# Freeze-Thaw Pre-Treatment of Cassava Tubers to Improve Efficiency of Mechanical Peeling
## 3 Results and Discussion
### Characteristics of Cassava Tubers
Speed of brushes, peeling time, and thawing incubation time significantly (\(p<0.05\)) influenced the peeled surface area of cassava tubers. Higher \(p\)-values for the thawing temperature and some interaction terms suggested little impact on the peeled surface area of cassava tubers. Figure 2 presents the surfaces plots for the peeled surface area as a function of the rotational speed of the brushes, peeling time, thawing temperature, and incubation time. The model was further verified with the normal probability plot for the externally studentized residuals. It was determined that most of the residuals were on a straight line (Figure 2d). This indicates the normal distribution of data. Furthermore, the plot of residuals versus predicted values, as presented in Figure 2e, shows no clear pattern among the data, which suggests the absence of biases. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Mean \(\pm\) SD** \\ \hline Mass of tuber (g) & 733.4 \(\pm\) 254.7 \\ Length of tuber (mm) & 240 \(\pm\) 40.0 \\ Diameter of tuber (mm) & 66.7 \(\pm\) 9.9 \\ Peel thickness (mm) & 2.9 \(\pm\) 0.2 \\ Penetration force, flesh (N/mm\({}^{2}\)) & 3.3 \(\pm\) 0.7 \\ Penetration force, peel (N/mm\({}^{2}\)) & 5.0 \(\pm\) 0.4 \\ Dry matter, flesh (\%) & 32.9 \(\pm\) 4.1 \\ Dry matter, peel (\%) & 43.3 \(\pm\) 19.4 \\ Proportion of peel by mass (\%) & 14.7 \(\pm\) 0.9 \\ \hline \end{tabular}
\end{table} 
Table 2: Characteristics of cassava tubers (n = 20). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **Degree of Freedom** & **Mean Square** & \(F\)**Value** & \(p\)**Value** \\ \hline Intercept & 18615.46 & 12.00 & 1551.29 & 11.51 & \textless{}0.0001 \\ X\({}_{1}\)-Rotational speed of brushes & 3225.20 & 1.00 & 3225.20 & 23.93 & 0.0001 \\ X\({}_{2}\)-Peeling time & 4214.43 & 1.00 & 4214.43 & 31.27 & \textless{}0.0001 \\ X\({}_{3}\)-Thawing temperature & 68.81 & 1.00 & 68.81 & 0.51 & 0.4846 \\ X\({}_{4}\)-Incubation time & 6252.99 & 1.00 & 6252.99 & 46.39 & \textless{}0.0001 \\ X\({}_{1}\)X\({}_{2}\) & 205.05 & 1.00 & 205.05 & 1.52 & 0.2342 \\ X\({}_{1}\)X\({}_{4}\) & 25.05 & 1.00 & 25.05 & 0.19 & 0.6718 \\ X\({}_{2}\)X\({}_{3}\) & 940.43 & 1.00 & 940.43 & 6.98 & 0.0171 \\ X\({}_{2}\)X\({}_{4}\) & 18.39 & 1.00 & 18.39 & 0.14 & 0.7164 \\ X\({}_{1}\)\({}^{2}\) & 1131.89 & 1.00 & 1131.89 & 8.40 & 0.01 \\ X\({}_{2}\)\({}^{2}\) & 1012.01 & 1.00 & 1012.01 & 7.51 & 0.014 \\ X\({}_{4}\)\({}^{2}\) & 1041.20 & 1.00 & 1041.20 & 7.72 & 0.0129 \\ X\({}_{1}\)X\({}_{2}\)\({}_{3}\)X\({}_{4}\) & 1116.43 & 1.00 & 1116.43 & 8.28 & 0.0104 \\ Residual & 2291.34 & 17.00 & 134.78 & – & – \\ Lack-of-fit & 1407.20 & 12.00 & 117.27 & 0.66 & 0.7412 \\ Pure error & 884.14 & 5.00 & 176.83 & – & – \\ Correction total & 20906.81 & 29.00 & – & – & – \\ \hline \hline \end{tabular} \(R^{2}\), 0.890; Adjusted \(R^{2}\), 0.813; and \(p<0.05\) indicates significance at the 95% level.  
\end{table} 
Table 4: ANOVA for reduced cubic equation for the effect of freeze–thaw pre-treatment (FTP), rotational speed of brushes, and peeling time on the peeled surface area (PSA) of cassava tubers. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Factor Variables**} & \multicolumn{4}{c}{**Responses**} \\ \cline{2-9} \multirow{2}{*}{**Run**} & **Rotational Speed** & **Peeling** & **Thawing** & **Incubation** & **Peel Surface** & \multirow{2}{*}{**Peel Loss (\%)**} \\  & **of Brushes (rpm)** & **Time (min)** & **Temperature (\({}^{\circ}\)C)** & **Time (s)** & & **Area (\%)** & \\ \hline  & **X\({}_{1}\)** & **X\({}_{2}\)** & **X\({}_{3}\)** & **X\({}_{4}\)** & **Exp \({}^{\circ}\)** & **Pred \({}^{\circ}\)** & **Exp & **Pred** \\ \hline  
The mathematical equation obtained from RSM for the peel loss (\(PL\)) of cassava tubers is presented in Equation (4). \[