This study investigates how to use regression adjustment to reduce variance in experimental data. We show that the estimators recommended in the literature satisfy an orthogonality property with respect to the parameters of the adjustment. This observation greatly simplifies the derivation of the asymptotic variance of these estimators and allows us to solve for the efficient regression adjustment in a large class of adjustments. Our efficiency results generalize a number of previous results known in the literature. We then discuss how this efficient regression adjustment can be feasibly implemented. We show the practical relevance of our theory in two ways. First, we use our efficiency results to improve common practices currently employed in field experiments. Second, we show how our theory allows researchers to robustly incorporate machine learning techniques into their experimental estimators to minimize variance.

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