What do polynomial combinations of model inputs enable a regression to do?

Polynomial combinations of model inputs allow a regression model to capture complex relationships within the data by introducing non-linearities. In many real-world scenarios, the relationship between the input features and the target variable is not simply linear; there can be interactions and curvilinear patterns that a basic linear regression would fail to represent accurately. By incorporating polynomial terms, such as squares, cubes, or higher-degree terms of the input variables, the model can fit a more flexible curve to the data. This enhanced flexibility enables the regression to better match the true underlying associations, leading to more accurate predictions.

Enhanced interpretability, while crucial in regression analysis, is not guaranteed when polynomial terms are introduced, as these transformations can complicate the relationship interpretation between input features and outputs. Furthermore, polynomial combinations can actually increase the risk of overfitting and prediction bias if not appropriately managed, particularly with very high-degree polynomials. Hence, the most direct impact of incorporating polynomial combinations is on improving the model's fit to the true input and target relationship, making this the correct choice.