Case Influence Statistics

• Leverage (measure of potential influence)
• DFBetas (measure of actual influence)
• Cook's Distance (measure of actual influence)

Toy Example to Illustrate Leverage

REAL EXAMPLE: PCB's and Estuaries Data

Let's revisit the issue of non-normal errors in the PCB data set from the takehome exam. Recall we had 37 observations with PCB measurments in ppb in 1984 and 1984. Our goal was to develop a short-term prediction model using the past year's data. In your analyses, you found two "outliers", Boston Harbor and Deleware Bay. We will take a look at this again and use some more formal methods for identifying outliers and "influential" cases.

Plots/output:

1. Simple Linear Regression with all datapoints.
2. Case Statistics (all datapoints)
3. Case Statistics (boxplots)
4. Simple Linear Regression (without Boston Harbor)
5. Simple Linear Regression with all datapoints log-log transformation
6. Case Statistics (all datapoints)
7. Case Statistics (boxplots)
8. Simple Linear Regression without Boston Harbor
9. Case Statistics (boxplots)
10. Case Statistics (without Boston Harbor)
11. Simple Linear Regression without Boston Harbor and Deleware Bay
12. Case Statistics (without Boston Harbor and Deleware Bay)

CONCLUSIONS