$E \left( Y \mid X _ { 1 } , \ldots , X _ { k } \right) = \operatorname { Pr } \left( Y = 1 \mid X _ { 1 } , \ldots , X _ { k } \right)$
means that
A) for a binary variable model, the predicted value from the population regression is the probability that Y=1 , given X .
B) dividing Y by the X 's is the same as the probability of Y being the inverse of the sum of the X 's.
C) the exponential of Y is the same as the probability of Y happening.
D) you are pretty certain that Y takes on a value of 1 given the X 's.

Question

$E \left( Y \mid X _ { 1 } , \ldots , X _ { k } \right) = \operatorname { Pr } \left( Y = 1 \mid X _ { 1 } , \ldots , X _ { k } \right)$
means that
A) for a binary variable model, the predicted value from the population regression is the probability that  Y=1 , given  X .
B) dividing  Y  by the  X  's is the same as the probability of  Y  being the inverse of the sum of the  X  's.
C) the exponential of  Y  is the same as the probability of  Y  happening.
D) you are pretty certain that  Y  takes on a value of 1 given the  X  's.

Quizplus · Accepted Answer

The expected value of Y given X1, ..., Xk is the probability that Y = 1 given X1, ..., Xk. This is the definition of the conditional expectation.

E(Y∣X1,…,Xk)=Pr⁡(Y=1∣X1,…,Xk)E \left( Y \mid X _ { 1 } , \ldots , X _ { k } \right) = \operatorname { Pr } \left( Y = 1 \mid X _ { 1 } , \ldots , X _ { k } \right)E(Y∣X1​,…,Xk​)=Pr(Y=1∣X1​,…,Xk​)

$E \left( Y \mid X _ { 1 } , \ldots , X _ { k } \right) = \operatorname { Pr } \left( Y = 1 \mid X _ { 1 } , \ldots , X _ { k } \right)$