Table 1 Evaluation matrix.

Mean square error (MSE)

\(MSE = \left( {\frac{1}{n}} \right)\sum {\left( {y_{i} - \bar{y}} \right)} ^{2}\) (8)

Where n is the number of data points, y_i is the i^th actual value, ȳ is the mean of the actual values

Root mean square error (RMSE)

\(RMSE=\:\sqrt{\left(\:\frac{1}{n}\:\right)\:\sum\:({y}_{i}\:-\:\stackrel{-}{y})2}\) (9)

Where n is the number of data points, y_i is the i^th actual value, ȳ is the mean of the actual values

Mean absolute error (MAE)

\(MAE = \left( {~\frac{1}{n}~} \right)~\sum (y_{i} - \bar{y})\) (10)

Where n is the number of data points, y_i is the i^th actual value, ȳ is the mean of the actual values

Coefficient of determination (R^2)

\(R^{2} = 1 - \left( {\frac{{\sum \left( {y_{i} - \bar{y}~} \right)^{2} }}{{\sum \left( {y_{i} - \hat{y}~} \right)^{2} }}} \right)\) (11)

Where y_i is the i^th actual value, ȳ is the mean of the actual values, ŷ is the predicted value.