*2.4. Response Surface Methodology (RSM)*

To investigate the optimal condition for bio-jet fuel production through microwaveassisted catalytic transesterification, response surface methodology (RSM) was applied by using Design Expert 11 software (Stat-Ease, Minneapolis, MN, USA). RSM was normally used to optimize an experiment based on the selected variables [43–45]. Traditionally, the one-factor-at-a-time (OFAT) methodology, which varies one variable at a time while maintaining the others as constant, is time-consuming and expensive because many experimental runs are required to evaluate the relationship between the studied variables. Hence, RSM is recommended as the optimization can be achieved with less experimental runs as compared to OFAT by varying different parameters at a time. Moreover, a mathematical model can be generated to describe the experiments by using a polynomial function that fitted by the least square method:

$$Y = \beta\_0 + \sum \beta\_i X\_i + \sum \beta\_{ij} X\_i X\_j + \sum \beta\_i \beta\_i X\_i X\_i + \varepsilon \tag{6}$$

where *Xi* indicates the studied variable, while *Y* symbolize the results to be optimized. *β0*, *βi*, and *βij*, however, are the regression coefficient. Finally, *e* represents the random error.

In this project, the Box–Behnken design was selected as it able to estimate the regression coefficient of a second-degree quadratic equation with less experimental runs in comparison to central composite design. In this optimization study, three parameters were considered, namely, coconut oil to ethanol molar ratio, reaction time, and microwave power. The respective levels of different parameters are summarized in Table 2 and note that the center point was repeated three times to determine the experimental errors. The 3-levels-3-parameters Box–Behnken Design was implemented and showed that a total 15 experimental runs with different reaction conditions (refer to Table 3) are required to conduct the optimization study. From there, bio-jet fuel was produced, and the result obtained was inserted into software for further analysis. Analysis of variance (ANOVA) was conducted to generate a mathematical model for the studied response, in this case, the biokerosene yield.


**Table 2.** Experimental level of studied parameters.

**Table 3.** Fit summary table.

