Suppose Di is an observed binary variable equal to one if an individual is assigned to treat- ment and equal to zero otherwise. Further, suppose Y; is an observed variable measuring some outcome of interest, that is hypothesized to be affected by Di. Recall that we express Y; in terms of the potential outcomes Yli and You as Yi Yli if Di = 1 = You if Di = 0 This means that if Di = 0, we observe You, while Yl; is the unobserved counterfactual outcome. Similarly, if Di = 1, we observe Y1i, while You is the unobserved counterfactual outcome.(6.2) In this setup, Yli - You is the causal effect of treatment for individual i. However, for any given individual we observe either Yi or You, not both. Of course, we would still like to use linear regression to estimate the causal effect of treatment. Assume the following: B = Yli - You Q = E[You] = Yoi - E[Yoi] Note that since there is no i subscript on S, we are assuming that the causal effect of treatment is the same for every individual. Show that we can write a simple regression model for Y as Yi = a+ BDit wi (6.3) Based on the linear regression model from (6.2), Write down equations for E[Y,| Di = 1] and E[Y:| Di = 0]. Interpret these quantities