Week 12: Residuals, outliers, and diagnostics (03/28/2024)

Ozlem Tuncel

otuncelgurlek1@gsu.edu

⚠️ CAUTION: DO NOT SOLELY RELY ON MY NOTES. THERE MIGHT BE TYPOS AND MISTAKES. ALWAYS TAKE YOUR NOTES!

✔️ The goal of this week is to understand the leverage, discrepancy, influence, and outliers.

Here are some key points from the lecture:

Outliers, even outside of OLS, will matter for us.
As t approaches to z as N increases, student’s t will converge to z distribution
Influence is combination of leverage and discrepancy - which shows how unusual that observation is
Most important two properties of a good estimator: unbiasedness and efficiency
- Unbiasedness (estimator is right on average) deals with our coefficients
- Efficiency deals with the variance
Outliers can mess with our estimates
Delete-1 statistics: Cook’s D, DFBETA, DFBETAS, COVRATIO
What do we do with these outliers? First, check your observation for coding mistakes. If you cannot fix it, drop it. If it is not a coding error, then you go back to theory. Not theoretically important, then feel free to drop it (if it is nonrelevant to the theory). And, make sure to add a footnote explaining your decision.