Measure

Calculation

Coefficient of determination (R²)

${\text{R}}^2=1-\frac{\frac{1}{N}{{\displaystyle \sum }}_{i=1}^N{\left(Y_i-\overline{Y}\right)}^2}{\frac{1}{N}{{\displaystyle \sum }}_{i=1}^N{\left(y_i-\overline{y}\right)}^2}$

Root mean square error (RMSE)

$\text{RMSE}=\sqrt{\frac{1}{N}{\displaystyle \sum }_{i=1}^N{\left(Y_i-y_i\right)}^2}$

Mean absolute error (MAE)

$\text{MAE}=\frac{1}{N}{\displaystyle \sum }_{i=1}^{N}abs\left(Y_i-y_i\right)$

Root mean absolute error (RMAE)

$\text{RMAE}=100\cdot \frac{\text{MAE}}{\overline{y}}$

Coefficient of efficiency (E)

$\text{E}\left(\%\right)=1-\frac{{{\displaystyle \sum }}_{i=1}^N{\left(Y_i-y_i\right)}^2}{{{\displaystyle \sum }}_{i=1}^N{\left(y_i-\overline{y}\right)}^2}$