Studentized residuals differ from standardized residuals in that they ...

• A. Use an estimate of standard deviation that varies from case to case, usually providing a more precise error variance.
• B. Are always identical to standardized residuals.
• C. Are computed by dividing by the overall standard deviation.
• D. Are not used in regression diagnostics.

Answer: (C)

The key idea is how you scale a residual to judge whether an observation is an outlier. Standardized residuals do the scaling with a single, model-wide estimate of the residual standard deviation, so every observation is divided by the same overall standard error. In contrast, studentized residuals use a standard deviation that varies for each case. Specifically, the standard deviation used in the division is computed with the observation either left out (externally studentized) or adjusted for that observation’s leverage (internally studentized). Because this denominator can differ from case to case, the resulting studentized residual tells you how many case-specific standard error units the residual is away from what would be expected if that observation weren’t influencing the estimate. This case-by-case scaling often provides a more precise assessment of outliers, especially for high-leverage points. The description of dividing by the overall standard deviation fits standardized residuals, not studentized residuals.