EasyDeepLearn

What is explained variance score and how does it differ from R2R^{2}?

hard

Answer

  • explainedvariance  =  1  −  Var⁡(y  −  yhat)  /  Var⁡(y)\mathrm{explained}_{\mathrm{variance}}\; = \;1\; - \;\operatorname{Var}(y\; - \;y_{\mathrm{hat}})\; / \;\operatorname{Var}(y).
  • It measures the fraction of variance the model captures.
  • R2  =  1  −  SSres  /  SStotR^{2}\; = \;1\; - \;\mathrm{SS}_{\mathrm{res}}\; / \;\mathrm{SS}_{\mathrm{tot}} uses the sum of squared residuals directly.
  • They are equal *only when the residuals have zero mean* (i.e., predictions are unbiased on average).
  • If predictions are systematically biased, explained variance can be high while R2R^{2} is much lower.
  • Use R2R^{2} for model comparison; use explained variance to diagnose bias-vs-variance in the errors.
Check yourself — multiple choice
  • They're always identical
  • Explained variance = 1 − Var⁡(residuals)/Var⁡(y)\operatorname{Var}(\mathrm{residuals}) / \operatorname{Var}(y); equals R2R^{2} only when residuals have zero mean
  • Explained variance is always negative
  • It's the same as MAPE

Explained variance  =  R2\mathrm{variance}\; = \;R^{2} when residuals have zero mean; otherwise diagnoses bias.

#metrics-regression

Practise Supervised Learning

215 interview questions in this topic.

Read the lessonFlashcardsTake the quiz

Related questions