FRM Part I · FRM Exam Part I · Regression Diagnostics
A regression has residual standard error s = 2.0. One observation has residual e = 7.0 and leverage h = 0.19. Using the internally studentized residual e / (s·√(1−h)), and a flagging cutoff of an absolute value above 3, what is the studentized residual and conclusion?
The studentized residual is 7 divided by (2 times the square root of 0.81), which is 7/1.8 = 3.89. This exceeds the cutoff of 3, so the observation is flagged as an outlier. Ignoring leverage gives 3.5, which understates it.
- A3.50, not flagged
- B3.89, flagged as an outlierCorrect
- C3.50, flagged as an outlier
- D3.89, not flagged
Explanation
√(1−0.19) = √0.81 = 0.9. Studentized residual = 7 / (2 × 0.9) = 7/1.8 = 3.89. This exceeds 3, so it is flagged. Ignoring leverage gives 3.50, the standardized residual, which understates the value.
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