## 4 Discussion
### Forecasting Electrical Characteristics of Flexible Sensing Materials by Regression Modelling
#### 4.3.1 Hysteresis  
RSM  
The ANOVA findings for the hysteresis performance response model of multicomponent sensing composites are presented in Table 10. The regression model exhibits an F-value of 26.81, with the relevance of the influencing factors ranked as follows: MT \(>\) Fe\({}_{3}\)O\({}_{4}\) \(>\) CNT \(>\) MLG. For quadratic terms, the ordering is \(x_{2}^{2}>x_{4}^{2}>x_{1}x_{3}>x_{1}x_{4}\). A higher F-value indicates a more substantial impact of the factors on the response value. The \(p\)-value for the model term is below 0.0001, signifying its significance; conversely, the \(p\)-value for the lack of fit term is 0.786, exceeding 0.05, indicating its insignificance. The R\({}^{2}\) of the RSM model is 0.8961, demonstrating a high degree of fit. The coefficient of variance (C.V%) is 3.53%, below 5%, suggesting that the model possesses good reliability and accurately represents the experimental data. Figure 12a,b illustrate the influence of the Fe\({}_{3}\)O\({}_{4}\) and carbon-based conductive fillers on the hysteresis of the flexible sensing material, with the variation in the hysteresis response value exhibiting relative smoothness due to the interaction of many nanoparticles. The hysteresis of the sensing material exhibits a gradual decline as the concentrations of Fe\({}_{3}\)O\({}_{4}\), CNT, and MLG increase. Notably, when carbon particles interact with Fe\({}_{3}\)O\({}_{4}\), the hysteresis variation becomes comparatively more stable, aligning with the findings in the literature [63], which indicate that Fe\({}_{3}\)O\({}_{4}\) particles positively influence the sensing material's ability to sustain a rapid response. Figure 12c,e,f illustrate the interaction between the filler and the MT, indicating that the hysteresis of the sensing material generally increases with temperature throughout the moulding process. This is supported by Equation (11), \begin{table}
\begin{tabular}{c c c c c c} \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & \(p\)**-Value** & **Status** \\ \hline Model & 29.48 & 14 & 4.25 & 26.81 & \textless{}0.0001 & Significant \\ \(x_{1}\)-Fe\({}_{3}\)O\({}_{4}\) & 1.5264 & 1 & 0.0002 & 75.632 & \textless{}0.0001 & \\ \(x_{2}\)-CNT & 6.829 & 1 & 26.89 & 6.86 & \textless{}0.0001 & \\ \(x_{3}\)-MLG & 1.70 & 1 & 1.70 & 1.74 & 0.0055 & \\ \(x_{4}\)-MT & 0.2506 & 1 & 0.2506 & 125.58 & 0.0229 & \\ \(x_{1}x_{2}\) & 0.3147 & 1 & 0.3147 & 1.99 & 0.1806 & \\ \(x_{1}x_{3}\) & 3.59 & 1 & 3.59 & 22.62 & 0.0003 & \\ \(x_{1}x_{4}\) & 3.36 & 1 & 3.36 & 21.23 & 0.0004 & \\ \(x_{2}x_{3}\) & 0.4212 & 1 & 0.4212 & 2.66 & 0.1253 & \\ \(x_{2}x_{4}\) & 0.1129 & 1 & 0.1129 & 0.7124 & 0.4128 & \\ \(x_{3}x_{4}\) & 0.0346 & 1 & 0.0346 & 0.2183 & 0.6475 & \\ \(x_{1}{}^{2}\) & 0.0954 & 1 & 0.0954 & 0.6018 & 0.4508 & \\ \(x_{2}{}^{2}\) & 2.075 & 1 & 20.75 & 130.91 & \textless{}0.0001 & \\ \(x_{3}{}^{2}\) & 2.18 & 1 & 2.18 & 13.78 & 0.0023 & \\ \(x_{4}{}^{2}\) & 3.72 & 1 & 3.72 & 23.48 & 0.0003 & \\ Residual & 2.22 & 14 & 0.1585 & & & \\ Lack of Fit & 1.94 & 10 & 0.1940 & 2.79 & 0.786 & Not \\ Pure Error & 0.2781 & 4 & 0.0695 & & & significant \\ Cor Total & 31.69 & 28 & & & \\ \(R^{2}\) & & 0.8961 & & & & \\ \(R^{2}_{Adj}\) & & 0.8891 & & & & \\ R\({}^{2}_{\text{Rpd}}\) & & 0.8633 & & & & \\ C.V\% & & 3.53 & & & \\ Adeq & & 28.1654 & & & & \\ Precision & & & & & \\ \hline \end{tabular}
\end{table} 
Table 10: Analysis of variance for hysteresis response. suggesting that an elevation in the MT results in a modification of the viscoelasticity of the filler matrix, which subsequently influences the mechanical properties of the sensing unit and causes an increase in hysteresis. According to the ANOVA regression coefficient of BBD, the response relationship of hysteresis with the filler content and moulding temperature can be expressed as follows:  
\[