## 3 Results and Discussion
### Growth Experiments with Fertilizer Addition through DoE
Moreover, it is relevant that the curvature is not significant, and therefore, the  
Figure 6: Basil plants obtained under 1 HR:1 DB LED lights. Figure 7: Basil plants obtained under 1 HR:3 DB LED lights. central points can be treated as additional data in the regression model, augmenting the design plan. R\({}^{2}\) and Pred-R\({}^{2}\) (Table 6) confirm the sufficient fit of the data and a quite fair predictive power for four responses, having R\({}^{2}\) > 0.45, with a particular high fitting for SLA parameters with R\({}^{2}\) = 0.75. Considering all the models' equations in Table 6 (where the coefficients of the variables in the model are reported), it is clear that NPK controlled-release fertilizer plays the main role in the performance of the responses, and this is consistent with the previous hypothesis, but a synergic effect has been shown and calculated for the SLA responses, which also corresponds to the model with higher fitting quality (higher R\({}^{2}\)). Figure 8 shows interaction graphs representing graphically each calculated model. A quite similar behavior can be detected for NoL, TFM, and LAI (Figure 8a-c), where an increasing of these responses is observed by introducing the NPK fertilizer independently of the LED lights combination. In contrast, the SLA parameter (Figure 8d) is clearly influenced by a synergic effect of NPK and LED lights: a restrained quantity of hyper red (1 HR:3 DB) is favorable to the SLA increase, independently of the presence of NPK, even if the highest value of SLA is obtained employing also controlled release NPK. The overall result is that a high quantity of hyper red LED light should be avoided to promote the basil growth. This result is in agreement with previous literature related to other plants' growth in an indoor and black environment such as lettuce, tomato, and flowers, where the employment of a high quantity of red LED light leads to reduced dry weight, plant height, and leaf area [22; 23; 41; 42]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Response** & **Transformation** & **R\({}^{2}\)** & **Pred-R\({}^{2}\)** & **Models’ Mathematical Expression** \\  & & & & **NPK = NO** & **NPK = YES** \\ \hline Height & NONE & 0.13 & 0.10 & - & \\ \hline NoL & NONE & 0.47 & 0.41 & = 8.000 & = 9.666 \\ \hline TFM & \begin{tabular}{c} Inverse Square \\ Root \\ \end{tabular} & 0.58 & 0.53 & = 2.032 & = 1.565 \\ \hline TDM & NONE & 0.28 & 0.19 & - & \\ \hline LAI & \begin{tabular}{c} Inverse Square \\ Root \\ \end{tabular} & 0.55 & 0.49 & = 0.543 & = 0.413 \\ \hline SLA & \begin{tabular}{c} Inverse Square \\ Root \\ \end{tabular} & 0.75 & 0.68 & \
\begin{tabular}{c} = 0.045 + 3.7 \(\times\) \\ 10\({}^{-5}\)\(\times\) HR:DB \\ \end{tabular} &
\begin{tabular}{c} = 0.039 + 3.7 \(\times\) \\ 10\({}^{-5}\)\(\times\) HR:DB \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: ANOVA results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Response** & **Intercept** & **NPK** & **HR:DB** \\ \hline NoL & 8.83 & 0.8333 & - \\ \hline TFM & 1.80 & \(-\)0.2340 & - \\ \hline LAI & 0.47 & \(-\)0.0615 & - \\ \hline SLA & 0.04 & \(-\)0.0032 & 0.0009 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Effect sizes for significant responses.