Studentized Residuals

Studentized residuals are residual values that are scaled to make them independent of the magnitude of the actual Residuals. This makes it easier to identify large errors in the estimates. Studentized residuals always have a Variance and Standard Deviation of 1. If the fitted model is correct, and basic assumptions about errors are true, then the residuals should be normally-distributed. Therefore, for a good model almost all studentized residuals should be between -3 and 3, with most between -2 and 2, and about 2/3 between -1 and 1.

If most Studentized residuals fall within these guidelines, but one or two runs stand out as poor, it may be that those runs are Outliers which should be corrected or removed. If many Studentized residuals fall outside these guidelines, then the model may not be accurate and may need more terms or a smaller range of factor values.

Troubleshooting: If the residuals are ~1e-10, then the regression is more-or-less an exact fit and many of the measures become undefined and/or lose their meaning.

The denominator is the standard error of the ith residual, so the studentized residual is the raw residual normalized by dividing by its Standard Error. This is also called the internally studentized residual. There is a variation called the externally studentized residual.