where β0 represents the intercept or regression coefficient, βi, βii, and βij are the linear, quadratic, and interaction coefficients, respectively, Xiand Xj are the independent variables, and k is the number of variables studied that can influence the response y. In this work, the independent variables were subjected to factorial planning of 23 (3 variables, and 2 levels) to optimize the yield of extraction of anthocyanins (mganthocyanins·mL−1) as the measured response function. Nineteen experiments were performed, including five replicates at the central point. A 90% confidence level was chosen to analyze the results. To verify the significance of the model parameters, the analysis of variance (ANOVA) was implemented. The coefficient of determination (R2) and adequate precision (F calculated value and p-value) were used to evaluate the adequacy of the polynomial equation for the response and optimum values. The experimental design, statistical analysis, and regression model were accomplished using Statistica version 13.5.0.17.
In this work, two factorial plannings were executed for both techniques of extraction, PLE and UAE. The first factorial planning was applied for PLE, in which the chosen levels of the independent variables were temperature (60, 80, and 100 °C), 1,2-propanediol concentration in water (15, 30, and 45 wt%), and pH (3.0, 4.5, and 6.0). The second factorial planning was carried out for UAE, in which amplitude (18, 30, and 42%), 1.2-propanediol concentration in water (15, 30, and 45 wt%), and pH (4.0, 7.0, and 10.0) were varied. All coded levels of independent variables used in the factorial planning for the optimization of operating conditions for both PLE and UAE was given in detail in