Kinetics and statistical analysis of the bio-stimulating effects of goat litter in crude oil biodegradation process

Beni-Suef University Journal of Basic and Applied Sciences

Table 1 Statistical error functions

Error functions	Equations	Refs.
ARED	$ \frac{1}{n}\ {\sum}_{\mathrm{i}=1}^n\left(\frac{\mathrm{Exp}{.}_{\mathrm{i}}-\mathrm{Pred}{.}_{\mathrm{i}}}{\mathrm{Exp}{.}_{\mathrm{i}}}\right)\times 100 $	[18]
RMSE	$ \sqrt{\sum_{\mathrm{i}=1}^n{\left(\mathrm{Exp}.\mathrm{i}-\mathrm{Pred}.\mathrm{i}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$\mathrm{n}$}\right.}} $	[19]
MAE	$ \frac{\mathrm{i}}{n}\ {\sum}_{\mathrm{i}=1}^n\left(\mathrm{Exp}{.}_{\mathrm{i}}-\mathrm{Pred}{.}_{\mathrm{i}}\right) $	[20]
SEP	$ \frac{\mathrm{RSME}}{\mathrm{Exp}{.}_{\mathrm{i}}}\times 100 $	[19]
R²	$ \frac{\sum_{\mathrm{i}=1}^n\left(\mathrm{pred}.\mathrm{i}-\mathrm{Exp}.\mathrm{i}\right)}{\sqrt{\sum_{\mathrm{i}=1}^n{\left(\mathrm{pred}.\mathrm{i}-\mathrm{Exp}.\mathrm{i}\right)}^2{\left(\mathrm{pred}.\mathrm{i}-\mathrm{Exp}.\mathrm{i}\right)}^2}} $	[21]

Error functions	Equations	Refs.
ARED	\( \frac{1}{n}\ {\sum}_{\mathrm{i}=1}^n\left(\frac{\mathrm{Exp}{.}_{\mathrm{i}}-\mathrm{Pred}{.}_{\mathrm{i}}}{\mathrm{Exp}{.}_{\mathrm{i}}}\right)\times 100 \)	[18]
RMSE	\( \sqrt{\sum_{\mathrm{i}=1}^n{\left(\mathrm{Exp}.\mathrm{i}-\mathrm{Pred}.\mathrm{i}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$\mathrm{n}$}\right.}} \)	[19]
MAE	\( \frac{\mathrm{i}}{n}\ {\sum}_{\mathrm{i}=1}^n\left(\mathrm{Exp}{.}_{\mathrm{i}}-\mathrm{Pred}{.}_{\mathrm{i}}\right) \)	[20]
SEP	\( \frac{\mathrm{RSME}}{\mathrm{Exp}{.}_{\mathrm{i}}}\times 100 \)	[19]
R²	\( \frac{\sum_{\mathrm{i}=1}^n\left(\mathrm{pred}.\mathrm{i}-\mathrm{Exp}.\mathrm{i}\right)}{\sqrt{\sum_{\mathrm{i}=1}^n{\left(\mathrm{pred}.\mathrm{i}-\mathrm{Exp}.\mathrm{i}\right)}^2{\left(\mathrm{pred}.\mathrm{i}-\mathrm{Exp}.\mathrm{i}\right)}^2}} \)	[21]