I have a no-intercept relationship:
$$y_{i} = \beta_{1}x_{i} + \varepsilon_{i}$$
where $\varepsilon_{i} \sim \text{ iid } \mathcal{N}(0, \sigma^{2})$, and $i = 1, \dots, n$.
How do I derive $\hat{\beta}_{1}$, the least-squares estimator of $\beta_{1}$?