## 3 Results and Discussion
### The Models Fitted for Quality Characteristics of Bread  
Analysis of variance (ANOVA) showed that the quadratic or reduced quadratic models adequately represented the data obtained for bread volume, height, and firmness, which are the major and representative quality characteristics (Table 4). For the volume of bread made from the fresh, RTP, and RTB doughs, the F-values were 27.89, 24.64, and 35.91, respectively, which indicated that all models showed significance at \(p<0.0001\), and the quadratic determination coefficients (R2) describing the goodness of fit of the models were 0.868, 0.916, and 0.867, respectively. For the height of bread made from the fresh, RTP, and RTB doughs, the F-values were 16.81, 45.58, and 37.76, respectively, which indicated that all of the models showed significance at \(p<0.0001\), and the quadratic determination coefficients (R2) were 0.952, 0.916, and 0.900, respectively. For the firmness of the bread made from the fresh, RTP, and RTB doughs, the F-values were 36.51, 60.00, and 33.91, respectively, which indicate that all of the models showed significance at \(p<0.0001\), and the quadratic determination coefficients (R2) describing the goodness of fit of the models were 0.869, 0.964, and 0.890, respectively. The three-dimensional response surface plots for the effects of the first fermentation time (A) and second fermentation time (B) on the volume, height, and firmness of the bread made from the fresh and the RTP and RTB frozen doughs are shown in Figure 2. Regarding bread volume, in Figure 2, the plots for the fresh, RTP, and RTB doughs were similar. In particular, the plots for the fresh and the RTP doughs were almost identical, and the plot for the RTB dough was slightly different. The first and second fermentation times had the most significant effects, and the dough formula with long first and second fermentation times produced the largest bread volume for all three doughs. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Response** & **Dough** & **Source** & **DF** & **Sum of Squares** & **Mean Square** & **F Value** & **R2** & **AdjR2** \\ \hline \multirow{8}{*}{Bread volume} & Fresh & Model & 5 & 11,065.60 & 2213.12 & 27.89 *** & 0.868 & 0.838 \\  & & Residual & 21 & 1666.30 & 79.35 & & & \\  & & Total & 26 & 12,731.90 & & & & \\ \cline{2-10}  & RTP & Model & 8 & 11,868.74 & 1483.59 & 24.64 *** & 0.916 & 0.879 \\  & & Residual & 15 & 12,858.01 & 857.20 & & & \\  & & Total & 29 & 92,832.24 & & & & \\ \cline{2-10}  & RTB & Model & 4 & 14,833.25 & 3708.31 & 35.91 *** & 0.867 & 0.843 \\  & & Residual & 22 & 2272.04 & 103.27 & & & \\  & & Total & 26 & 17,105.29 & & & & \\ \hline \multirow{8}{*}{Bread height} & Fresh & Model & 14 & 1486.24 & 106.16 & 16.81 *** & 0.952 & 0.895 \\  & & Residual & 12 & 75.80 & 6.32 & & & \\  & & Total & 29 & 1562.04 & & & & \\ \cline{2-10}  & RTP & Model & 5 & 1468.86 & 293.77 & 45.58 *** & 0.916 & 0.896 \\  & & Residual & 21 & 135.34 & 6.44 & & & \\  & & Total & 26 & 1604.20 & & & & \\ \cline{2-10}  & RTB & Model & 5 & 1264.40 & 252.88 & 37.76 *** & 0.900 & 0.876 \\  & & Residual & 21 & 793.01 & 52.87 & & & \\  & & Total & 26 & 2889.05 & & & & \\ \hline \multirow{8}{*}{Bread firmness} & Fresh & Model & 4 & 63.70 & 15.93 & 36.51 *** & 0.869 & 0.845 \\  & & Residual & 22 & 9.60 & 0.44 & & & \\ \cline{2-10}  & Total & 26 & 73.30 & & & & \\ \cline{2-10}  & RTP & Model & 8 & 148.00 & 18.50 & 60.00 *** & 0.964 & 0.948 \\ \cline{1-1}  & & Residual & 18 & 5.55 & 0.31 & & & \\ \cline{1-1}  & & Total & 26 & 153.55 & & & & \\ \cline{1-1} \cline{2-10}  & RTB & Model & 5 & 57.91 & 11.58 & 33.93 *** & 0.890 & 0.864 \\ \cline{1-1}  & Residual & 21 & 7.17 & 0.34 & & & & \\ \cline{1-1}  & Total & 26 & 65.08 & & & & & \\ \hline \end{tabular}
\end{table} 
Table 4: Analysis of variance of the response surface quadratic or reduced quadratic models for volume, height, and firmness of bread made with each frozen dough.