We have $y_t = bu_t + e_t$ where $u_t$ is the input signal and I'm trying to find an expression for the variance of the estimate for b that is determined to be
$$\hat{b} = \underset{b}{\mathrm{argmin}} \sum_{t=1}^N [y_t - bu_t]^2 $$
Any ideas? The arg min confuses me because because I can't just calculate the variance of the entire sum that would be pointless?