## 3 Results and Discussion  
The results of all the characterizations of the lettuce plants are reported in Table 8. From a first consideration of the measured data, it is possible to assess the possible benefit of the statistical approach. In fact, it must be considered that each response shows fairly good data variability among the selected range of the independent variable. This fact suggests that the selected input factors may affect the responses and thereafter a mathematical model can be drawn. Nevertheless, it is not possible to evaluate a specific trend at this point of the analysis; therefore, a statistical analysis should be performed, and a quantitative calculation of the effects of the input factors on the selected responses, also considering the block related to each different time period. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Response Variable** & **Acronym** & **Unit of Measurement** \\ \hline Average fresh weight & FW & g \\ Root total dry weight & RDW & g \\ Average plant height & Height & cm \\ Number of plants after 3 days & NoP3 & / \\ Number of plants after 7 days & NoP7 & / \\ Average leaf area & LA & cm\({}^{2}\) \\ Organic carbon & C & \% \\ Nitrates & NO\({}_{3}\) & mg kg\({}^{-1}\) \\ Aluminum & Al & mg kg\({}^{-1}\) \\ Silicon & Si & mg kg\({}^{-1}\) \\ Solid residue at 105 \({}^{\circ}\)C & SR & \% \\ Chlorophyll a & Ch\({}_{\text{a}}\) & \(\mu\)g mg\({}^{-1}\) \\ Chlorophyll b & Ch\({}_{\text{b}}\) & \(\mu\)g mg\({}^{-1}\) \\ Carotenoids & Car & \(\mu\)g mg\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Response variables used to characterize grown lettuce plants. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Response Variable** & **Goal** & **Importance** \\ \hline Average fresh weight & to maximize & 4 \\ Root total dry weight & to maximize & 5 \\ Average plant height & to maximize & 5 \\ Number of plants after 3 days & to maximize & 3 \\ Number of plants after 7 days & to maximize & 5 \\ Average leaf area & to maximize & 5 \\ Organic carbon & to maximize & 2 \\ Nitrates & to minimize & 3 \\ Aluminum & to minimize & 3 \\ Silicon & to minimize & 3 \\ Solid residue at 105 \({}^{\circ}\)C & to minimize & 5 \\ Chlorophyll a & to maximize & 4 \\ Chlorophyll b & to maximize & 4 \\ Carotenoids & to maximize & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Desirability function parameters. The statistical analysis highlighted that there is no difference among the same runs performed in different blocks, shown in Table 5. This confirms the repeatability of the growth tests characterized by the same light recipe and the comparability of their results. The ANOVA results (Table 9) showed that input variables have a significant influence only on five response variables out of the fourteen considered. The values of R\({}^{2}\) and predicted R\({}^{2}\) (Pred-R\({}^{2}\)) are reported in Table 9, together with the coefficients that quantify the influence of every input variable on the single response variable. The morphologic properties, namely FW, Height, and LA, have higher R\({}^{2}\) and Pred-R\({}^{2}\) with respect to the chemical properties (C and SR). It must be stressed that the Pred-R\({}^{2}\) related to C and SR is insignificant and, therefore, these two models cannot be employed for predictive purposes but only for the description of responses considering the already collected data. Taking into account the coefficients in Table 9, the input variable that has the most diffuse effect is the Aggregates Number alone or in combination with LED. The values of these coefficients are graphically reported in Figure 3 for a better understanding. The Aggregates Number, taken alone, is also the only variable with negative values, in particular for the response variable and C (Figure 3d), meaning that increasing the number of aggregates in general could not be a viable way to promote lettuce growth, as too many nutrients could have a toxic effect on this cultivation.