## 4 Results and Discussion  
### Results  
Table 3 shows the analysis of variance to test the differences among group means. The R-square and R-square adjusted values are 99.9% and 99.5%, respectively. This result indicates the model is highly effective for explaining the changes in values. Moreover, the p-value of the ANOVA test also demonstrates a high model fit. In addition, the results of fitting a linear regression model, including the second-order interactions to the response data, are shown in Table 4.  
According to the coefficients table, all the main factors were shown to be significant in the rumor spreading model. Additionally, the second-order interactions represent the interactions of \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Term** & **Coefficients** & **Standard Errors** & **VIF** \\ \hline constant & 30.89 ** & 0.35 & \\ \(\times\)1 & \(-\)2.32 ** & 0.19 & 1.24 \\ \(\times\)2 & 6.41 ** & 0.19 & 1.27 \\ \(\times\)3 & 8.35 ** & 0.19 & 1.25 \\ \(\times\)4 & \(-\)2.85 ** & 0.19 & 1.16 \\ \(\times\)5 & \(-\)1.02 ** & 0.18 & 1.29 \\ \(\times\)12 & \(-\)0.11 & 0.58 & 2.15 \\ \(\times\)22 & \(-\)0.17 & 0.55 & 2.14 \\ \(\times\)32 & 0.34 & 0.58 & 1.81 \\ \(\times\)42 & 0.35 & 0.53 & 2.20 \\ \(\times\)52 & \(-\)0.96 & 0.50 & 2.26 \\ \(\times\)1 ** \(\times\)2 & 0.95 & 0.51 & 1.34 \\ \(\times\)1 ** \(\times\)3 & 0.80 & 0.53 & 1.36 \\ \(\times\)2 *\(\times\)3 & 0.73 & 0.53 & 1.16 \\ \(\times\)1 *\(\times\)4 & \(-\)0.89 & 0.60 & 1.43 \\ \(\times\)2 *\(\times\)4 & 1.57 & 0.60 & 1.43 \\ \(\times\)3 *\(\times\)4 & 0.72 & 0.53 & 1.27 \\ \(\times\)1 *\(\times\)5 & \(-\)1.60 & 0.59 & 1.34 \\ \(\times\)2 *\(\times\)5 & \(-\)3.10 ** & 0.57 & 1.46 \\ \(\times\)3 *\(\times\)5 & \(-\)1.70 ** & 0.49 & 1.28 \\ \(\times\)4 *\(\times\)5 & 2.32 * & 0.58 & 1.39 \\ \hline \hline \end{tabular} Note: \(a\), \(E\), \(L\), \(o\) and \(s\in[-1,1]\).  
\end{table} 
Table 4: The coefficients of the terms in the regression model including interactions up to 2 nd order. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Run** & \(a\) (\(\times\)1) & \(E\) (\(\times\)2) & \(L\) (\(\times\)3) & \(\sigma\) & **Highly Strength (\(\times\)5)** & **\%Infected** \\ \hline
18 & \(-\)0.031 & \(-\)0.816 & 0.099 & \(-\)0.019 & \(-\)0.34 & 25.87 \\
19 & 0.621 & \(-\)0.404 & 0.359 & 0.315 & 0.38 & 27.93 \\
20 & 0.416 & \(-\)0.43 & \(-\)0.155 & \(-\)0.498 & 0.373 & 27.27 \\
21 & 0.212 & 0.008 & 0.769 & 0.229 & \(-\)0.361 & 37.40 \\
22 & 0.556 & 0.276 & \(-\)0.355 & 0.234 & 0.275 & 27.20 \\
23 & \(-\)0.497 & \(-\)0.184 & 0.599 & \(-\)0.539 & \(-\)0.243 & 37.60 \\
24 & 0.367 & \(-\)0.5 & \(-\)0.615 & \(-\)0.026 & \(-\)0.319 & 21.36 \\
25 & \(-\)0.737 & 0.569 & 0.239 & 0.096 & \(-\)0.029 & 37.73 \\ \hline \hline \end{tabular} Note: \(a\), \(E\), \(L\), \(o\) and \(s\in[-1,1]\).  
\end{table} 
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Term** & **Coefficients** & **Standard Errors** & **VIF** \\ \hline constant & 30.89 ** & 0.35 & \\ \(\times\)1 & \(-\)2.32 ** & 0.19 & 1.24 \\ \(\times\)2 & 6.41 ** & 0.19 & 1.27 \\ \(\times\)3 & 8.35 ** & 0.19 & 1.25 \\ \(\times\)4 & \(-\)2.85 ** & 0.19 & 1.16 \\ \(\times\)5 & \(-\)1.02 ** & 0.18 & 1.29 \\ \  
environmental bias, including the counseling of leader, and social network usage with power of influencers. All the variance inflation factors (VIF) values were under 10, which means that the multicollinearity problem was not serious [42]. The normal score vs. the residuals plot in Figure 3 showed an approximately linear range, which indicates that the error terms were normally distributed. The result of the normal plot also suggests that our model was accurate and met all assumptions. The main effects plot in Figure 3 shows the predicting response model of five interactive factors. The slope of factors is referred to as the intensity of the effects of each factor. The results, which are given in Table 4 and Figure 4, indicate that both \"environmental bias\" and \"counseling of leader\" have a positive effect on the percentage of infection.