R² Score
The R² score, also called the coefficient of determination, is a key metric for evaluating regression models. It measures the proportion of the variance in the dependent variable that is predictable from the independent variables. Building on concepts like MSE, RMSE, and MAE, which quantify average error, the R² score provides a normalized measure of how well your model explains the observed outcomes compared to a simple mean prediction.
The formula for R² is:
R2=1−∑i=1n(yi−yˉ)2∑i=1n(yi−y^i)2- yi: true values;
- y^i: predicted values;
- yˉ: mean of the true values.
The numerator represents the sum of squared errors of the model, while the denominator is the total variance in the data. An R² value of 1 means perfect prediction; 0 means the model is no better than always predicting the mean; negative values indicate the model performs worse than simply using the mean.
123456789from sklearn.metrics import r2_score # Example true values and predictions y_true = [3, -0.5, 2, 7] y_pred = [2.5, 0.0, 2, 8] # Calculate R² score r2 = r2_score(y_true, y_pred) print(f"R² score: {r2:.2f}")
Interpreting R² Values and Understanding Limitations
Interpreting R² values helps you understand model performance in context:
- An R² score close to 1 means your model explains most of the variance in the target variable;
- A score near 0 shows the model does not improve over simply predicting the mean;
- Negative values indicate your model performs worse than always predicting the mean.
However, R² has important limitations:
- It does not show whether your predictions are biased;
- It cannot detect overfitting or model complexity issues;
- It may be misleading when comparing models with different numbers of features or on data with outliers.
Always use R² alongside other regression metrics and validation strategies to get a complete and reliable assessment of your model's quality.
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The R² score, also called the coefficient of determination, is a key metric for evaluating regression models. It measures the proportion of the variance in the dependent variable that is predictable from the independent variables. Building on concepts like MSE, RMSE, and MAE, which quantify average error, the R² score provides a normalized measure of how well your model explains the observed outcomes compared to a simple mean prediction.
The formula for R² is:
R2=1−∑i=1n(yi−yˉ)2∑i=1n(yi−y^i)2- yi: true values;
- y^i: predicted values;
- yˉ: mean of the true values.
The numerator represents the sum of squared errors of the model, while the denominator is the total variance in the data. An R² value of 1 means perfect prediction; 0 means the model is no better than always predicting the mean; negative values indicate the model performs worse than simply using the mean.
123456789from sklearn.metrics import r2_score # Example true values and predictions y_true = [3, -0.5, 2, 7] y_pred = [2.5, 0.0, 2, 8] # Calculate R² score r2 = r2_score(y_true, y_pred) print(f"R² score: {r2:.2f}")
Interpreting R² Values and Understanding Limitations
Interpreting R² values helps you understand model performance in context:
- An R² score close to 1 means your model explains most of the variance in the target variable;
- A score near 0 shows the model does not improve over simply predicting the mean;
- Negative values indicate your model performs worse than always predicting the mean.
However, R² has important limitations:
- It does not show whether your predictions are biased;
- It cannot detect overfitting or model complexity issues;
- It may be misleading when comparing models with different numbers of features or on data with outliers.
Always use R² alongside other regression metrics and validation strategies to get a complete and reliable assessment of your model's quality.
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