2.2 Standardized Residuals

Standardized residuals, allow the residuals to be compared on the ``standard scale''. Plus/Minus 2 indicates something unusual, Plus/Minus 3 indicates something really out of the ordinary and Plus/Minus 4 is something from outer space (it just shouldn't happen).

Subtle point

Problem. The standardized residuals, s_i, still start off with $y_i - \hat y_i$ and the problem is that if y_i is really leveraged then it will drag the regression line toward it, influencing the estimate of the residual itself.

Solution. Fit the regression line excluding y_i and base the residual on $y_i - \hat y_{i,(-i)}$, where $\hat y_{i,(-i)}$ denotes the fit based on a regression line estimated excluding y_i.

This idea leads to the studentized residuals.