In this article, we will delve into the calculation of the R2 value in the popular Python library, Scikit-learn. The R2 value, also known as the coefficient of determination, is a statistical measure used to evaluate the quality of a regression model. It describes the proportion of variance in the dependent variable that is predictable from the independent variables. This measure plays a crucial role in assessing how well your predictive model fits the actual data.

Technical Explanation of R2 `Score`

The R2 score evaluates the goodness-of-fit of a regression model and is calculated using the following formula:

$$R^2 = 1 - \frac{\text{SS}*{\text{res}}}{\text{SS}*{\text{tot}}}$$

Where: • $\text{SS}_{\text{res}}$ (Residual Sum of Squares) is the sum of squares of residuals, which are the differences between the actual and predicted values. • $\text{SS}_{\text{tot}}$ (Total Sum of Squares) is the total variance in the dependent variable, calculated as the sum of squares of differences between the actual values and their mean.

Calculation in Scikit-learn

Scikit-learn provides the function `sklearn.metrics.r2_score` to calculate the R2 value for a given set of true and predicted values. The function signature is as follows:

• `y_true`: Array of true values. • `y_pred`: Array of predicted values. • `sample_weight`: Optional, a list of weights to apply to individual samples. • `multioutput`: Determines how multiple output values are handled.

• R2 = 1: Indicates a perfect fit. The model explains all the variability of the target variable. • 0 < R2 < 1: The model explains a proportion of the variance. Higher values indicate a better fit. • R2 = 0: The model does not explain any variability in the response data. • R2 < 0: The model is worse than a horizontal line (simple mean of the dependent variable). • `n` is the number of observations. • `k` is the number of predictors.