How does adding polynomial combinations of inputs influence regression analysis?

Adding polynomial combinations of inputs in regression analysis allows for complex associations to be captured effectively. In linear regression, the relationship between the independent and dependent variables is assumed to be linear. However, in many real-world scenarios, the relationship may not be straightforward and could be more complex.

By incorporating polynomial terms, such as squares or higher degrees of the input variables, the model gains the flexibility to fit non-linear patterns in the data. This means that the regression model can now represent curves and more intricate interactions among the variables. As a result, it can provide a better fit to the data and improve the model's predictive power.

When polynomial combinations are included, the model can more accurately capture the underlying trends and relationships present in the data, leading to enhanced performance in prediction tasks. This is particularly important in applications where the response variable is influenced by non-linear factors, and a simple linear model would fail to provide an accurate representation.