Deleted residual

The deleted residual is the residual value for the respective case, had it not been included in the regression analysis, that is, if one would exclude this case from all computations. If the deleted residual differs greatly from the respective standardized residual value , then this case is possibly an outlier because its exclusion changed the regression equation.
See also, standard residual value , Mahalanobis distance , and Cook's distance.

In addition to standardized residuals several methods (including studentized residuals , studentized deleted residuals, DFFITS , and standardized DFFITS ) are available for detecting outlying values (observations with extreme values on the set of predictor variables or the dependent variable). The formula for studentized deleted residuals is given by
SDRESIDi= DRESIDi/ s(i)
for
DRESID = ei/(1- i)
and where
s(i) = 1/(C-p-1)1/2 * ((C-p)s2/1-hi) - DRESIDi 2)1/2
ei is the error for the ith case
hi is the leverage for the ith case
p is the number of coefficients in the model
and
i=1/N + hi
For more information see Hocking (1996) and Ryan (1997).