## 2 Materials and Methods
### Design of Experiments and Statistics  
In this study, the simultaneous effects of two factors, particle size at three fractions (L, M and S) and addition level of quinoa flour (QF) in wheat flour at five levels (0, 5, 10, 15 and 20%) on the Falling number (FN) index were investigated; water absorption of quinoa-wheat flour dough and rheological properties, as responses, were also investigated. The main and interaction effects of the factors, particle size and addition level of QF in wheat flour, on the responses were evaluated by using response surface methodology (RSM) by means of a general factorial design. RSM has been widely used in the design and formulations of new products, and optimization in conjunction with desirability function to find, the optimal condition during processing [44] or to obtain the optimum factors, describing the relationships between responses and factors [45]. A numerical optimization technique was used in the optimization process as showed in some studies [46; 47; 48; 43] allowing us to find the optimal value of the factors in relation with dough rheology. In Table 1 shows the experimental design with the coded and real values of the factors used in this study, consisting of 15 combinations. For all responses a polynomial quadratic regression model (Equation (4)) was proposed.  
\[\mathrm{Y}\;=\;\mathrm{b_{o}}\;+\;\mathrm{b_{1}}\mathrm{\cdot}\mathrm{X_{1}}\;+ \;\mathrm{b_{2}}\mathrm{\cdot}\mathrm{X_{2}}\;+\;\mathrm{b_{11}}\mathrm{\cdot }\mathrm{X_{1}^{2}}\;+\;\mathrm{b_{22}}\mathrm{\cdot}\mathrm{X_{2}^{2}}\;+\; \mathrm{b_{12}}\mathrm{\cdot}\mathrm{X_{1}}\mathrm{\cdot}\mathrm{X_{2}} \tag{4}\]  
In the model, Y represents the response variable and \(\mathrm{b_{o}}\), \(\mathrm{b_{1}}\), \(\mathrm{b_{2}}\), \(\mathrm{b_{11}}\), \(\mathrm{b_{22}}\) and \(\mathrm{b_{12}}\) are the regression coefficients represented as intercept, linear, quadratic and interaction effects of \(\mathrm{X_{1}}\) (particle size of quinoa flour) and \(\mathrm{X_{2}}\) (level of quinoa flour added in wheat flour) factors.  
The most adequately predictive model for each response was chosen through sequential \(F\)-test, coefficients of determination (\(R^{2}\)), adjusted coefficients of determination (\(Adj\)-\(R^{2}\)) and significant probabilities. For this purpose, a multiple linear regression analysis was applied to fit the data obtained for response to linear, two-factor interactions, quadratic and cubic models. The statistical significance of the coefficients in each predictive model were found by analysis of variance (ANOVA) and the experimental and predictive values were compared by paired \(t\) test (\(p<0.05\)) to determine the validity of the model for each response. The polynomial response surfaces were generated to show the dependence between factors, particle size and addition level, and responses. Design-Expert software, trial version 12 (Stat-Ease, Inc., Minneapolis, MN, USA) was used to carry out the experimental design,the model analysis, generation of the response surface graphs, test of model adequacy and the optimum level of formulation factors finding.  
For numerical optimization, the desired goal for each response was selected as follows: dough stability (ST) and starch gelatinization (C3-2) at maximum value, protein weakening (C1-2) and starch recrystallization during paste cooling (C5-4) were minimized, while all remaining responses were kept within range. Through one-way analysis of variance (ANOVA) the significant difference within means was tested at a 5% significance level.