Often times a statistical analyst is handed a set dataset and asked to fit a model using a technique such as linear regression. Very frequently the dataset is accompanied with a disclaimer similar to "Oh yeah, we messed up collecting some of these data points -- do what you can".
This situation leads to regression fits that are heavily impacted by the presence of outliers that may be erroneous data. Given the following:
It is dangerous from both a scientific and moral standpoint to throw out data for no reason other than it "makes the fit look bad".
In real life, the people who collected the data are frequently not available to answer questions such as "when generating this data set, which of the points did you mess up, exactly?"
What statistical tests or rules of thumb can be used as a basis for excluding outliers in linear regression analysis?
Are there any special considerations for multilinear regression?