A New Approach in Regression Analysis for Modeling Adsorption Isotherms

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	^𝑛∑𝑖=1𝑞𝑒𝑖,exp−𝑞𝑒𝑖,cal𝜎𝜀𝑖^2+𝐶𝑒𝑖,exp−𝐶𝑒𝑖,cal𝜎^𝑒𝛿𝑖^2
Ordinary least squares	OLS	Experimental	^𝑛∑𝑖=1𝑞𝑒𝑖,exp−𝑞𝑒𝑖,cal^2
Orthogonal distance regression	ODR	Experimental	^𝑛∑𝑖=1𝑞𝑒𝑖,exp−𝑞𝑒𝑖,cal𝑞𝑒𝑖,exp^2+𝐶𝑒𝑖,exp−𝐶𝑒𝑖,cal𝐶𝑒𝑖,exp^2
Marquardt’s percent standard deviation	MPSD	Experimental	^𝑛∑𝑖=1𝑞𝑒𝑖,exp−𝑞𝑒𝑖,cal𝑞𝑒𝑖,exp^2
Hybrid fractional error function	HYBRD	Experimental	^𝑛∑𝑖=1𝑞𝑒𝑖,exp−𝑞𝑒𝑖,cal^2𝑞𝑒𝑖,exp