Polynomial Regression
Fitting ordinary linear regression on top of powers of the input, letting a linear method draw curved shapes instead of only straight lines.
Degree acts as a direct dial on model capacity: low degree underfits a curved trend, while a degree high enough can pass through every training point exactly, at the cost of wild oscillation between them. Training error decreases monotonically as degree rises, so it can never be used to choose degree — only held-out validation error reveals which degree actually generalizes.
The best degree matches the true underlying trend's complexity, not the model's maximum flexibility.