# Data Mining - Root mean squared (Error|Deviation) (RMSE|RMSD)

Root mean squared (Error|Deviation) in case of regression.

The RMSD represents the sample standard deviation of the differences between predicted values and observed values.

The RMSE serves to aggregate the magnitudes of the errors in predictions into a single measure of predictive power.

RMSE is a good measure of accuracy, but only to compare forecasting errors of different models for a particular variable and not between variables, as it is scale-dependent.

Each RMSE can be interpreted as the average prediction error within the same scale (unit).

## 3 - Formula

The RMSE is the square root of the average value of the square of the residual (actual - predicted)

$$\text{Root mean squared error (RMSE|RMSD)}= \sqrt{\frac{\displaystyle \sum_{i=1}^N (Y_i-\hat{Y_i})^2}{N}}$$