## 3 Results and Discussion
### Response Analysis and Optimization  
Figure 3 shows the contour plots of the estimated response surface. These plots are helpful for selecting the levels of the factors that optimize the response of interest. For example, from Figure 3a, it is evident that safranal increases when water volume increases close to 4 mL and sample weight decreases to 15 mg.  
Figure 3b indicates that the optimum extraction temperature is around 45 \({}^{\circ}\)C and a further temperature increase has negative impacts on the response. Similarly, an increase on exposure time above 20 min results in a gradual decrease in safranal (Figure 3c). The influence of extraction temperature and exposure time in the volatile fraction of solid samples of safron has been investigated by [PERSON] et al. (2018) and [PERSON] et al. (2018) by using a three-level factorial design of experiments. In both studies, the optimum exposure time was found at 30 min, while the optimum extraction temperature was at 45 \({}^{\circ}\)C ([PERSON] et al., 2018) and 50 \({}^{\circ}\)C ([PERSON] et al., 2018). Although, in the current study, the amount of safron sample and the addition of water proved to be significant and had a high contribution on the obtained amount of safranal, a lack of literature reports still exists regarding the evaluation of these factors in the safron aroma. Previous research studies utilized higher amounts of safron for the SPME-GC-MS analysis of aroma, increasing the cost of the analysis. [PERSON] et al. (2018) used 20-40 mg of safron for the SPME experiments, while other studies used 50 mg ([PERSON] et al., 2018) and 100 mg ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018). In the present study, the RSM model suggested that only 15 mg of safron was required for SPME-GC-MS analysis.  
The desirability function was used in order to find the optimum isolation conditions of safranal. The four factors were set to the option \"in range,\" while safranal was set to the \"maximize\" option. The upper limit for safranal was set at 97.0% area. Then, the software provided 100 optimization solutions; however, based on the highest desirability value obtained (0.828), the software suggested that the optimum conditions for the extraction of safranal were A: 15 mg; B: 4 mL; C: 45 \({}^{\circ}\)C; and D: 20 min (Figure 4). The predicted mean (% area) was estimated from the model at 96.1 \(\pm\) 0.5%. A test set comprising 10 samples was analyzed under the optimized extraction conditions. The obtained results were within the prediction interval, providing an experimental average of 95.6%.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **DF 1** & **Mean Square** & **F-Value** & _p-Value_ \\ \hline Model & 19.04 & 4 & 4.76 & 18.05 & \textless{}0.0001 2 \\ A-Sample weight & 1.57 & 1 & 1.57 & 5.96 & 0.0221 \\ B-Water volume & 3.37 & 1 & 3.37 & 12.80 & 0.0015 \\ C-Extraction temperature & 9.17 & 1 & 9.17 & 34.78 & \textless{}0.0001 \\ D-Exposure time & 4.92 & 1 & 4.92 & 18.67 & 0.0002 \\ Residual & 6.59 & 25 & 0.26 & & \\ Lack of fit & 5.76 & 20 & 0.29 & 1.75 & 0.2801 3 \\ Pure error & 0.83 & 5 & 0.17 & & \\ Cor. total & 25.63 & 29 & & & \\ \hline \hline \end{tabular} \({}^{1}\) DF: degree of freedom; 2 significant; 3 not significant.  
\end{table}
Table 2: Analysis of variance results for the experimental design.