Regression and Other Stories

So far, we have been interpreting regressions predictively: given the values of several inputs, the fitted model allows us to predict y, typically considering the n data points as a simple random sample from a hypothetical infinite “superpopulation” or probability distribution. Then we can make comparisons across different combinations of values for these inputs. This section of the book considers causal inference, which concerns what would happen to an outcome y as a result of a treatment, intervention, or exposure. This chapter introduces the notation and ideas of causal inference in the context of randomized experiments, which allow clean inference for average causal effects and serve as a starting point for understanding the tools and challenges of causal estimation.