  Stepwise regression building procedures are commonly used applied statistical
tools, despite their well-known drawbacks. While many of their limitations have
been widely discussed in the literature, other aspects of the use of individual
statistical fit measures, especially in high-dimensional stepwise regression
settings, have not. Giving primacy to individual fit, as is done with p-values
and $R^2$, when group fit may be the larger concern, can lead to misguided
decision making. One of the most consequential uses of stepwise regression is
in health care, where these tools allocate hundreds of billions of dollars to
health plans enrolling individuals with different predicted health care costs.
The main goal of this "risk adjustment" system is to convey incentives to
health plans such that they provide health care services fairly, a component of
which is not to discriminate in access or care for persons or groups likely to
be expensive. We address some specific limitations of p-values and $R^2$ for
high-dimensional stepwise regression in this policy problem through an
illustrated example by additionally considering a group-level fairness metric.
