Parametrized predictors are exclusively linear models and cannot represent non-linear relationships in data.

Parametrized predictors are models that use a set of parameters to describe the relationship between inputs and outputs, but they are not limited to linear forms; the functional form can be any expression that involves those parameters. For example, a polynomial regression model uses parameters to weight powers of the input, creating a nonlinear curve while still being parametrized. Neural networks are another case: each layer’s weights are parameters, yet the activation functions produce highly nonlinear mappings. A simple illustration is a quadratic predictor \(y = \theta_0 + \theta_1x + \theta_2x^2\), which can fit a curved relationship between \(x\) and \(y\). Thus, parametrized predictors can capture non‑linear patterns just as well as linear ones.