## 3 Results and Discussion
### Optimization and Validation of the Predicted Model for Brewing Conditions of Cold Brew Coffee  
The optimal levels of each parameter were determined for the TDS of 1.35%, which was the TDS of coffee brewed using the French Press method. The Design Expert software generated the following conditions to achieve a TDS of 1.35% (Table 4). Three experimental runs using the predicted optimized conditions were conducted to validate the RSM model. Table 5 displays the predicted mean, including a 95% prediction interval (PI), and the observed mean with standard deviation. The test run showed that the model was significant, and the observed means fell within the 95% prediction interval. Thus, the model was validated and could be used for prediction. In this study, water temperature, C2 WR, and coffee mesh size significantly influenced the TDS of CBC. The TDS increased with the increase in extraction temperature from \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Brewing Conditions**} \\ \hline
**Water Temperature** & **Coffee-to-Water** & **Coffee Mesh Size** & **Extraction Time (h)** \\ (°C) & **Ratio (g/mL)** & **(mm)** & **Extraction Time (h)** \\ \hline
4 & 1:14 & 0.71 & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimized brewing conditions generated by Design Expert software. Figure 1: 3D contour plots generated by Design Expert (Stat Ease, Inc.) of the significantly interacting model terms (**a**) A: water temperature and B: C2 WR; (**b**) B: C2 WR; and C: coffee mesh size. The dots indicated the axial and centre design points. The red zone showed high values of TDS obtained, whereas the lower TDS percentage were shown as the color that changed towards the blue zone. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Response** & **Predicted** & **95\% PI Low** & **Observed** & **95\% PI High** & **Std. Dev.** \\  & **Mean** & & **Mean** & & \\ \hline TDS \({}^{*}\) & 1.31 & 1.16 & 1.37 & 1.45 & 0.07 \\ \hline \hline \end{tabular} \({}^{*}\)Significant model with insignificant lack of fit.  
\end{table} 
Table 5: Response surface methodology (RSM) model validation via predicted values vs. observed values. 4 to 30 \({}^{\circ}\)C. This can be attributed to the increased solubility of solutes. At a higher water temperature, water is able to extract solutes that are moderately water-soluble at lower temperatures [20]. Similar to our findings, [PERSON] et al. (2020) reported a significantly higher total soluble solid content for coffee brewed at 25 \({}^{\circ}\)C than for coffee brewed at 10 \({}^{\circ}\)C [21]. [PERSON] et al. (2019) also reported similar findings, showing that temperature significantly affected more total solids in coffee prepared at 22 \({}^{\circ}\)C compared with 5 \({}^{\circ}\)C [22]. When other brewing conditions (water temperature of 4 \({}^{\circ}\)C, coffee mesh size of 0.71 mm, extraction time of 7 h) were kept constant, it was found that the TDS increased from 1.19 to 3.06% as the C2 WR increased. TDS refers to the amount of dissolved material mass in the beverage and can consist of volatile and non-volatile compounds [11]. A higher C2 WR indicates that a higher amount of volatile and non-volatile compounds may naturally be present [23] and thus would produce a higher TDS. Aside from that, coffee mesh size appeared to significantly influence the TDS of coffee. The TDS had an inverse relationship with the coffee mesh size. At a constant brewing condition (water temperature 17 \({}^{\circ}\)C, C2 WR 11.46 \(\times\) 10\({}^{-2}\) g/mL, extraction time 15.5 h), the TDS measured for 0.25 mm and 0.71 mm coffee mesh sizes were 2.72% and 2.32%, respectively. This can be explained by the higher surface area of the coffee grind. A smaller coffee particle exhibits a larger surface area, resulting in more efficient extraction of solutes [24]. Other studies published different findings. For example, a study by [PERSON] et al.