Theory and illustration of regression influence diagnostics

Regression diagnostics are an important tool of the professional statistician, and they are neglected at one's peril. Deletion and local influence diagnostics (see Cook 1977, 1986 for origins) relevant to Normal linear regression are considered here, as these are in most common use. The presentation extends beyond the traditional parameter estimate influence to indicate the possibilities for model test influence and model goodness of fit influence, both also based on familiar uses of the likelihood. Two real-life data sets are presented and analysed using some of the more traditional diagnostics.