Predict a target y from several X's. Toggle predictors and watch R² climb. Then watch Adjusted R² stop climbing — it penalizes useless predictors.
R²—
Adjusted R²—
SSE—
Predictors used—
y = ...
The trap: R² always goes up (or stays equal) when you add any predictor — even pure noise. Adjusted R² subtracts a penalty for each extra predictor, so it can drop when you add a worthless one. Trust Adjusted R² when comparing models with different numbers of features.