EasyDeepLearn

R2R^{2} vs adjusted R2R^{2} — when do you use each?

easy

Answer

  • R2  =  1  −  RSS/TSSR^{2}\; = \;1\; - \;\mathrm{RSS} / \mathrm{TSS}: fraction of variance explained; always increases when you add features (even garbage ones).
  • Adjusted R2  =  1  −  (1  −  R2)  ⋅  (n−1)/(n−p−1)R^{2}\; = \;1\; - \;(1\; - \;R^{2})\; \cdot \;(n - 1) / (n - p - 1): penalizes model complexity; only increases if the new feature improves fit beyond noise.
  • Use adjusted R2R^{2} to compare models with different numbers of features.
  • For prediction focus, use AIC / BIC / cross-validated R2R^{2}.
  • Warning: neither is a substitute for holdout evaluation.
Check yourself — multiple choice
  • Same thing
  • R2R^{2}: variance explained, monotone in features; Adjusted R2R^{2}: penalty for complexity, used to compare models of different sizes
  • Only adjusted matters
  • Only R2R^{2}

R2R^{2} always ↑ with features; adjusted R2R^{2} penalizes complexity.

#regression

Practise Statistics Fundamentals

215 interview questions in this topic.

Read the lessonFlashcardsTake the quiz

Related questions