Regression Diagnostics
The estimation and inference from the regression model depends on several assumptions. These assumptions need to be checked using regression diagnostics.
We divide the potential problems into three categories:
- Error: 𝜀 ~ N(0, 𝜎2I); i.e. the errors are:
- Independent
- Have equal variance
- Are normally distributed
- Model: The structure part of model E[y] = Xβ is correct
- Unusual observations: Sometimes just a few observations do not fit the model but might change the choice and fit of the model
Diagnostic Techniques
- Graphical
- More flexible but harder to definitively interpret
- Numerical
- Narrower in scope but require no intution
Model building is often an interativve and interactive process. It is quite common to repeat the diagnostics on a succession of models.