## 3 Results and Discussion
### Analysis of Variance of the Responses  
Results of ANOVA analysis are shown in Table 7. As shown from the reported \(p\)-values, all the models are statistically significant, with only two exceptions, NoP_15D and NoP_20D, that show \(p\)-values well above 0.05. Therefore, for the great majority of the responses it was possible to continue the analysis by evaluating the quality of the fitting and, eventually, the significant factors. Regarding the quality of the fitting, the great majority of the responses showed fairly good values as they were around 0.5 or over. Nevertheless, it is important to note that responses such as Height_30D, NoP_30D and LAI_15D, showed too low R\({}^{2}\) values (around 0.3) to consider associated models representative of the data, and, for this reason, these responses were not further considered in the analysis. Observing the data (Table 6), this result is due to the fact that for Height and NoP, increasing the time of observation, had well enough constant data registered at the highest value possible for the plant, independently of the growing conditions. At the same time, LAI observations for different experiments at too few days resulted in data too similar to each other, due to the fact that the leaf area observed was generally restrained. Taking into consideration the evolution of the same property over time, models associated with LAI and Water responses better explained variations over time, as R\({}^{2}\) increased with the number of days of observation. In contrast, among responses related to Height, the highest R\({}^{2}\) value was \begin{table}
\begin{tabular}{c c c} \hline \hline
**Response** & **Goal** & **Importance** \\ \hline Height & to maximize & 4 \\ Number of Plants & to maximize & 4 \\ Leaf Area Index & to maximize & 3 \\ Water & to minimize & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Desirability function parameters employed for each period of growth. for the observation at 20 days. The predicted R\({}^{2}\) values (Table 7) show the same trends as R\({}^{2}\), according to its definition [36]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c} \hline \multicolumn{13}{c}{**Factors**} & \multicolumn{13}{c}{**Respenses**} \\ \hline  & **1** & **2** & **3** & & & & & & & & & & & & & & & & & & & & & & & & \\ \hline
**Run** & **Distance (cm)** & **HR:DB** & **White** & **15D** & **20D** & **25D** & **30D** & **15D** & **20D** & **25D** & **30D** & **15D** & **20D** & **25D** & **30D** & **15D** & **20D** & **25D** & **30D** \\ \hline
1 & 80 & 50 & YES & 8.009 & 10.450 & 14.996 & 24.517 & 3 & 3 & 3 & 3 & 0.033 & 0.072 & 0.139 & 0.347 & 200 & 270 & 320 & 350 \\ \hline
2 & 70 & 25 & NO & 6.935 & 9.068 & 15.538 & 21.443 & 4 & 4 & 5 & 5 & 0.028 & 0.069 & 0.131 & 0.347 & 220 & 290 & 340 & 390 \\ \hline
3 & 70 & 50 & NO & 6.611 & 10.660 & 15.467 & 23.953 & 3 & 3 & 3 & 3 & 0.022 & 0.053 & 0.119 & 0.346 & 180 & 270 & 320 & 370 \\ \hline
4 & 60 & 25 & YES & 7.904 & 10.176 & 14.634 & 24.586 & 4 & 4 & 5 & 5 & 0.029 & 0.073 & 0.187 & 0.532 & 220 & 290 & 340 & 410 \\ \hline
5 & 60 & 75 & NO & 6.361 & 10.782 & 15.253 & 21.420 & 4 & 4 & 4 & 4 & 0.022 & 0.058 & 0.131 & 0.428 & 220 & 290 & 340 & 410 \\ \hline
6 & 60 & 50 & YES & 7.595 & 11.318 & 16.968 & 24.976 & 3 & 3 & 4 & 4 & 0.031 &  
plants, guaranteeing in first approximation the same irradiance for all the nine pots used in the same test. Figure 4: Coefficients of the significant factors for statistically reliable models associated to NoP. The associated error is equal to 0.05%. Figure 5: Coefficients of the significant factors for statistically reliable models associated to LAI. The associated error is equal to 0.05%. Moreover, Distance becomes more and more relevant when increasing the number of days of observation, as its coefficients (in absolute values) increase (for example from \(-17.49\) to \(-40.27\) for water-related responses), becoming the only significant factor for all the responses at 30 days.