Regression and Other Stories

In the usual regression context, predictive inference relates to comparisons between units, whereas causal inference addresses comparisons of different treatments if applied to the same units. More generally, causal inference can be viewed as a special case of prediction in which the goal is to predict what would have happened under different treatment options. Causal interpretations of regression coefficients can only be justified by relying on much stronger assumptions than are needed for predictive inference. As discussed in the previous chapter, controlled experiments are ideal settings for using regression to estimate a treatment effect because the design of data collection guarantees that treatment assignment is independent of the potential outcomes, conditional on the information used in the design. This chapter illustrates the use of regression in the setting of controlled experiments, going through issues of adjustment for pre-treatment predictors, interactions, and pitfalls that can arise when building a regression using experimental data and interpreting coefficients causally.