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

Table 4

Values of Langmuir, Freundlich, Redlich and Peterson, Multilayer, and Fritz and Schlunder model parameters for the system p-NP—Rhizopus Oryzae obtained through nonlinear regression analysis and error deviation data using six error functions.

	ERRSQ	HYBRID	MPSD	ARE	EABS	AICC	𝜆𝑖
Langmuir model
𝐾𝐿	3.9939	6.1036	6.1037	6.1038	7.1577
𝑎𝐿	0.8428	1.4228	1.4228	1.4228	1.6142
Error	0.6678	8.8101	29.6806	2.5861	1.6665	2.49	4.75×10^3
Freundlichmodel
𝐾𝐹	2.1825	2.1945	2.1946	2.1946	2.2393
𝑛𝐹	0.3110	0.3073	0.3073	0.3073	0.3002
Error	0.0226	0.2928	5.4105	0.1757	0.2210	−14.44	1.00
Redlich and Peterson model
𝐾𝑅	1307.7861	1170.0995	1018.8770	1018.6101	1000.0155
𝑎𝑅	588.4872	531.9036	463.0101	462.8754	572.1642
𝑏	0.6974	0.6937	0.6938	0.6938	0.5793
Error	0.0255	0.4483	6.7061	0.1799	1.2184	8.19	8.21×10^4
Multilayer model
𝐾1	2.8903	3.2225	3.2224	3.2224	2.7971
𝐾2	0.0317	0.0336	0.0336	0.0336	0.0265
𝑄𝑚	3.1784	3.0834	3.0834	3.0834	3.4010
Error	0.1218	2.0060	14.1635	0.8024	0.5022	16.01	4.09×10^6
Fritz and Schlunder model
𝐴	4.4335	4.5110	5.9346	3.5962	2.7281
𝛼	0.3109	0.3073	0.3073	0.3075	0.2956
𝐵	1.0314	1.0555	1.7042	0.6388	0.2182
𝛽	−6.7×10^−6	−8.5×10^−9	−2.6×10^−5	0.0004	−0.0263
Error	0.0226	0.8783	9.3716	0.1757	0.2213	−10.97	5.67

Note. The lowest ERRSQ, HYBRID, MPSD, ARE, EABS, and AIC_c are in bold.