In the Context of a Controlled Experiment, Consider the Simple $\hat \beta _ { 1 }$

Multiple Choice

In the context of a controlled experiment, consider the simple linear regression formulation Y_i = ?₀ + ?₁X_i + u_i. Let the Y_i be the outcome, X_i the treatment level when the treatment is binary, and u_i contain all the additional determinants of the outcome. Then calling $\hat \beta _ { 1 }$ a differences estimator

A) makes sense since it is the difference between the sample average outcome of the treatment group and the sample average outcome of the control group.
B) and $\hat \beta _ { 0 }$ the level estimator is standard terminology in randomized controlled experiments.
C) does not make sense, since neither Y nor X are in differences.
D) is not quite accurate since it is actually the derivative of Y on X.