Diagnose outliers and influence in linear regression

Give definitions for outliers, high-leverage points, and influential observations in ordinary least squares. Derive Cook's distance and describe its relationship to leverage and studentized residuals. Then: (1) Lay out a step-by-step diagnostic workflow, including plots and statistics, for detecting each. (2) Illustrate how conclusions can change when the top-1 influential point is removed, and suggest robust alternatives (e.g., Huber, Tukey biweight, RANSAC). (3) Explain how to document and justify decisions about such points in a model review.

Overview: This question assesses a data scientist's skill in diagnosing outliers, high-leverage points, influential observations, and Cook's distance in OLS regression, as well as recognizing robust alternatives and the rationale for reporting model-review decisions.