A regression line can be stated as follows:
$E(Y|x) = a + x\beta$
where alpha and beta are constants. My question is, is this just some type of abbrevation as putting a number in place of x in the equation makes no sense. Instead it should be:
$E(Y|x=X) = a + x\beta $
Now by putting a number in place of x, the equation actually makes sense:
$E(Y|x=2) = \alpha + 2 \beta $
In contrast to:
$E(Y|2) = \alpha + 2 \beta $
The two refers to nothing.