# Raw residuals versus standardised residuals versus studentised residuals - what to use when?

This looks like a similar question and didn't get many responses.

Omitting tests such as Cook's D, and just looking at residuals as a group, I am interested in how others use residuals when assessing goodness-of-fit. I use the raw residuals:

1. in a QQ-plot, for assessing normality
2. in a scatterplot of $y$ versus residuals, for eyeball check of (a) hetereoscedasticity and (b) serial autocorrelation.

For plotting $y$ versus residuals to examine the values for $y$ where outliers may occur, I prefer to use the studentized residuals. The reason for my preference is that it allows easy viewing of which residuals at which $y$-values are problematic, although standardised residuals provide an extremely similar result. My theory on which is used is that it depends on which university one went to.

Is this similar to how others use residuals? Do others use this number of graphs in combination with summary statistics?

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Studentized residuals are udoubtedly better in detecting outliers, and, maybe, a little bit better in heteroscedasticity inspection. For other purposes, it makes no difference for me what residuals to use. – ttnphns Feb 12 '12 at 6:04
To bring attention to a question, Michelle, or ask for a change in its status (such as CW), please follow the "flag" link beneath the question. This will automatically notify all moderators. Embedding requests in questions, comments, or replies is hit-or-miss because it relies on the hope a moderator (or other high-rep user) will actually read it within a reasonable time! – whuber Feb 16 '12 at 15:28
@whuber Ah, see I did think one of you would read it eventually. :) Thanks for the tip on using flags. – Michelle Feb 16 '12 at 19:23
Hi @ttnphns Why would they be better? In particular, why would studentized be better than standardized? (I've never really known the answer here) – Peter Flom Oct 4 '12 at 19:12
@Peter, Studentized residuals are less "distorted" by the OLS fitting algo and are closer to theoretical notion of "errors". They can be directly compared at different regions of the fit line, thence are better in decision if a point is an outlier. – ttnphns Oct 5 '12 at 6:58

Re: plots,

There is such a thing as overfitting, but overplotting cannot really do much harm, especially at diagnostics stage. A standardized normal probability plot cannot hurt next to your QQ-plot. I find it better to assess the middle of the distribution.

Re: residuals,

I run both standardized and studentized residuals at draft stage and usually end up coding the standardized ones. I don't know what other people actually run, because diagnostics are really coded down in the replication material that I find online.

Re: diagnostics,

For a linear model, I usually add variance inflation factors (with the vif command in Stata) and a few homoscedasticity tests (e.g. with the hettest command in Stata), as well as model decomposition with nested regression to check if the $R^2$ makes any sense.

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