In this study, Ni doped Ferric Oxy-hydroxide FeO(OH) nanowires (Ni:FeO(OH)-NWs) were synthesized and loaded on activated carbon (AC). Synthesized adsorbent was characterized by field emission scanning electron microscopy (FESEM) and X-ray diffraction analysis (XRD). Isotherms and kinetic behaviors of Safranin-O (SO) and Indigo Carmine (IC) adsorption onto Ni:FeO(OH)-NWs-AC were explained by extended Freundlich and pseudo second order kinetic models. The adsorption performance was critically analyzed using response surface methodology (RSM), artificial neural network (ANN) and linear algebra based models and compared. The influence of process variables (initial dyes concentration, adsorbent mass and sonication time) on the removal of both dyes was investigated by central composite rotatable design (CCRD) of RSM, Multi -Layer Perceptron (MLP) neural network and Doolittle Factorization Algorithm (DFA). All the models (RSM, ANN and DDA) were statistically compared by the coefficient of determination (R-2), root mean square error (RMSE), mean absolute error (MAE) and absolute average deviation (AAD) based on the validation data set. The coefficient of determination (R-2) calculated from the validation data for RSM, ANN and DDA models were 0.98, 0.99 and 0.99 For IC and 0.99, 0.99 and 0.99 for SO dye, respectively. The ANN model was found to be more precise compared to the other models. However, it was demonstrated that DDA can reduce the orders of data and needs a little time for analysis. So it has bright prospects in chemometrics and it is feasible that the Doolittle Algorithm could be applied to model the real systems. The sensitivity analysis confirmed that sonication time was the essential factor affecting the removal of SO and IC with the relative importance of 36.63% and 12.60%, respectively. The monolayer adsorption capacity of the IC and SO was 29.09 and 37.85 mg g(-1), respectively. (C) 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.