root mean squared error

Let $n$ be the total number of observations, $i\in {\mathbb{N}}_{[1,n]}$ an index and $y_i$ be the $i-$th observation. The root mean squared error is given by $\text{RMSE}=\sqrt{\frac{1}{n}{\sum }_{i=1}^n(y_i-{\hat{y}}_i{)}^2}.$

The root mean squarred error is related to mean squared error (MSE) by the equation $\text{MSE}=\sqrt{\text{RMSE}}.$ It is also related to residual sum of squares (RSS) by the equation $\text{MSE}=\sqrt{\frac{\text{RSS}}{n}}.$