# Is there an accepted name for this error metric?

I've come across an error metric used to quantify a model's reconstruction error: $$\varepsilon = \frac{\sum_i{\left(y_i-m_i\right)^2}}{\sum_i{\left(y_i-\bar{y}\right)^2}}$$ where $y_i$ is the $i$th data point, $m_i$ is the model's estimate of the $i$th data point, and $\bar{y}$ is the mean of all data points. The numerator is the total squared error of the model, and the denominator is the squared deviation from the mean of the data.

Does this metric have a standard name? If not, what would you call it?

• Error metrics seem on-topic to me. – Silverfish Mar 29 '17 at 19:53
• it's not so obscure, we use it compare models in-sample when the specifications are very different and usual metrics such as AIC are not applicable. e.g. comparing AIC/BIC of difference and levels models is meaningless – Aksakal Mar 29 '17 at 20:24

This is related to a coefficient of determination ($R^2$), actually, it's $1-R^2$, also called fraction of variance unexplained