Table 1 Evaluation metrics for regression and time series forecasting.
Metric | Description | Formula |
|---|---|---|
MAE | Average magnitude of errors | \(\:MAE\:=\:\frac{1}{n}\:\sum\:_{i=1}^{n}\left|{y}_{i}\:-\:\widehat{y}i\right|\) |
MSE | Average of the squares of the errors | \(\:MSE\:=\:\frac{1}{n}\:{\sum\:}_{i=1}^{n}{\left({y}_{i}\:-\:\widehat{y}i\right)}^{2}\) |
RMSE | Square root of MSE | \(\:RMSE\:\:=\sqrt{\frac{1}{n}\:{\sum\:}_{i=1}^{n}{\left({y}_{i}\:-\:{\stackrel{-}{y}}_{i}\right)}^{2}}\:\) |
R² | Proportion of variance explained by the model | \(\:{R}^{2\:=\:}1\:-\:\:\:\frac{\frac{1}{n}\:{\sum\:}_{i=1}^{n}{\left({y}_{i}\:-\:{\stackrel{-}{y}}_{i}\right)}^{2}}{\:\frac{1}{n}\:{\sum\:}_{i=1}^{n}{\left({y}_{i}\:-\:{\stackrel{-}{y}}_{i}\right)}^{2}}\) |
MAPE | Forecast accuracy as a percentage | \(\:MAPE\:=\:\frac{1}{n}\:\sum\:_{i=1}^{n}\left|\frac{{y}_{i}-\:{\widehat{y}}_{i}}{{y}_{i}}\right|\:x\:100\) |
sMAPE | Symmetric percentage error measure | \(\:sMAPE\:=\:\frac{1}{n}\:\sum\:_{i=1}^{n}\frac{\left|{y}_{i}-\:{\widehat{y}}_{i}\right|}{\frac{\left|{y}_{i}\right|-\:\left|{\widehat{y}}_{i}\right|}{2}}\:x\:100\) |
MASE | Compare forecast error to naive forecast error | \(\:MASE\:=\:\frac{MAE}{MAE\:of\:naive\:forecast}\:\) |
