As an extension of interactions, polynomial expansion systematically provides an automatic means of creating both interactions and non-linear power transformations of the original variables. Power transformations are the bends that the line can take in fitting the response. The higher the degree of power, the more bends are available to fit the curve.
For instance, if you have a simple linear regression of the form:
By a second degree transformation, called quadratic, you will get a new form:
By a third degree transformation, called cubic, your equation will turn into:
If your regression is a multiple one, the expansion will create additional terms (interactions) increasing the number of new features derived from the expansion. For instance, a multiple regression made up of two predictors (x1 and x2), expanded using the quadratic transformation, will become:
Before proceeding, we have to note two aspects of the expansion procedure:
Polynomial expansion rapidly increases the...
