## 3 Results and Discussion
### Performance Modeling  
One of the most important objectives of this study was to determine the optimum working conditions for qualified sage seeding using a micro-granule applicator equipped with the conveyor belt seed-mereing unit. For this purpose, model equations were developed by preparing data sets in cubic form for in-row seed distribution uniformity (as V\({}_{\text{f}}\) and \(\lambda\)) based on the data given in Tables 6 and 7. Detailed analyses conducted using the Minitab statistical package program, a statistically significant cubic at the third-degree models were developed for CV\({}_{\text{fu}}\) and for V\({}_{\text{f}}\) at the 99% significance level, while the third-degree model was developed for \(\lambda\) was at the 90% significance level. Based on the analysis conducted using stepwise regression, we developed model equations for flow uniformity (y\({}_{\text{CVfu}}\)), variation factor (y\({}_{\text{Vf}}\)), and goodness criteria (y\({}_{\lambda}\)) in sage seeding with a micro-granule applicator equipped with a conveyor belt seed-mereing unit. The results from Minitab for these equations are presented in Tables 8-10. \[ \begin{array}{c}\text{Inv}_{\text{CVfu}}=0.5507-0.576\chi_{1}^{2}-0.565\chi _{2}-0.365\chi_{1}^{3}+0.387\chi_{1}\chi_{3}+0.313\chi_{1}^{2}\chi_{3}+\\ 0.158\chi_{2}^{2}+0.321\chi_{1}(\text{R}_{2}=91.61\%)\\ \end{array}  \tag{4}\]  
\[ \begin{array}{c}\text{y}_{\text{V}_{\text{f}}}=2.020-0.216\chi_{2}^{3}+0.1 297\chi_{2}^{2}+0.0622\chi_{3}^{3}+0.136\chi_{1}\chi_{3}-0.059\chi_{1}-\\ 0.111\chi_{1}\chi_{2}\chi_{3}-0.0753\chi_{3}^{2}+0.087\chi_{2}-0.0593\chi_{1} \chi_{2}^{2}(\text{R}_{2}=97.34\%)\\ \end{array}  \tag{5}\]  
\[ \begin{array}{c}\text{y}_{\lambda}=49.59+2.84\chi_{2}^{3}-3.28\chi_{3}^{3}-2. 29\chi_{1}\chi_{3}+2.29\chi_{1}\chi_{2}\chi_{3}+1.67\chi_{1}-1.34\chi_{1}^{2}- \\ 1.10\chi_{2}^{2}-0.75\chi_{3}^{2}+1.66\chi_{3}(\text{R}_{2}=92.27\%)\\ \end{array}  \tag{6}\]  
Based on the model equations, which were established with 19 variables in cubic form, the results of the stepwise regression analysis included 7, 9, and 9 variables considered for CV\({}_{\text{fu}}\), V\({}_{\text{f}}\), and \(\lambda\), respectively. As shown in Table 8, the predictor that entered the CV\({}_{\text{fu}}\) model in the first step was X\({}_{1}\)\({}^{2}\), which individually explained approximately 32% of the system. The predictor added in the second step was X\({}_{2}\), which accounted for approximately 27% of the system. The forward speed variable, which was included in the model singularly and in the form of interactions from the third step onwards, was found as the independent variable that affected the \"CV \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Run \#**} & \multicolumn{3}{c}{**Independent Variables**} & \multirow{2}{*}{**S\({}^{2}\)**} & \multirow{2}{*}{**V\({}_{\text{f}}\)**} & \multirow{2}{*}{**Evaluation**} & \multirow{2}{*}{**\(\mu\)**} & \multirow{2}{*}{**\(\lambda\)**} & \multirow{2}{*}{**Evaluation**} \\ \cline{2-2} \cline{6-9}  & \(\mathbf{X_{1}}\) & & & & & & & & \\ \hline  
\hline \hline \end{tabular}
* NBD: Negative binomial distribution.  
\end{table} 
Table 7: The results of the in-row seed distribution uniformity performance of the seed-mereing unit. model\" the most for sage seeding. The predictors \(\text{X}_{2}\)3 and \(\text{X}_{2}\)2, which were included in the \(\text{V}_{\text{f}}\) model at the first and second steps, represent the cubic and quadratic forms of the seed rate. Notably, the seed rate as the independent variable accounted for the majority of the system's explanation, contributing 71.73% on its own. The independent variables of seed falling angle and forward speed, which came in the following steps, contribute to the model to a small extent.