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R², or the Coefficient of Determination, is a statistical measure that indicates how well a regression model fits the data. It represents the proportion of variance in the dependent variable that can be explained by the independent variables in the model. In classical linear regression, R² values range from 0 to 1, where 0 indicates that the model does not explain any variance and 1 indicates that it explains all the variance.

However, in non-linear models, R² can take on negative values. This occurs when the model’s predictions perform worse than simply using the mean of the dependent variable as a prediction. In such cases, a negative R² indicates that the model is not a good fit for the data, and it may be necessary to reconsider the model or the features being used ¹.

While R² can provide insights into model performance, it should not be the sole metric for evaluation. Other metrics, such as Mean Absolute Error (MAE) or Mean Squared Error (MSE), can also be useful in assessing model accuracy ¹.

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Tutorial for calculating R² using Python with data provided from MacroTrends. Full working code provided to the reader. This article serves as a step by step tutorial for the R² method with full work...

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The Pearson correlation coefficient (r) is used to identify patterns in things whereas the coefficient of determination (R²) is used to identify the strength of a model.

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