˉ and yˉ\bar{y}yˉ​ are the average x and y values.

8. Q: How is the slope of the LSRL interpreted?
A: For every unit increase in the explanatory variable, the model predicts an average increase or decrease (equal to the slope) in the response variable.

9. Q: How is the y-intercept of the LSRL interpreted?
A: When the explanatory variable is 0, the predicted value of the response variable is the y-intercept (though it may not always be meaningful in context).

10. Q: What is the coefficient of determination (R2R^2R2)?
A: It represents the proportion of variation in the response variable explained by the explanatory variable in the model.

11. Q: What does high leverage indicate in a data point?
A: A point far from xˉ\bar{x}xˉ (mean of x values) that can strongly affect the slope and position of the LSRL.

12. Q: What impact do outliers have in regression?
A: Outliers can significantly affect both correlation and the regression line.

13. Q: What is extrapolation, and why is it risky?
A: Making predictions outside the data's range, which may be unreliable as trends might not continue.

14. Q: How does the residual plot help assess a model?
A: It highlights possible trends in residuals, making it easier to evaluate model fit.

15. Q: What is the purpose of summing squared residuals in LSRL?
A: It minimizes the sum of squared errors to find the line of best fit.