ABSTRACT
Suppose we have a response y and predictors x1, . . . ,xp. A linear model takes the form:
y = β0+ p
β jX j + ε
We can include transformations and combinations of the predictors among the xs, so this model can be very flexible. However, it can often be difficult to find a good model, given the wide choice of transformations available. We can try a systematic approach of fitting a family of transformations. For example, we can try polynomials of the predictors, but particularly if we include interactions, the number of terms becomes very large, perhaps greater than the sample size. Alternatively, we can use more interactive and graphical approaches that reward intuition over brute force. However, this requires some skill and effort on the part of the analyst. It is easy to miss important structure; a particular difficulty is that the methods only consider one variable at a time, when the secret to finding good transformations may require that variables be considered simultaneously.
