# Why root mean “square” error?

Root-mean-square error is frequently used in for calculating the error between a predicted value and actual value. The formula for RMSE is given below:

$\mathrm{RMSE} = \sqrt{\frac{\sum_{t=1}^{n}{(y_t - \hat{y}_t)^2}}{n}}$

My question is; why we raise the absolute error to the second power (and then calculate the square-root of the whole thing), but not something else(e.g., 3 or 4)? Is it just a convention, or there is a mathematical explanation for it? Thanks.

$\mu$ minimizes $E(X-t)^2$
In other words, you're trying to find parameter values such that your predictions are as close to the conditional mean of $y_i$ given $x_i$ as possible (assuming regression context).