## Standardized and Studentized Residuals

For linear models, the variance of the residual
*r*_{i} is

and an estimate of the standard error of the residual is

Thus, the residuals can be modified
to better detect unusual observations.
The ratio of the residual to its standard
error, called the *standardized residual*, is

If the residual is standardized with an independent estimate of
, the result has a Student's *t*
distribution if the data satisfy the normality assumption.
If you estimate by
*s*^{2}_{(i)}, the estimate
of obtained after deleting the
*i*th observation, the result is a studentized residual:

Observations with | *r*_{ti}|>2
may deserve investigation.

For generalized linear models,
the standardized and studentized residuals are

where is the
estimate of the dispersion parameter ,and is a one-step approximation of after
excluding the *i*th observation.
The standardized residuals are stored in variables named
**RS_****yname** and the Studentized residuals are stored
in variables named **RT_****yname** for each response
variable, where **yname** is the response variable name.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.