  The Average Treatment Effect (ATE) is a global measure of the effectiveness
of an experimental treatment intervention. Classical methods of its estimation
either ignore relevant covariates or do not fully exploit them. Moreover, past
work has considered covariates as fixed. We present a method for improving the
precision of the ATE estimate: the treatment and control responses are
estimated via a regression, and information is pooled between the groups to
produce an asymptotically unbiased estimate; we subsequently justify the random
X paradigm underlying the result. Standard errors are derived, and the
estimator's performance is compared to the traditional estimator. Conditions
under which the regression-based estimator is preferable are detailed, and a
demonstration on real data is presented.
