R-squared › Interpretation

Michael BrenndoerferApril 4, 20251 min read
Machine Learning from ScratchAll chapters
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Chapter 24R-squared › Interpretation
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  • R2=1R^2 = 1: The model explains all the variability of the response data around its mean (perfect fit).
  • R2=0R^2 = 0: The model explains none of the variability (no better than using the mean).
  • R2<0R^2 < 0: The model performs worse than simply using the mean as a predictor (rare but possible with poor models).
  • Between 0 and 1: Indicates the proportion of variance explained by the model.

Example:
If R2=0.85R^2 = 0.85, then 85% of the variance in the dependent variable is explained by the model.

Practical Guidelines

While R-squared interpretation depends on context, here are general guidelines: R2>0.9R^2 > 0.9 indicates excellent fit (though be cautious of overfitting), 0.7≤R2≤0.90.7 \leq R^2 \leq 0.9 suggests good fit, 0.5≤R2<0.70.5 \leq R^2 < 0.7 shows moderate fit, and R2<0.5R^2 < 0.5 indicates poor fit. However, these are rough guidelines.in some domains like social sciences, R2=0.3R^2 = 0.3 might be considered good, while in others like physics, R2<0.95R^2 < 0.95 might be unacceptable.