Table 4 Evaluation indicators.

From: Carbon price prediction based on decomposition technique and extreme gradient boosting optimized by the grey wolf optimizer algorithm

Indicators

Definition

Formula

MSE

Mean square error

\(MSE=\frac{1}{n}{{\sum }_{i=1}^{n}\left({y}_{i}-\widehat{{y}_{i}}\right)}^{2}\)

MAE

Mean absolute error

\(MAE=\frac{1}{n}{\sum }_{i=1}^{n}\left|{y}_{i}-\widehat{{y}_{i}}\right|\)

RMSPE

Root mean square percentage error

\(RMSPE=\sqrt{\frac{1}{n}{\sum }_{i=1}^{n}{\left|\frac{{y}_{i}-\widehat{{y}_{i}}}{{y}_{i}}\right|}^{2}}*100\%\)

MAPE

Mean absolute percentage error

\(MAPE=\frac{1}{n}{\sum }_{i=1}^{n}\left|\frac{{y}_{i}-\widehat{{y}_{i}}}{{y}_{i}}\right|*100\%\)

\({R}^{2}\)

Coefficient of determination

\({R}^{2}=1-\frac{S{S}_{residual}}{S{S}_{total}}\)