Let $Y_1,Y_2,...,Y_n$ be $n$ independent random variables such that each $Y_i \sim POI(\beta x_i) $, where $\beta$ is an unknown parameter. If $\{(x_1,y_1),(x_2,y_2),...,(x_n,y_n)\}$ is a dataset where $y_1,y_2,...,y_n$ are the observed values based on $x_1,x_2,..,x_n$, then find the least squares estimator of $\beta$.
The thing is I know how to find the MLE of $\beta$. But how to find the LSE, especially what is the model specified here?? Can anyone help?