I came across the following in explaining the log-linear regression model.
Given the model $\log(Y_i) = β_0 + β_1X_i + u_i$
The expected value of $\log(Y)$ given $X$ is $β_0 + β_1X$.
So far, so good. But then it says:
'When $X$ is $X+ΔX$, the expected value is given by $\log(Y+ΔY)$'.
I don't see why this is necessarily the case. Could someone explain why $\log(Y+ΔY) = β_0 + β_1(X+ΔX)$?