Linear and Nonlinear Regression Methods for Equilibrium Modelling of p-Nitrophenol Biosorption by Rhizopus oryzae: Comparison of Error Analysis Criteria

Table 2

Error functions used to discriminate between models.

Error function		Definition	References
Coefficient of determination (𝑅^2)	(10)	∑^𝑝𝑖=1𝑞𝑒^mod−𝑞𝑒^exp𝑖^2∑^𝑝𝑖=1𝑞𝑒^mod−𝑞𝑒^exp𝑖^2+𝑞𝑒^mod−𝑞𝑒^exp𝑖^2	[24, 25, 41]
Sum of the squares of errors (ERRSQ)	(11)	^𝑝∑𝑖=1𝑞𝑒^mod−𝑞𝑒^exp𝑖^2	[34]
Hybrid fractional error function (HYBRID)	(12)	100𝑝−𝑛^𝑝𝑖∑=1𝑞𝑒^exp−𝑞𝑒^mod𝑖^2𝑞𝑒^exp𝑖	[42]
Marquardt’s percent standard deviation (MPSD)	(13)	1001𝑝−𝑛^𝑝𝑖∑=1𝑞𝑒^exp−𝑞𝑒^mod𝑖^2𝑞𝑒^exp𝑖	[43, 44]
Average relative error (ARE)	(14)	100𝑝^𝑝𝑖∑=1𝑞𝑒^exp−𝑞𝑒^mod𝑖^2𝑞𝑒^exp𝑖	[24, 45]
Sum of the absolute errors (EABS)	(15)	^𝑝∑𝑖=1𝑞𝑒^exp−𝑞𝑒^mod𝑖	[46]
Corrected Akaike information criterion (AICC)	(16)	()AIC+2𝑛𝑛+1𝑝−𝑛−1,	[46–48]
	(17)	where AIC=2𝑛−𝑝lnSSR(𝑝−𝑛)
Akaike weight for the ith model (𝜆𝑖)	(18)	𝜆𝑖=exp−(1/2)Δ𝑖∑^𝑅𝑖=1exp−(1/2)Δ𝑖,
	(19)	where Δ𝑖=AIC𝐶𝑖−minAICC