Design expert software v 6

A five-level, three-variable, central composite rotatable design was used, resulting in 20 treatments (Table 1), which were analyzed using response surface methodology. The independent variables were: MC (X₁), SP (X₂), and ET (X₃). Significant differences were assumed at p < 0.05, and the fitted second-order polynomial equation was obtained by Equation (3): Yi=b0+∑j=13bjXj+∑J=13bjjXj2+∑J=12∑k=j+13bjkXjXk
where Y_i is the response variable for experiment i, X_i is the predictor variable, and b₀, b₁, b₂, b₁₁, b₂₂, and b₁₂ are estimated coefficients. Analysis of variance, regression, canonical analyses and optimization of process conditions were performed using Design Expert software v.6.01 (Stat-Ease, Inc., Minneapolis, MN, USA). The critical values of the variables (maximum, minimum and saddle points) were determined using JMP Statistical Discovery software v.11.0 (SAS Institute, Cary, NC, USA). Pearson correlations were performed to relate the independent variables using Minitab software v.17.1.0 (Minitab LLC, State College, PA, USA).

A second-order, three-variable, five-level, central-composite design was used, resulting 20 treatments, which axial and central points were done by duplicate. The results were analyzed using response surface methodology [65 ]. The feed moisture content, extrusion temperature, and screw speed were independent variables. The fitted second-order polynomial is given by:
$Y_i={\mathit{b}}_0+{\sum }_{\mathit{j}=1}^3{b}_j{X}_j+{\sum }_{\mathit{j}=1}^3{b}_{jj}{\mathit{X}}_{\mathit{j}}^2+{\sum }_{\mathit{j}=1}^2{\sum }_{\mathit{k}=\mathit{j}+1}^3{b}_{jk}{X}_j{X}_k,$
where Y_i is the predicted response, X_i and X_j are the input variables, b₀, b_i, b_ii, b_ij are regression coefficients of the intercept, linear effects, squared effects, and interactions respectively. The variable combination is shown in Table 7. Analysis of variance, regression, and canonical analysis for the nature of the response variable were performed on Design Expert software v. 6.01 (Stat-Ease Inc. 2001, Minneapolis, MN, USA) and Minitab Release 14.1 software (Minitab Inc., State College, PA, USA). Significant differences were defined as (p < 0.05).