Using linear regression to identify data points with significant influence

It is not unusual to find that a few observations have a surprisingly high degree of influence on our model, our parameter estimates, and our predictions. This may or may not be desirable. Observations with significant influence may be unhelpful if they reflect a different social or natural process than the rest of the data does. For example, let's say we have a dataset of flying animals that migrate a great distance, and this is almost exclusively bird species, except for data on monarch butterflies. If we are using the wing architecture as a predictor of migration distance, the monarch butterfly data should probably be removed.

We should return to the distinction we made in the first section between an extreme value and an outlier. We mentioned that an outlier can be thought of as an observation with feature values, or relationships between feature values, that are so unusual that they cannot help...