## 4 Results and Discussions
### Proposed Regression Model of the Response
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Term** & **Effect** & **Coef** & **SE Coef** & **T-Value** & \(p\)**-Value** & **VIF** \\ \hline Constant & & 4.03383 & 0.00598 & 674.32 & 0.000 & \\ ut & 0.80109 & 0.40055 & 0.00598 & 66.96 & 0.000 & 1.00 \\ Xba1 & \(-\)0.01922 & \(-\)0.00961 & 0.00598 & \(-\)1.61 & 0.111 & 1.00 \\ Xba2 & \(-\)0.04359 & \(-\)0.02180 & 0.00598 & \(-\)3.64 & 0.000 & 1.00 \\ Xba3 & 0.02766 & 0.01383 & 0.00598 & 2.31 & 0.023 & 1.00 \\ AS1 & \(-\)0.25172 & \(-\)0.12586 & 0.00598 & \(-\)21.04 & 0.000 & 1.00 \\ AS2 & 0.43266 & 0.21633 & 0.00598 & 36.16 & 0.000 & 1.00 \\ AS3 & \(-\)0.16828 & \(-\)0.08414 & 0.00598 & \(-\)14.07 & 0.000 & 1.00 \\ Tout & \(-\)0.08484 & \(-\)0.04242 & 0.00598 & \(-\)7.09 & 0.000 & 1.00 \\ Cgh & 0.03328 & 0.01664 & 0.00598 & 2.78 & 0.006 & 1.00 \\ Cg & \(-\)0.27141 & \(-\)0.13570 & 0.00598 & \(-\)22.68 & 0.000 & 1.00 \\ Cs & 0.17766 & 0.08883 & 0.00598 & 14.85 & 0.000 & 1.00 \\ ut*AS1 & \(-\)0.08766 & \(-\)0.04383 & 0.00598 & \(-\)7.33 & 0.000 & 1.00 \\ ut*AS2 & 0.07359 & 0.03680 & 0.00598 & 6.15 & 0.000 & 1.00 \\ ut*AS3 & \(-\)0.03422 & \(-\)0.01711 & 0.00598 & \(-\)2.86 & 0.005 & 1.00 \\ ut*Cgh & 0.05672 & 0.02836 & 0.00598 & 4.74 & 0.000 & 1.00 \\ ut*Cg & 0.14391 & 0.07195 & 0.00598 & 12.03 & 0.000 & 1.00 \\ ut*Cs & \(-\)0.14016 & \(-\)0.07008 & 0.00598 & \(-\)11.71 & 0.000 & 1.00 \\ Xba1*Tout & 0.02953 & 0.01477 & 0.00598 & 2.47 & 0.015 & 1.00 \\ Xba2*Cs & \(-\)0.02859 & \(-\)0.01430 & 0.00598 & \(-\)2.39 & 0.019 & 1.00 \\ Xba3*Cg & \(-\)0.03141 & \(-\)0.01570 & 0.00598 & \(-\)2.63 & 0.010 & 1.00 \\ AS1*AS3 & 0.03047 & 0.01523 & 0.00598 & 2.55 & 0.012 & 1.00 \\ AS1*Cg & \(-\)0.09891 & \(-\)0.04945 & 0.00598 & \(-\)8.27 & 0.000 & 1.00 \\ AS1*Cs & 0.08203 & 0.04102 & 0.00598 & 6.86 & 0.000 & 1.00 \\ AS2*Cg & 0.02484 & 0.01242 & 0.00598 & 2.08 & 0.040 & 1.00 \\ AS2*Cs & \(-\)0.02672 & \(-\)0.01336 & 0.00598 & \(-\)2.23 & 0.028 & 1.00 \\ AS3*Cg & 0.02578 & 0.01289 & 0.00598 & 2.15 & 0.034 & 1.00 \\ Tout*Cg & 0.03234 & 0.01617 & 0.00598 & 2.70 & 0.008 & 1.00 \\ Cgh*Cs & \(-\)0.04734 & \(-\)0.02367 & 0.00598 & \(-\)3.96 & 0.000 & 1.00 \\ Cg*Cs & \(-\)0.08578 & \(-\)0.04289 & 0.00598 & \(-\)7.17 & 0.000 & 1.00 \\ \hline \hline \multicolumn{6}{c}{Coded Coefficients.} \\ \hline
**S** & \multicolumn{2}{c}{**R-sq**} & \multicolumn{2}{c}{**R-sq**(**adj**)} & \multicolumn{2}{c}{**R-sq**(**pred**)} \\ \hline
0.0676794 & 98.77\% & 98.41\% & 97.90\% \\ \hline \hline \end{tabular} Model Summary.  
\end{table} 
Table 4: Estimated Effects and Coefficients for \(u_{2}\). The regression equation of this response can be presented as following model (Regression Equation in Uncoded Units):  
\[ \begin{split} u_{3}&=-16.99+0.19\;X_{ba1}+29.9\;X_{ba3} +0.01838\;AS_{1}-0.005652\;AS_{2}+0.0599\;AS_{3}\\ &\quad+0.000197\;T_{out}-0.1537\;C_{gh}-0.079\;C_{g}+0.072\;C_{s}- 0.000575\;X_{ba1}{}^{*}T_{out}\\ &\quad+1.404\;X_{ba1}{}^{*}C_{s}-0.0737\;X_{ba3}{}^{*}AS_{3}-0.000 53\;AS_{1}{}^{*}AS_{3}+0.000524\;AS_{1}{}^{*}C_{g}\\ &\quad-0.000528\;AS_{3}{}^{*}C_{g}+0.01440\;C_{gh}{}^{*}C_{g}-0.0 3934\;C_{g}{}^{*}C_{s}\end{split}  \tag{37}\]  
The results in Table 5 also report that the experimental data are highly consistent with the proposed model when the minimum value of R-square approximately 92.02% (all of them are more than 92.02%). However, this is less reliable when compared to that of \(u_{2}\) response. Based on previous analysis, it can be said that the proposed models of \(u_{2}\) and \(u_{3}\) can be utilized to get the optimum gear ratio of the second and third stages. As a consequence, the optimum gear ratio of the first stage can be obtained by \(u_{1}=u_{t}/(u_{2}\cdot u_{3})\).