Polynomial curve fitting is a linear regression problem where the features are given by the polynomial powers of the original input. For a single feature $x$ and a corresponding real-valued label $y$, the goal is to estimate a polynomial of degree $d$ using the formula $\hat{y}= \sum_{i=0}^d x^i w_i$. Here, $w_i$ represents the model's weights and $w_0$ acts as the bias (since $x^0 = 1$ for all $x$). Because it is a linear regression problem, the squared error is typically used as the loss function.