## 3 Results and Discussion
### Surface Plot Analysis  
We performed a three-dimensional surface plot analysis to examine the interaction factor (two factors varied simultaneously between their operating levels when the other factors stayed at fixed middle levels) effects on the performance of biodiesel yield.  
1. Figure 4a explains the interaction factor effects of M:O and CC, where a reaction time of 90 min and a temperature of 57.5 \({}^{\circ}\)C were kept at fixed mid-values. A gradual reduction in biodiesel yield was observed after the mid-point values of both M:O and CC. The desired higher biodiesel yield was found to be nearer the mid-values of M:O and CC. Excess quantity of M:O results in an increase in the glycerol solubility, whereas a higher amount of CC results in higher viscosity, which then affects the mixing ability and produces soap formation and emulsions, which ensures lower biodiesel yield. Similar observations are reported for Pithecellobium dulce seed oil [35] and flaxseed oil [45].
2. The impact of two variables (such as M:O and RT) varied between their respective levels after the two parameters were held at respective mid-values (see Figure 4b). A simultaneous increase in M:O and RT, wherein the rate of reaction increases such that it pushes the reaction forward, could favor biodiesel yield. When compared to M:O, the impact of reaction temperature was found to be negligibly small. A similar effect was obtained corresponding to the transesterification of soybean oil with ethanol [38].
3. Figure 4c displays the interaction factor effects of M:O and RT when two of the parameters (i.e., reaction temperature of 57.5 \({}^{\circ}\)C and catalyst concentration of 7.5 wt.%) are maintained constant. The biodiesel yield tends to increase with increased values of M:O and tends to decrease with an increase in reaction time. Higher biodiesel yield was obtained at a shortened duration corresponding to the middle level of the reaction temperature and catalyst concentration.
4. The effect of CC and RT was analyzed after varying two factors simultaneously between their operating levels (refer to Figure 4d). The biodiesel yield tends to increase with increased values of catalyst concentration up to 1 wt.%, wherein the reaction temperature was found to have negligible impact. It was also observed that yield was found to decrease with high values of catalyst concentration and reaction temperatures that favor the triglyceride saponification reaction. The results are analogous to biodiesel yield production from jatropha seed oil [88].
5. The impact on biodiesel yield by varying two variables simultaneously, such as CC and RT (refer to Figure 4e). The combination of higher catalyst concentration and mid-values of reaction time resulted in higher biodiesel yield. An increase in weight percent of catalyst concentration ensures supplying more catalyst for the reacting samples that could accelerate the biodiesel yield. It was also observed that there was no significant improvement in the yield after ensuring a sufficient reaction time of 90 min.
6. The effect of reaction time and reaction temperature when variables simultaneously varied between the operating levels were analyzed for the fixed values of CC of 1 wt.% and M:O of 7.5 (see Figure 4f). The resultant surface plot is seen to appear almost flat, which clearly indicates the biodiesel yield tends to have negligible influence on the interaction effect of reaction temperature and time. With increased values of reaction time, the biodiesel yield was found to have a negligible effect with an increasing trend (required time to attain the equilibrium point of a reaction wherein reaction rate increases), and beyond the limit, there might be a possibility to attain a reversible reaction when the reaction rate increases with the increased temperature [89].