## 2 Materials and Methods
### Statistical Analysis and Experimental Design for Optimization  
The AC values of the baked biscuits were analyzed by five-fold determination of each methanolic extract obtained by conventional extraction and UAE within the same day using the modified DPPH method. The results obtained were presented as the mean \(\pm\) standard deviation (SD). All data were statistically evaluated by the analysis of variance (ANOVA) test. A post hoc Duncan's test was applied for the calculation of the significant differences among mean values of characteristic oil parameters at the probability level \(p<0.05\).  
The RSM was applied to study the simultaneous effects of the RPC content and SAFA content in fats used for biscuits preparation on their AC determined by DPPH method and sensory characteristics. The levels of RPC and SAFA for a CCD and RSM were determined on the basis of preliminary experiments carried out and were varied from 0 to 40 g and 2.3-24.9 g, respectively. The experimental design used for the analysis was a CCD with two factors and three levels. In this experimental design, the factor levels were coded using \"\(-\)1\" for the lowest level (0 g and 2.3 g for RPC content and SAFA content, respectively), \"1\" for the highest level (40 g and 24.9 g for RPC content and SAFA content, respectively), and \"0\" for neutral (middle) level (20 g and 7.8 g for RPC content and SAFA content, respectively). The experiments consisted of 11 runs with two factors and two replicates of the central point for the estimation of pure error. The effect of the two independent variables (RPC content and SAFA content) on the responses (Y\({}_{n}\), Y\({}_{1}\)--DPPH\({}_{\text{CE}}\), Y\({}_{2}\)--DPPH\({}_{\text{UAE}}\), Y\({}_{3}\)--color, Y\({}_{4}\)--odor, Y\({}_{5}\)--texture, Y\({}_{6}\)--flavor, Y\({}_{7}\)--overall acceptability, and Y\({}_{8}\)--purchase intent) was modeled using a polynomial response surface. The second-order response function for the experiments was predicted by the following equation:  
\[\text{Y}_{n}=\ \beta_{0}+\ \beta_{1}\text{RPC}\ +\ \beta_{2}\text{SAFA}\ +\ \beta_{11}\text{RPC}^{2}+\ \beta_{22}\text{SAFA}^{2}+\ \beta_{12}\text{RPC}\ \times\ \text{SAFA} \tag{1}\]  
where Y\({}_{n}\) is one of the eight responses; RPC and SAFA represent the independent variables; \(\beta_{0}\) is the constant; \(\beta_{1}\), \(\beta_{2}\) are the linear-term coefficients; \(\beta_{11}\), \(\beta_{22}\) are the quadratic-term coefficients; and \(\beta_{12}\) is the cross-term coefficient.  
The fitness of the model was evaluated by the determination coefficient R\({}^{2}\), the fraction of the variation explained by the model, and analysis of variance (ANOVA). The F-test was applied to confirm whether the variance explained by the regression model was significantly larger than the variance of the residual and to evaluate the model lack-of-fit (model error).  
The effects of two factors (RPC content and SAFA content) and their interactions on DPPH in methanolic extracts of biscuits obtained by conventional extraction and UAE, as well as sensory characteristics, were displayed in surface and contour plots. The chemometric analyses were constructed using the Statistica 8.0 software (StatSoft, Tulsa, OK, USA). However, Fizz software (Biosystemes, Courtenon, France) was applied for the collection of all sensory data.