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 polyno-

mials 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 con-

sider one variable at a time, when the secret to finding good transformations may

require that variables be considered simultaneously.