Week 12: Residuals, outliers, and diagnostics (04/06/2023)

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.
$H$ is a matrix (see slides)
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
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.