Diagnose outliers and influence in linear regression
CitadelData Scientist · Technical Screen
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This question evaluates a data scientist's competency in diagnosing outliers, high-leverage points, influential observations, and Cook's distance in ordinary least squares regression, including recognition of robust alternatives and rationale for reporting model-review decisions.
In ordinary least squares, define outliers, high-leverage points, and influential observations. Derive Cook’s distance and explain its relationship to leverage and studentized residuals. Then: (1) Describe a step-by-step diagnostic workflow (plots and statistics) to detect each. (2) Show how conclusions can change if you remove the top-1 influential point, and propose robust alternatives (e.g., Huber, Tukey biweight, RANSAC). (3) Explain how to report and justify decisions about such points in a model review.
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