In a statistics textbook I saw that the linear simple regression model is defined as \begin{equation} Y = \alpha + \beta x + e \end{equation} where $x$ is a value of the independent variable, $Y$ is the response, $\alpha$ and $\beta$ are the parameters, and $e$ is a random error with a mean of 0.
Then this textbook talks about estimators. It says $A$ is an estimator of $\alpha$, and $B$ is an estimator of $\beta$. Also, $A+Bx$ is an estimator of $\alpha+\beta x$. However, according to the textbook, $A+Bx$ is an estimator of $Y$. I don't understand that $A+Bx$ can be an estimator of $Y$, since $Y$ is a random variable but not a parameter. Am I wrong?
To me it makes sense only to say that $A+Bx$ is an estimator of the 'mean' of the random variable $Y$. Then, given that the mean of $e$ is zero, $A+Bx$ is an estimator of the mean of $\alpha + \beta x + e$.