Performing polynomial expansion
Existing variables can be combined to create new insightful features. We discussed how to combine variables using mathematical and statistical operations in the previous two recipes, Combining features with mathematical functions and Combining features to reference variables. A combination of one feature with itself – that is, a polynomial combination of the same feature – can also return more predictive features. For example, in cases where the target has a quadratic relation with a variable, creating a second-degree polynomial of the feature allows us to use it in a linear model, as shown in the following figure:
Figure 8.4 – Change in the relationship between a target and a predictor variable after squaring the values of the latter
In the plot on the left, due to the quadratic relationship between the target, y, and the variable, x, there is a poor linear fit. Yet, in the plot on the right, we appreciate...