Error Function Abbreviation Formula References Residual Root Mean Square Error RMSE $\sqrt{\frac{1}{n-2}\sum _{i=1}^{N}{\left({Q}_{e,exp}-{Q}_{e,cal}\right)}^{2}}$ [35] Chi-Square Test χ2 $\sum _{i=1}^{N}\frac{{\left({Q}_{e,exp}-{Q}_{e,cal}\right)}^{2}}{{Q}_{e,cal}}$ [35] Sum Square of Errors ERRSQ $\sum _{i=1}^{N}{\left({Q}_{e,exp}-{Q}_{e,cal}\right)}_{i}^{2}$ [35] Hybrid Fractional Error Function HYBRID $\frac{100}{N-p}\sum _{i=1}^{N}\left[\frac{{\left({Q}_{e,i,exp}-{Q}_{e,i,cal}\right)}^{2}}{{Q}_{e,i,exp}}\right]$ [33] Average Relative Error ARE $\frac{100}{N}\sum _{i=1}^{N}|\frac{{Q}_{e,i,cal}-{Q}_{e,i,exp}}{{Q}_{e,i,exp}}|$ [33] Marquardt’s Percent Standard Deviation MPSD $100{\sqrt{\frac{1}{N-p}\sum _{i=1}^{N}\left(\frac{{Q}_{e,exp}-{Q}_{e,cal}}{{Q}_{e,exp}}\right)}}^{2}$ [33] Sum of Absolute Errors EABS $\sum _{i=1}^{N}{|{Q}_{e,exp}-{Q}_{e,cal}|}_{i}$ [35] Coefficient of Determination R2 $\frac{\sum _{i=1}^{N}{\left({Q}_{e,cal}-{Q}_{mexp}\right)}^{2}}{\sum _{i=1}^{N}{\left({Q}_{e,cal}-{Q}_{mexp}\right)}^{2}+{\left({Q}_{e,cal}-{Q}_{mexp}\right)}^{2}}$ [33]