# Why is R plotting standardized residuals against theoretical quantiles in a Q-Q plot?

In R, why do the default settings of qqplot(linear model) use the standardized residuals on the y-axis? Why doesn't R use the "regular" residuals?

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When you use the standardized residuals, the expected value of the residuals is zero and the variance is (approximately) one. This has two benefits:

1. If you rescale one of your variables (say change kilometres to miles), the residual plots remain unchanged.
2. In the qqplot, the residuals should lie on the line y = x
3. You expect 95% of your residuals to lie between -1.96 and 1.96. This makes it easier to spot outliers.
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Could you please give me a reference, that 95% should lie between -1.96;1.96 . In other words, why should standardized residuals be $d_i\sim N(0,1)$? – MarkDollar Jul 7 '11 at 15:42
@Mark: Just google "standardised residuals" and look at the first few hits. – csgillespie Jul 8 '11 at 9:29

The theoretical residuals in a linear model are independent identically normally distributed. However the observed residuals are not independent and do not have equal variances. So standardizing the residuals divides by the estimated standard deviation associated with that residual making them more equal in their variances (using information from the hat matrix to compute this). This is a more meaningful residual to look at in the qqplot.

Also, are you really running qqplot on the fitted model? or is this the qqplot from runing plot on the model?

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Hey! I'm talking about the qqplot from running plot(>lm<). Thanks for your answer. I'd like to give cs the mark, because his answer was faster. I hope that is ok for you :) – MarkDollar Jun 27 '11 at 20:28