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

Multiple Choice

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

A) the OLS estimator of the slope will be inconsistent in the case of a randomly assigned $X _ { i }$ since there are omitted variables present.
B) $X _ { \mathrm { j } } \text { and } u _ { \mathrm { i } }$ will be independently distributed if the $X _ { \mathrm { i } }$ be are randomly assigned.
C) $\beta _ { 0 }$ represents the causal effect of X on Y when X is zero.
D) $E ( Y \mid X = 0 )$ is the expected value for the treatment group.