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Also known as: Coefficient of Determination
A regression goodness-of-fit measure indicating the proportion of variance in the dependent variable explained by predictors.
DESCRIPTION
The coefficient of determination (R²) summarizes how well a statistical model explains observed variability in the dependent variable. Values range from 0 to 1, with higher values indicating better fit. It can be misleading with overfitting or in nonlinear contexts. Adjusted R² penalizes unnecessary predictors, aiding model comparison. R² should be considered alongside residual diagnostics and predictive performance metrics. It is widely reported in regression analysis across science and business.
ALTERNATIVE DEFINITIONS
Wikipedia
In statistics, the coefficient of determination, denoted R2, is a measure of the proportion of variance in the dependent variable that is predictable from the independent variables.
Formal description stressing predictability and variance proportion.
Penn State Eberly College of Science
R-squared is the proportion of the variation in the response that is explained by the regression model.
Concise teaching-oriented definition highlighting explained variation.
NIST/SEMATECH e-Handbook of Statistical Methods
R-squared is the proportion of variation in the response that is explained by the regression model.
Concise engineering/statistical handbook definition focused on regression.
RELATED TERMS
Linear Model Mean Squared Error Residuals Pearson Correlation Coefficient Model Overfitting Cross-Validation Variance Analysis Prediction Interval Explained Variance Residual Analysis Goodness of Fit
COMPETING TERMS
Adjusted R-squared Explained Variance Score Akaike Information Criterion
RELATIONS
- Narrower: Adjusted R-squared
KNOWLEDGE AREAS
Data Science AI Mathematics Testing & Validation
TARGET AUDIENCE
Data Scientist AI Engineer MLOps Engineer BI Specialist Data Analyst
EXTERNAL SOURCES
- Wikipedia - Coefficient of determination
- scikit-learn - R2 scoring in model evaluation
- statsmodels - rsquared attribute reference
- NIST - Regression and residual analysis context
- Penn State STAT 501 - Course notes on R-squared
TOP QUESTIONS
When is R-Squared misleading?
With many predictors or non-linear relationships, R-squared can overstate fit. Use adjusted R-squared, cross-validation, and residual plots to validate.
Category: Mistakes
Can R-Squared be negative?
Yes. If the model performs worse than a constant baseline, R-squared can be negative, indicating poor predictive fit.
Category: Misunderstanding
How does R-Squared compare to Adjusted R-Squared?
Adjusted R-squared penalizes adding predictors, providing a more reliable comparison across models with different feature counts.
Category: Alternatives
Is a higher R-Squared always better?
Not necessarily. Overfitting can inflate R-squared without improving generalization; consider out-of-sample performance and domain needs.
Category: Opinion
How should I interpret R-Squared in time series?
Use caution; autocorrelation can bias results. Alternatives like MAPE or out-of-sample RMSE are often more meaningful.
Category: Misunderstanding
What’s a good R-Squared value?
It depends on the domain and noise level. Compare against benchmarks and use residual diagnostics to judge adequacy.
Category: Opinion
How does R-Squared relate to correlation?
For simple linear regression, R-squared equals the squared Pearson correlation between x and y.
Category: Example
Why monitor R-Squared in production models?
Shifts in R-squared can signal data drift or degraded fit. Pair with stability and residual checks.
Category: Management
What alternatives complement R-Squared?
Use MAE, RMSE, and explained variance along with residual plots and cross-validation for robust assessment.
Category: Alternatives