Regression Wisdom

1. Regression Wisdom Ch. 9

2. Linear Regression (partial) Conditions Straight Enough Condition The form of the scatterplot must be straight enough that a linear relationship makes sense Does the Plot Thicken? Condition There should be no patterns or unusual features in the residual plot

3. Appropriate Linear Regression No Pattern Pattern Pattern in the residual plot indicates that the underlying relationship is likely not linear and a linear model is likely • No pattern in the residual plot indicates that the underlying relationship may be linear and a linear model may be appropriate.

4. Warning • A linear model can be appropriate but not good • Scatter in the scatterplot of the residuals can tell us the form of the relationship • The correlation coefficient (or the original scatterplot) tells us the strength

5. Emperor Penguins The most accomplished diving birds Tallest and heaviest penguin Adorable

6. Dive Heart Rate vs. Dive Duration

7. RESIDUALS!!! • No regression analysis is complete without a display of the residuals • Residuals plots can • Check that a linear model is reasonable • Reveal subtleties that were not clear in the plot of the original data • Help confirm or refine our understanding

8. Da Bears

9. Da Bears

10. Da Bears

11. Da Bears Residuals

12. Da Cubs

13. Regression Model With Old Bear Without Old Bear

14. Outliers, Leverage, and Influence • Outlier – a point separated from the bulk of the data • Often a data value with a large residual • Leverage – a data point that is far from the mean of the x-values • Often a data value with a low residual • Influential – a data point that results in a meaningful difference in the model when omitted

15. Da Bears

16. Da Bears Residuals