Polynomial Regression

Polynomial regression extends a linear model by adding higher-degree terms of a predictor variable. This approach captures curved relationships between a predictor and an outcome, while retaining the core idea of fitting coefficients in a regression framework. The general form of a polynomial model of n-th degree is:

\[\hat{y} = b_0 + b_1 \cdot x + b_2 \cdot x^2 + ... + b_j \cdot x^{n-1}\]

Even though it incorporates non-linear terms of \(x\), the model remains linear in its parameters \((b_0, b_1, \ldots, b_n)\), preserving much of the interpretability of ordinary linear regression.