What R² measures

R² (coefficient of determination) measures how much variance in the target is explained by the model.

• R² = 1 → perfect predictions
• R² = 0 → no better than predicting the mean
• R² < 0 → worse than predicting the mean

The intuition

R² compares:

• your model error
• vs baseline error (predicting the mean)

Why R² can be misleading

• adding more features can increase R² even if features are useless
• doesn’t tell you the error magnitude (RMSE/MAE do)

Adjusted R²

Adjusted R² penalizes adding features that don’t help much.

It’s useful for comparing models with different numbers of predictors.

Scikit-learn example

from sklearn.metrics import r2_score
 
r2 = r2_score(y_true, y_pred)
print("R2:", r2)

from sklearn.metrics import r2_score
 
r2 = r2_score(y_true, y_pred)
print("R2:", r2)

What metrics to use in practice

Use a combination:

• MAE (mean absolute error): easy to interpret
• RMSE: punishes big errors
• R²: variance explanation (but not sufficient alone)

Mini-checkpoint

If your model has R² = 0.92 but RMSE is huge, what does that imply?

• It might explain variance well but still be too inaccurate for real use.