Table 4.

Definitions of error functions in cases when there are no replicated concentration measurements.

Name	Abbreviation	Domain	Expression
Theoretical orthogonal distance regression	TODR	Theoretical	${\displaystyle \sum }_{i=\mathrm{1}}^n\left[{\left(\frac{q_{\mathrm{e}i,\exp }-q_{\mathrm{e}i,\text{cal}}}{{\mathrm{\sigma }}_{\mathrm{\epsilon }i}}\right)}^{\mathrm{2}}+{\left(\frac{C_{\mathrm{e}i,\exp }-C_{\mathrm{e}i,\text{cal}}}{{\mathrm{\sigma }}_{\mathrm{\delta }i}^{\mathrm{e}}}\right)}^{\mathrm{2}}\right]$
Ordinary least squares	OLS	Experimental	${\displaystyle \sum }_{i=\mathrm{1}}^n{\left(q_{\mathrm{e}i,\exp }-q_{\mathrm{e}i,\text{cal}}\right)}^{\mathrm{2}}$
Orthogonal distance regression	ODR	Experimental	${\displaystyle \sum }_{i=\mathrm{1}}^n\left[{\left(\frac{q_{\mathrm{e}i,\exp }-q_{\mathrm{e}i,\text{cal}}}{q_{\mathrm{e}i,\exp }}\right)}^{\mathrm{2}}+{\left(\frac{C_{\mathrm{e}i,\exp }-C_{\mathrm{e}i,\text{cal}}}{C_{\mathrm{e}i,\exp }}\right)}^{\mathrm{2}}\right]$
Marquardt's percent standard deviation	MPSD	Experimental	${\displaystyle \sum }_{i=\mathrm{1}}^n{\left(\frac{q_{\mathrm{e}i,\exp }-q_{\mathrm{e}i,\text{cal}}}{q_{\mathrm{e}i,\exp }}\right)}^{\mathrm{2}}$
Hybrid fractional error function	HYBRD	Experimental	${\displaystyle \sum }_{i=\mathrm{1}}^n\frac{{\left(q_{\mathrm{e}i,\exp }-q_{\mathrm{e}i,\text{cal}}\right)}^{\mathrm{2}}}{q_{\mathrm{e}i,\exp }}$