Regression models form the workhorse of much of statistical practice.
A curious aspect of regression is that statisticians tend to treat the
predictors as fixed quantities. In a majority of applications,
however, the data are observational and hence the predictors are as
random as the response. The division of the variables into predictors
and response is therefore a human decision that is pragmatic as
opposed to necessary -- unless it is justified by a very strong causal
theory. In this talk we recount the historic roots as well as the
theoretical justification for treating predictors as fixed. We next
examine when and why this treatment and its justification are
problematic. We end with some practical recommendations that use
readily available tools in a new way.
JOINT WITH: Richard Berk, Lawrence Brown, Mikhail Traskin,
Kai Zhang, Emil Pitkin, Linda Zhao, Ed George