Say we have the following regression model: $Y_i = \alpha + \beta(x_i - \mathrm{mean}(x)) + R_i$
where $R_1,\ldots,R_{20} \sim G(0, \sigma)$
If we have $\mu(x) = \alpha + \beta(x - \mathrm{mean}(x))$, how do I go about finding the MLE of $\mu(5)$?
I have a given data set with some calculations done for me, but not sure how to approach this?