Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 37 / 1 / e

The largest positive regression residual divided by the residual standard error is about $26.6071/5.942=4.48$, $24.7151/5.710=4.33$, and $24.5908/5.737=4.29$ in the three models. In comparison, the most negative regression residual is only about two residual standard errors below zero. At least one observation is much heavier than its fitted value, even after adjusting for sex and height.

A standardized regression residual is $e_i/[s\sqrt{1-h_{ii}}]$, so the regression leverage adjustment can make these ratios larger. The maximum is selected among 100 correlated regression residuals, however; it is not a prespecified single standard-normal observation. These summaries do not give a formal regression outlier test or identify which student is extreme. Ask to check the measurement and data entry, examine residual plots and a normal quantile-quantile plot, and inspect regression leverage and influential observations. A valid observation might reveal a heavier-tailed error distribution, an omitted predictor, or a nonlinear relation. Do not remove it solely because it is unusual, and do not infer from the three summaries alone that all three maxima belong to the same student.