The response surface methodology (RSM) model using quadratic and higher-order polynomial (HOP) regression provided a detailed understanding of the relationships between key variables and the distribution coefficient (Kd) for PFAS adsorption. The HOP regression model captured linear, non-linear, and interaction effects of the variables, including surface area, pHpzc, molecular weight, pKa, pH, temperature, log Kow, adsorbent dose, initial concentration, and Abraham solvation parameters (A, B, S, E, V). The regression coefficients, standard errors (SE), t-statistics, and p-values were calculated to evaluate the significance and statistical soundness of each linear, non-linear, and interactive term. However, the significance level of these linear, nonlinear, and interactive terms was found to be different, as shown in Table and Table . Table presents the results of a Higher-Order Polynomial Response Surface Methodology (HOP-RSM) regression model, which estimates the influence of various physicochemical parameters on the distribution coefficient (Kd). The coefficients (Estimate) represent the magnitude and direction of each parameter's effect on Kd, while the standard error (SE), t-statistic (t-Stat), and pvalue (p-value) provide insight into the statistical significance of each predictor.