## 3 Result and Discussion
### Statistical Analysis  
The first proposed model by the Design-Expert(r) Software was the polynomial quadratic model, and the analysis was performed based on this model. The proposed model based on Analysis of Variance (ANOVA) is shown in Equation (2).  
\[\begin{array}{l}\text{Conversion (\%)}=68.04246+3.38036\times A+7.67297\text{ }^{*}B-3.75617\text{ }^{*}\text{C}-1.49131\text{ }^{*}\text{ A}\text{ }^{*}\text{ B}\\ +2.25024\text{ }^{*}\text{ A}\text{ }^{*}\text{ C}+0.19561\text{ }^{*}\text{ B}\text{ }^{*}\text{C}-5.48508\text{ }^{*}\text{ A}2-0.31950\text{ }^{*}\text{ B}2-4.36231\times 10^{-4}\times\text{C2}\end{array} \tag{1}\]  
where A is Catalyst concentration (wt %), B is molar ratio (methanol to oil) and C is reaction time (min). Table 6 shows the proposed model by RSM. Also, in Table 7, the results of variance analysis of  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Instruments** & **Measuring Range** & **Accuracy** & \begin{tabular}{c} **Percentage** \\ **Uncertainties** \\ \end{tabular} \\ \hline \hline AVL DITEST GAS 1000 & CO 0–15\% vol. & \begin{tabular}{c} \textless{}10.0\% vol.: \(\pm\)0.02\% vol., \(\pm\)3\% \\ \(\text{o.M.}\)\(\geq\)10.0\% vol: \(\pm\)5\% o. M. \\ \end{tabular} & \(\pm\)0.3 \\ \hline \hline \multirow{4}{*}{HC 0–30,000 ppm vol.} & \begin{tabular}{c} \textless{}16.0\% vol.: \(\pm\)0.3\% vol., \(\pm\)3\% \\ \(\text{o.M.}\)\(\geq\)16.0\% vol: \(\pm\)5\% o. M. \\ \end{tabular} & \(\pm\)0.2 \\ \hline \hline \multirow{4}{*}{HC 0–30,000 ppm vol.} & \begin{tabular}{c} \textless{}200 ppm vol.: \(\pm\)4 ppm vol., \(\pm\)3\% \\ \(\text{o.M.}\)\(\geq\)5000 ppm vol.: \(\pm\)5\% o. \\ \end{tabular} & \(\pm\)0.2 \\ \cline{1-1}  & \begin{tabular}{c} M.\(\geq\)10,000 ppm vol.: \(\pm\)10\% o. M \\ \end{tabular} & \(\pm\)0.2 \\ \hline \hline \multicolumn{1}{c}{O\({}_{2}\) 0–25\% vol.} & \
\begin{tabular}{c} \textless{}0.02\% vol.\(\pm\)1\% o. M. \\ \end{tabular} & \(\pm\)0.3 \\ \hline \hline NO\({}_{\text{s}}\) 0–5000 ppm vol. &
\begin{tabular}{c} \textless{}5 ppm vol.\(\pm\)1\% o. M. \\ \end{tabular} & \(\pm\)0.2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Percentage uncertainties of various instruments.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Units** & **Measured Property** \\ \hline Density & g/cm\({}^{3}\) & 0.92 \\ Kinematic viscosity & mPa-s & 33 \\ Acid value & Mg KOH/g & 0.89 \\  & oil & \\ Water content & mg/g & 0.10 \\ Palmitic acid (C16:0) & wt \% & 4.53 \\ Stearic acid (C18:0) & wt \% & 1.94 \\ Oleic acid (C18:1) * & wt \% & 11.12 \\ Linoleic acid (C18:2) * & wt \% & 15.15 \\ Linolenic acid (C18:3) * & wt \% & 23.01 \\ Other fatty acids & wt \% & 44.25 \\ \hline \hline \end{tabular}  
* Carbon atoms number: double bond number.  
\end{table}
Table 5: Chemical and physical properties of the used CSO.  
the RSM model are shown based on ANOVA analysis. The probability value (p-value) for the model is less than 0.01. Therefore, ANOVA shows that the model is statistically significant. The catalyst concentration (wt %), molar ratio (methanol to oil) and reaction time (min) have a significant effect on biodiesel yield. Also, the interaction of the catalyst concentration (wt %)--reaction time (min) and interaction of the molar ratio (methanol to oil)--reaction time (min) are significant.