Measurement of Model's Fit - R2 Score in Python
The R² score, also known as the coefficient of determination, is a valuable metric used to evaluate the performance of a linear regression model. This score measures the proportion of variance in the dependent variable that is explained by the independent variable(s) in the model.
A higher value of R² is desirable as it indicates better results. The best possible score is 1.0, which signifies a perfect fit between predicted and actual values. On the other hand, values close to 0 or below indicate poor fitting.
To compute the R² score in Python, you can use the function from the module. Here's a step-by-step guide:
- After training a linear regression model and making predictions, import :
- Given true values and predictions , compute the R² score with:
Interpreting the R² score is crucial, as it has some limitations in model evaluation. For instance, higher R² values generally indicate better model performance, but they do not guarantee model accuracy or absence of bias. Moreover, if overfitting occurs or irrelevant variables inflate R², the score may be misleading.
The R² score assumes a linear relationship between the input and output variables and does not account for the presence of outliers in the data. Furthermore, the r2 score for a model with poor performance can fall below 0.0, and for a worse model, it can even be negative. On the other hand, a model that predicts the mean value always will have an r2 score of 0.0.
In summary, the R² score helps us understand how well-observed results are reproduced by the model, depending on the ratio of the total deviation of results described by the model. It's an essential tool for assessing the quality of a linear regression model, but it's crucial to interpret it carefully and consider its limitations.
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