= Solution
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. \b[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.
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