y. If there are multiple exchangeable outcomes being estimated, <span class="math inline">\(z_1, \ldots, z_N,\)</span> then it is common to report <em>mean square error</em> (MSE), <span class="math display">\[
\textrm{mse}
= \frac{1}{N} \sum_{n = 1}^N \left( \hat{z}_n - z_n\right)^2.
\]</span> To put the error back on the scale of the original value, the square root may be applied, resulting in what is known prosaically as <em>root mean square error</em> (RMSE), <span class="math display">\[
\textrm{rmse} 