Coefficient of determination
The coefficient of determination, or R-squared, is a regression metric measuring the proportion of target variation explained by a fitted model relative to a mean-value baseline.
Effective Data Analysis
R2 is the proportion of variation in an outcome explained by a fitted regression model relative to a baseline model.
- How it is used
- Communicates how much outcome variation a fitted regression model explains, especially when presenting its fit to stakeholders.
- How deep it goes
- Defines and interprets R² in model summaries and contrasts it with adjusted R², without deriving a formula.
- Examples
- Interprets R² values of 0.836 for house prices and 0.588 for daily rat-sighting calls.
- What you can do after
- Evaluate/understand a regression model’s explained variation while checking other metrics and residuals before judging its fit.
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Statistics Every Programmer Needs
The coefficient of determination, commonly denoted R-squared, is a regression metric measuring the proportion of dependent-variable variance explained by a fitted model.
- How it is used
- Assesses how much observed response variation a linear regression explains and helps compare models fitted to the same data.
- How deep it goes
- Derives R² from explained and total sums of squares, works through a Python calculation, and cautions against judging fit from one statistic.
- Examples
- Uses runners’ Stage 1 and Stage 2 split times, a fitted regression line, and NumPy sums of squares yielding R² ≈ 0.575.
- What you can do after
- Evaluate/understand it by calculating R² from fitted values and observed responses, interpreting explained variation, and checking whether other diagnostics support the fit.
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Starting Data Analytics with Generative AI and Python
R2 is the proportion of variance in a dependent variable explained by a regression model's independent variables.
- How it is used
- Assesses how much variation in shipping costs regression inputs explain when comparing models based on product weight and volume.
- How deep it goes
- Defines variance explained and calculates R2 in Python, but does not derive its formula.
- Examples
- Compares freight-value models using weight, volume, and both together; also considers a retention-campaign result.
- What you can do after
- Evaluate/understand it to compare regression results without mistaking explained variation for precise individual predictions.
Causal Inference for Data Science
R squared is the coefficient of determination measuring the proportion of outcome variation explained by a model.
- How it is used
- Uses R squared to compare predictive fit while warning that fit alone cannot guide redesigned or intervention-driven settings.
- How deep it goes
- Explains model comparison with synthetic data and predictions, but stops short of treating R squared as evidence of causal usefulness.
- Examples
- Compares bonuses-only and bonuses-plus-ghosts regressions using synthetic Pac-Man level data and counterfactual-looking predictions.
- What you can do after
- Evaluate predictive models by comparing R squared with predictions under redesigned combinations of variables.
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Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI
R-squared is a goodness-of-fit metric measuring the proportion of variance in the target explained by a predictive model.
- How it is used
- Uses cross-validation predictions to assess model fit, compare approaches, and expose underfitting or overfitting.
- How deep it goes
- Defines variance captured, calculates the metric in Python, and interprets it alongside plots and error metrics; it stops short of mathematical derivation.
- Examples
- Uses Tokyo Airbnb linear-regression predictions, diagnostic plots, outlier checks, and an XGBoost-versus-fastai metric table.
- What you can do after
- Evaluate model fit and compare regressors using R-squared together with RMSE, MAE, cross-validation predictions, and diagnostic plots.
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.
- How it is used
- Evaluates regression models and helps select decision-tree depth using training and test performance.
- 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 you can do after
- Evaluate regression models with R² and identify generalization problems by comparing averaged training and test scores.
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Statistics Slam Dunk
R2, or the coefficient of determination, is the proportion of variation in a response explained by a regression model.
- How it is used
- Evaluates how much variation in NBA regular-season wins a regression model explains.
- How deep it goes
- Defines R² and adjusted R², interprets output, and stops short of deriving their formulas.
- Examples
- Uses an NBA wins model, broom output, fitted wins, and an average absolute error of 8.27 wins.
- What you can do after
- Evaluate regression fit with broom’s glance() output and distinguish raw R² from adjusted R².
Read how Statistics Slam Dunk explains coefficient of determination →
Related concepts
- linear regressionmeasures · Linear regression is a statistical modeling method that estimates a continuous response as a linear combination of predictor variables and fitted coefficients.
- correlationequivalent to · Correlation is a statistical relationship describing how two or more variables or quantities vary together, including the strength and direction of their association, without by itself implying causation.
- goodness-of-fit measuremeasures · A goodness-of-fit measure quantifies how closely a statistical model or representation agrees with observed data or specified relationships.
- adjusted r-squaredincludes · Adjusted R-squared is a regression goodness-of-fit statistic that modifies R-squared to account for the number of predictors and the sample size.
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