Track 9 · Correlation and Regression · Lesson 12 of 15
Outliers, leverage and influence
Distinguish outliers, high-leverage points and influential points, measure them with leverage, studentized residuals and Cook's distance, and decide what to do about them.
35 minAdvanced7 graded exercisesMembers
One unusually committed runner trains over 100 km a week — far more than anyone else in the club. Does that one person shape the club's estimate of how training relates to race times? A single observation can tilt a regression line, and good analysts check which points the conclusions depend on before reporting them.
Three different ideas are often lumped together as “outliers”:
- An outlier in regression is a point with a large residual: its is far from what the model predicts for its .
- A high-leverage point has an unusual (or an unusual combination of predictors). It sits far from the centre of the predictor values, so the line is free to pivot towards it.
- An influential point is one whose removal changes the fitted model noticeably. Influence needs both some leverage and some departure from the pattern of the other points.
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It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Distinguish an outlier (large residual), a high-leverage point (unusual x) and an influential point
- Calculate leverage and read studentized residuals and Cook's distance
- Check how much a fit changes when an influential point is removed
- Decide what to do with unusual points without deleting inconvenient data