Studentized Deleted Residuals

The deleted residual and Studentized residual approaches can be combined for a more powerful test in a process of dividing the deleted residual, 4, by the standard deviation of the deleted residual. 

MSe) = mean square error of the regression without the /th value in the regression equation. 

in practice, the tc formula is cumbersome, because MSe, must be repeatedly calculated for each new t,. 

if the statistical software package one is using does not have the ability to perform the test, it can easily be adapted to do so. Just use the form  

Those values high in absolute terms are potential problems in the y,- values— perhaps even outliers. A formal test—a Bonferroni procedure—can be used to determine not the influence of the y, values, but whether the largest absolute values of a set of y, values may be outliers. 

---

Under the assumption that the residuals are independent, normally distributed with mean 0 and constant variance, when the sample size is large, studentized residuals greater than 2 are often identified as suspect observations. Like standardized residuals, studentized residuals are not bound by —oo and +oo, but are bounded by - /(n — p) (Gray and Woodall, 1994). An alternative statistic, one that is often erroneously interchanged with standardized residuals, are studentized deleted residuals, which are sometimes called jackknifed... 

Instead of removing a specific value, an analogy to a trim mean might be employed. Say 10% of the most extreme absolute residual values. Cook s distance values, or deleted Studentized values are simply removed this is 5% of the extreme positive residuals and 5% of the negative ones. This sort of determination helps prevent distorting the data for one s gain. 

---