## 3 Results
### Tensile Strength  
According to the surface plots presented in Figure 5, an increase in SSP content exhibits a clear decreasing trend in tensile strength. This may be attributed to increased filler loading weakening the interfacial bonding between the matrix and filler within the composite structure. As the EPA content increases, a slight reduction in tensile strength is also observed; however, this effect appears to be limited and can be tolerated up to a certain threshold. By contrast, increasing EPB content has a positive influence, leading to an improvement in tensile strength. In the contour plots evaluating the combined effects of SSP and EPA, a decline in tensile performance is observed as the contents of both components increase. This indicates a negative synergy between the two parameters, which jointly deteriorate the mechanical properties. In the case of the combined effect of SSP and EPB, the opposing effects (SSP reducing and EPB enhancing tensile strength) tend to counterbalance each other, resulting in a more moderate performance profile. Tensile strength increases with rising EPB content. However, EPA limits this effect, so optimal strength occurs at moderate levels of both components. These findings suggest that optimizing EPB content is essential to improving tensile strength, while SSP and EPA contents must be carefully balanced to avoid compromising mechanical integrity. The quadratic model proposed by the RSM design for tensile strength prediction is presented in Equation (7). Excessive SSP disrupts matrix continuity and weakens bonding. EPB improves tensile strength by enhancing matrix flexibility and adhesion.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Source** & **Sum of Squares** & **Mean Square** & **F-Value** & \(p\)**-Value** \\ \hline Model & 5.79 & 0.6435 & 132.37 & \textless{}0.0001 \\ A-SSP (g) & 5.08 & 5.08 & 1045.62 & \textless{}0.0001 \\ B-EPA (g) & 0.1246 & 0.1246 & 25.63 & 0.0015 \\ C-EPB (g) & 0.0397 & 0.0397 & 8.17 & 0.0244 \\ AB & 0.0200 & 0.0200 & 4.11 & 0.0821 \\ AC & 0.0200 & 0.0200 & 4.11 & 0.0821 \\ BC & 0.0200 & 0.0200 & 4.11 & 0.0821 \\ A\({}^{2}\) & 0.4359 & 0.4359 & 89.67 & \textless{}0.0001 \\ B\({}^{2}\) & 0.0046 & 0.0046 & 0.9389 & 0.3648 \\ C\({}^{2}\) & 0.0001 & 0.0001 & 0.0107 & 0.9206 \\ Residual & 0.0340 & 0.0049 & & \\ Lack of Fit & 0.0290 & 0.0058 & 2.32 & 0.3279 \\ Pure Error & 0.0050 & 0.0025 & & \\ Cor Total & 5.83 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: ANOVA analysis for Shore D hardness of the bio-composites.  
Table 6 summarizes the ANOVA results for the effects of SSP, EPA, and EPB contents on the tensile strength of the bio-composites. The model is statistically significant overall (F = 436.31, \(p<0.0001\)), indicating that the selected variables reliably capture their influence on tensile performance. SSP emerges as the dominant factor, with a notably high F-Value (F = 1288.26), confirming its substantial role in reducing tensile strength--likely due to matrix disruption and weakened interfacial bonding at higher filler loadings. EPA also demonstrates a statistically significant but less pronounced effect (F = 15.38, \(p=0.0018\)), suggesting it should be carefully controlled in formulation design. By contrast, EPB shows a positive contribution to tensile strength (F = 5.30, \(p=0.0384\)), albeit more limited in magnitude. While the lack of fit test was significant (\(p=0.0228\)), indicating that the model may not fully capture all system variability, the overall low residual error supports its general reliability. Therefore, the model provides a solid foundation for understanding the relative impacts of the input variables. Future enhancements, particularly the inclusion of interaction and quadratic terms, could improve the model's accuracy and allow better prediction of complex behaviors in composite performance.