## 3 Results and Discussion
### Model Optimization Result and Its Final Accuracy  
Statistical analysis was required to indicate which interactions between optimized parameters are statistically important and should be included in the final model equations. [PERSON]'s correlation was used to arbitrarily determine the importance (see Table 5). The average \(p\)-value within all samples tested was 0.58. However, for the weight of the berry, the correlations were generally weaker, varying between 0.3289 and 0.4801. For this reason, the threshold was assumed to be 0.45. Any correlations below this value were assumed to be too weak to be considered in the model. In the result, the number of clusters was recognized to be connected to the number of berries, the weight of the berries, and the Brix Extract. The number of clusters is backward-related to the number of clusters, as well as with the extract. The weight of the berries indicated a correlation only with the number of clusters. The extract was correlated with the number of berries but also with its weight. No backward correlation was recognized with the weight of the berry.  
The benchmark of obtained model equations (see Model Development and Optimization Section) indicated a very high correlation between predicted values and actual measurements. The total error was calculated as the mean of relative errors (where n is the number of experimental points) for all variables, which was also the objective function for the _fmincon_ algorithm.  
\[\begin{split} E_{total}&=\frac{1}{n}\sum\frac{NC_{ inter}-NC_{experimental}}{NC_{experimental}}+\sum\frac{NB_{inter}-NB_{experimental}}{NB_{experimental}}\\ &\quad+\sum\frac{BW_{inter}-BW_{experimental}}{BW_{experimental}}+ \sum\frac{EB_{inter}-EB_{experimental}}{EB_{experimental}}\end{split} \tag{6}\]  
Figure 4: Principal component analysis of yield quantity and quality of Regent grapevines irrespective of rootstock type considered in the extreme years of the study.  
\begin{table}
\begin{tabular}{l l l l l l} \hline  & \multicolumn{1}{c}{**Number of Clusters (pcs)**} & \multicolumn{1}{c}{**Number of**} & \multicolumn{1}{c}{**of**} & \multicolumn{1}{c}{**Berry**} & \multicolumn{1}{c}{**Weight**} & \multicolumn{1}{c}{**Extract, \({}^{\circ}\)Brix**} \\  & \multicolumn{1}{c}{**Clusters (pcs)**} & \multicolumn{1}{c}{**Datasets(pcs)**} & \multicolumn{1}{c}{**Datasets(pcs)**} & \multicolumn{1}{c}{**Datasets(pcs)**} & \multicolumn{1}{c}{**Datasets(pcs)**} & \multicolumn{1}{c}{**Datasets(pcs)**} \\ \hline
**Short name** & **NC** & **NB** & **BW** & **EB** \\
**Number of clusters (pcs)** & \(1\) & 0.7458 & 0.4801 & 0.7707 \\
**Number of berries per clusters** & 0.7458 & \(1\) & \(<\)0.0001 & \(<\)0.0001 & \(<\)0.0001 \\
**(pcs)** & \(<\)0.0001 & \(1\) & \(<\)0.0001 & \(<\)0.0001 \\
**Berry weight (g)** & 0.4801 & 0.3289 & 0.3951 \\  & \(<\)0.0001 & \(<\)0.0001 & \(1\) & \(<\)0.0001 \\
**Extract, \({}^{\circ}\)Brix** & 0.7707 & 0.7705 & 0.3951 & \(1\) \\  & \(<\)0.0001 & \(<\)0.0001 & \(<\)0.0001 & \(1\) \\ \hline \end{tabular}
\end{table}
Table 5: [PERSON]’s analysis for optimized constants.  
An interesting observation can be also noted for specific rootstock types (Table 6). The total sum of relative errors for all four tested parameters was the lowest for SO4 (under 7%), while significantly higher for SORI and 125 AA. The own root was ranked in the middle. It is also worth looking at 5 BB rootstock. This is the only one case where including interaction had a mixed impact on the accuracy of measured parameters. The precision slightly decreased for the number of clusters, berry weight, and Brix extract but strongly increased for the number of berries. This resulted in a more balanced distribution of errors between variables but insignificantly better total accuracy (0.70%). The opposite tendency can be noticed for SO4 and own root, where the interactions raised the precision by over 35%, the most strongly for the number of berries prediction. This proves that any of the presented rootstocks indicate different properties and should be considered individually.