The discharge of oily wastewater is dangerous, carcinogenic, and deteriorates water resources along with destroying the ecosystem [17]. Wastewater contaminated with fats, oils, greases, and other organic and inorganic substances is generated by a variety of industries, including oil refineries, metalworking plants, restaurants, slaughterhouses, food processing industries, edible oil mills, petrochemical plants, and tanneries [6]. Conventional oily wastewater treatment methods include froth flotation, ultrasonic irradiation, electrochemical separation, solvent extraction, centrifugation, microwave irradiation, adsorption, and membrane filtration [8]. Ultrafiltration is a favourable oil-water emulsion treatment method due to its small pore size, no phase change capability, and low-pressure operation [18]. Ceramic membranes are preferred in wastewater reclamation, owing to its hydrophilicity, physical stability and chemical resistance. However, fouling is an inevitable natural phenomenon during the filtration of oily wastewater [25]. Membrane surface modification and process optimization are the two efficient methods in fouling mitigation and improving the oil-water performance [25].

Conducting polymers sustain a charged surface's fundamental features using π bond overlap, robust material, hydrophilicity, and convenient surface functionalization [36]. Therefore, conducting polymers are recommended when modifying membranes for various sorts of wastewater treatment to increase their hydrophilicity and resistance to foulant deposits on their surface [26,32,43]. Recently, polypyrrole has gained interest because to its high conductivity, nontoxicity, superior mechanical properties, and ease of synthesis. Recent studies have investigated the utilization of polypyrrole decorated alumina ceramic membranes for oil-water emulsion separation [13]. Polypyrrole deposited ceramic membrane displayed a superior oil rejection of 99% of various oil-water emulsions with an excellent flux. Membrane modeling has aided in the scaling up of membrane processes by predicting and optimizing membrane performance.

Chemometric modeling is a recent development in the field of membrane technology that aims to predict membrane performance based on the intrinsic physiochemical properties of the membrane [31]. Regression models are a form of chemometric model used to predict a continuous response variable from a set of independent inputs. Linear regression (LR) is a statistical technique that uses a simple equation to model the relationship between a dependent variable and one or more independent variables. It is a powerful tool that can be used to predict the value of the dependent variable based on the values of the independent variables [9,23]. Three key characteristics in regression model of membrane technology are interpretability, prediction accuracy, and the ability to model linear relationships as a function of flow and rejection [5]. Linear models are widely used in various membranes for wastewater treatment and desalination applications [12,14,19,21,24,40]. LR models displayed superior performance in prediction of membrane performance. Such linear modeling on conductive polymer-modified ceramic membranes for an oil-water emulsion is not yet studied. In this research, robust linear regression (RLR), stepwise linear regression (SWR) and LR were proposed to evaluate the performance of membranes. It includes (i) the stability and box-plot analysis of input variables that were studied, (ii) the efficacy of regression models on the prediction of oil-water separation efficiency (SE) and permeate flux (PF) and (iii) the probability distribution function of oil-water (SE) and (PF).