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

Table 3

Isotherm error deviation data related to the biosorption of p-NP on R. oryzae dead biomass using seven commonly applied error functions—linear regression analysis.

Model	Langmuir	Freundlich	Redlich and Peterson	Multilayer (second-order polynomial form)
Parameters	𝐾𝐿 3.535	𝐾𝐹 2.208	𝐾𝑅 1115.864	𝐾1 1.935
	𝑎𝐿 0.705	𝑛𝐹 0.303	𝑎𝑅 533.949	𝐾2 0.026
			𝑏 0.666	𝑄𝑚 3.399
Error functions
𝑅^2	0.9833	0.9956	0.9997	0.9967
ERRSQ	0.7090	0.0255	0.5987	0.1827
HYBRID	12.639	0.3040	19.1130	4.4978
MPSD	35.5410	5.5138	58.3339	31.9740
ARE	14.3110	2.0128	10.3833	7.1261
EABS	0.7156	0.1006	0.5192	0.3563

Note. The highest 𝑅² and the lowest ERRSQ, HYBRID, MPSD, ARE, and EABS are in bold.