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Coefficient of determination

As explained in Ensemble Methods for Machine Learning

The coefficient of determination, or R² score, is a regression metric measuring the proportion of target variance explained by a model relative to a constant-mean baseline.

The coefficient of determination, or R² score, measures how much variation in regression labels is predictable from features. It compares residual error with total label variation: R² = 1 − RSS/TSS. A perfect model scores 1, strong models approach 1, and sufficiently poor models can score below 0. section 1.3.1

Use R² to compare regression models while checking performance on unseen data:

  • Split examples into training and test subsets, then train models with different settings such as tree depth. section 1.3.1
  • Compute R² on both subsets; a large training score paired with weaker test performance signals overfitting. section 1.3.1
  • Repeat random splits and average scores to reduce the influence of a lucky or unlucky split. section 1.3.1

Comparing tree depths

On Friedman-1 regression data, evaluate decision trees with depths from 1 through 10. A validation curve with scikit-learn's scoring='r2' reports mean training and test scores across five ShuffleSplit runs. section 1.3.1

How Ensemble Methods for Machine Learning covers it

How deep it goes
Defines R² through RSS and TSS, explains negative scores, and demonstrates repeated validation without deriving the statistic further.
Examples
Uses Friedman-1 data, tree depths from 1 through 10, five random splits, and a scikit-learn validation curve.
What it assumes
Assumes regression datasets with features and labels, then reinforces training-test evaluation and regression-error concepts.
What you can do after
Evaluate regression models with R² and identify generalization problems by comparing averaged training and test scores.
How it connects
Connects regression with mean squared error, decision trees, train-test splits, cross-validation, and overfitting.
Cover of Ensemble Methods for Machine Learning
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