Python - Coefficient of Determination-R2 score Last Updated : 13 Aug, 2025 Comments Improve Suggest changes Like Article Like Report The Coefficient of determination, also called R² score, is used to evaluate the performance of a linear regression model. It is the amount of the variation in the output dependent attribute that is predictable from the input independent variable(s). It is used to check how well-observed results are reproduced by the model, depending on the ratio of the total deviation of results described by the model. Mathematical Formula:R2= 1- \frac{SS_{res}}{SS_{tot}}Where, SS_{res} is the sum of squares of the residual errorsSS_{tot} is the total sum of the errorsInterpretation of R2 score Assume R2 = 0.68. It can be inferred that 68% of the changeability of the dependent output attribute can be explained by the model, while the remaining 32 % of the variability is still unaccounted for. R2 indicates the proportion of data points that lie within the line created by the regression equation. A higher value of R2 is desirable as it indicates better results. ExamplesCase 1 (Model gives accurate results):R^2 = 1 - \frac{0}{200} = 1Case 2 (Model gives same results always):R^2 = 1 - \frac{200}{200} = 0Case 3 (Model gives ambiguous results):R^2 = 1 - \frac{600}{200} = -2We can import r2_score from sklearn.metrics in Python to compute R2 score.Python ImplementationStep 1: Import r2_score from sklearn.metrics Python from sklearn.metrics import r2_score Step 2: Calculate R2 score for all the above cases. Python ### Assume y is the actual value and f is the predicted values y =[10, 20, 30] f =[10, 20, 30] r2 = r2_score(y, f) print('r2 score for perfect model is', r2) Output:r2 score for perfect model is 1.0 Python ### Assume y is the actual value and f is the predicted values y =[10, 20, 30] f =[20, 20, 20] r2 = r2_score(y, f) print('r2 score for a model which predicts mean value always is', r2) Output:r2 score for a model which predicts mean value always is 0.0Code 3: Python ### Assume y is the actual value and f is the predicted values y = [10, 20, 30] f = [30, 10, 20] r2 = r2_score(y, f) print('r2 score for a worse model is', r2) Output:r2 score for a worse model is -2.0ConclusionThe best possible score is 1 which is obtained when the predicted values are the same as the actual values. R2 score of baseline model is 0.During the worse cases, R2 score can even be negative. Comment More infoAdvertise with us E ektamaini Follow Improve Article Tags : Machine Learning AI-ML-DS Python numpy-Statistics Functions AI-ML-DS With Python Practice Tags : Machine Learning Similar Reads Machine Learning Tutorial Machine learning is a branch of Artificial Intelligence that focuses on developing models and algorithms that let computers learn from data without being explicitly programmed for every task. In simple words, ML teaches the systems to think and understand like humans by learning from the data.Do you 5 min read Introduction to Machine LearningIntroduction to Machine LearningMachine learning (ML) allows computers to learn and make decisions without being explicitly programmed. It involves feeding data into algorithms to identify patterns and make predictions on new data. 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