In the Context of a Controlled Experiment, Consider the Simple $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i }$

In the context of a controlled experiment, consider the simple linear regression formulation $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i }$
Let the $Y _ { \mathrm { i } }$ be the outcome, $X _ { \mathrm { i } }$ the treatment level when the treatment is binary, and u_i contain all the additional determinants of the outcome. Then calling $\widehat { \beta } _ { 1 }$ 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 $\widehat { \beta _ { 0 } }$ 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 .