Easy

R-squared Score

Easy

~15 min

code completion

R² (Coefficient of Determination)

MSE tells you how large the errors are, but not how well you're doing relative to a baseline. R² answers: "How much better is my model than just predicting the mean?"

R^{2} = 1 - \frac{S S _{res}}{S S _{tot}}

where:

S S_{res} = \sum (y_{i} - \overset{y}{^}_{i})^{2}

— residual sum of squares

S S_{tot} = \sum (y_{i} - \overset{y}{ˉ})^{2}

— total sum of squares

Interpretation:

R² = 1.0: perfect predictions

R² = 0.0: no better than predicting the mean

R² < 0: worse than predicting the mean

Your task:

Implement r_squared(y_true, y_pred).

Example Tests

Perfect predictions: R2 = 1.0

Input: {"y_pred":[1,2,3,4,5],"y_true":[1,2,3,4,5]}

Expected: 1

Predicting the mean: R2 = 0.0

Input: {"y_pred":[6,6,6,6,6],"y_true":[2,4,6,8,10]}

Expected: 0

Good but not perfect predictions

Input: {"y_pred":[1.5,2,2.5],"y_true":[1,2,3]}

Expected: 0.75

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