## 3 Results and Discussions
### Mathematical Modelling and Analysis of Variance for BW and BH  
For the evaluation of the response variables beyond the experimental matrix, a mathematical regression analysis was employed using the RSM approach. Minitab v17 was utilized for generating the equations. Equations (6) and (7) shows the obtained regression equations for BW, and BH, respectively.  
\[\text{BW}=284.2-9.3\cdot x_{1}-0.331\cdot x_{2}-19.36\cdot x_{3}+1.031\cdot{x_ {1}}^{2}+0.3326\cdot{x_{3}}^{2}+0.01669\cdot x_{2}\cdot x_{3} \tag{6}\]  
\[\text{BH}=75.9-3.88\cdot x_{1}-0.249\cdot x_{2}-0.2462\cdot x_{3}+0.511\cdot{x _{1}}^{2}+0.000257\cdot{x_{2}}^{2} \tag{7}\]  
where \(x_{1}\) represents the WFS, \(x_{2}\) represents travel speed, and \(x_{3}\) represents the voltage.  
Furthermore, the robustness and adequacy of the obtained regression equations were analyzed by using the ANOVA technique. Table 4 shows the ANOVA for BW and BH. ANOVA was further utilized for the identification of significant and non-significant models in terms of BW and BH. The relevance of the model terms was assessed at a 95% significance level, which is necessary for identifying relevance of the model terms. A \(p\)-value lower than 0.05 suggests that the particular model had an influential effect on the respective response values [29]. Higher F-values at a 95% confidence interval, along with lower probability \(p\)-values (less than 5%), for the model terms were observed. For BW, the regression model, term along with the linear, square, and interaction terms, was found to be significant as their \(p\)-values were <0.05. For BH, the regression model term and a linear model had a significant impact on deciding the BH response. For both the responses, a negligible contribution of error term suggests that the developed model is highly suitable for predictions of responses with the least error. The non-significance of lack-of-fit is considered another important aspect for the verification of the ANOVA results. The value of lack-of-fit was observed to be more than 0.05 for both the responses of BW and BH, which shows the non-significance of lack-of-fit. The non-significance of lack-of-fit for the response suggests the suitability of the model to forecast the response value [30]. This significance of the developed model terms indicates that the obtained regression equations are adequate and reliable for the prediction of future values BW and BH. R\({}^{2}\) values were used to define the adequacy of the proposed  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Std.** & **Run** & **WFS** & **Travel Speed** & **Voltage** & **BW** & **BH** \\
**Order** & **Order** & **(m/min)** & **(mm/min)** & **(V)** & **(mm)** & **(mm)** \\ \hline
15 & 1 & 5.0 & 455 & 18 & 5.61 & 4.75 \\
10 & 2 & 5.6 & 425 & 20 & 7.61 & 6.01 \\
16 & 3 & 6.2 & 455 & 20 & 8.95 & 6.21 \\
27 & 4 & 5.6 & 455 & 19 & 6.62 & 5.34 \\
9 & 5 & 5.0 & 45 model. An R\({}^{2}\) value of 0.9815 and adj. R\({}^{2}\) value of 0.9630 were depicted for BW, and an R\({}^{2}\) value of 0.9494 and adj. R\({}^{2}\) value of 0.9356 were depicted for BH. For both the responses of BW and BH, R\({}^{2}\) and adj. R\({}^{2}\) were found to be near unity, suggesting the fitness of the model for the present data and the prediction of new observations [31]. The negligible deviance between R\({}^{2}\) and Adj. R\({}^{2}\) recommends the fitness of the model for the present data and the prediction of new observations. Therefore, this determines that the regression equation for BW and BH were appropriate for predicting the response values inside the selected range.