3.3.2. Relative Absolute Error

The relative absolute error (RAE) is the ratio of the total absolute error produced by a model to the total absolute error of a simple predictor. In this case, the simple predictor is just the average of the target values. The RAE is thus computed as

$$RAE = \frac{\sum\_{i=1}^{n} |P\_i - A\_i|}{\sum\_{i=1}^{n} |\bar{A} - A\_i|} \times 100\% \tag{10}$$

where *Pi* is the predicted value by a model for an instance *i* out of a total number of *n* instances, *Ai* is the target value for the instance *i*, and *A*¯ is the mean of the target values given by

$$\bar{A} = \frac{1}{n} \sum\_{i=1}^{n} A\_i \tag{11}$$

One advantage of the RAE metric compared to the root mean square error (RMSE) described later is that it treats each error equally by ensuring that only the absolute value is considered and not the square of the error. Consequently, systems that are invariant to the effects of outliers can be best evaluated by the RAE instead of the RMSE.
