## 5 Dynamical Results of the Stimulus Response Model (SRM)
Note that the scores' residual dispersion is again much higher than that for Participant 1, in correspondence with the lower values of the determination coefficients, \(R^{2}=0.51\) for ES and \(R^{2}=0.10\) for SFS, although the Anderson-Darling test of the residuals (respectively, 0.80 and 0.25) indicate us that the residuals are random. The conclusion from these data is very important: compared with Participant 1, the part of the data variability explained by the SRM for Participant 2 provides in a very low way his happiness response to the caffeine stimulus. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Symbol** & **ES** & **SFS** \\ \hline Dose & \(M\) & 330.0 & 330.0 \\ Inhibitor effect delay & \(\tau\) & (104.076, 126.348) & (93.4624, 115.972) \\ Assimilation rate & \(\alpha\) & (0.00242, 0.00307) & (0.00237, 0.00294) \\ Consumption rate & \(\beta\) & (0.00174, 0.00234) & (0.00167, 0.00223) \\ Homeostatic control power & \(a\) & (0.04088, 0.04595) & (0.05661, 0.06551) \\ Tonic or basal happiness & \(b\) & (18.4502, 18.9933) & (6.33578, 6.57401) \\ Excitation effect power & \(p\) & (0.02217, 0.02913) & (0.05159, 0.07140) \\ Inhibitor effect power & \(q\) & (0.00395, 0.00483) & (0.00360, 0.00438) \\ Initial happiness (initial state) & \(y_{0}\) & 1.0 & 1.0 \\ Initial drug in blood & \(s_{0}\) & 0.0 & 0.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameters’ confidence intervals (0.95 confidence level) and values of SRM provided by genetic algorithm for ES and SFS for Participant 1 in Phase C (see dimensions and units in Table 4). Figure 6: Phase C, Participant 1. ES (**left**) and SFS (**right**) scores (dots) and curves with uncertainty predicted by the stimulus response model. For ES: \(R^{2}=0.84\), \(p\) value = 0.35. For SFS: \(R^{2}=0.80\), \(p\) value = 0.43. In addition, Table 9 shows the parameters' confidence intervals of the SRM provided by the genetic algorithm for phase C of Participant 2, except for the dose and the initial values that are known and then presented with its respective single values. The corresponding \(opp\) confidence intervals (\(opp=a+p+q\cdot\tau\)) obtained from Table 9 are (2.03852, 2.49726) min\({}^{-1}\) for ES and (3.13283, 5.17100) min\({}^{-1}\) for SFS (confidence level 0.95). In Section 6 these data are compared with those of Participant 1. In this case, the model predictions must be taken again very carefully, due to the low effect of the caffeine stimulus for participant happiness. However, although the part of the data variability explained by the SRM for Participant 2 provides in a very low way the happiness response to the caffeine stimulus, compared with Participant 1, it can be advanced, by comparing the respective \(opp\) intervals, that Participant 2 feels significantly more intensively the effect of caffeine consumption than Participant 1 for both happiness scales, despite the initial happiness values of Participant 2 are higher for both happiness scales than for Participant 1 (\(y_{0}=8.0\) for the ES and \(y_{0}=5.0\) for the SFS). A general conclusion of this section is that the SRM is a mathematical tool that predicts how much a stimulus (alcohol or caffeine) affects individual happiness along time as well as the happiness dynamics pattern of this change. In addition, the SRM highlights the individual differences between the responses to both drugs that the inferential statistics approach of Section 3 has discovered: (a) the jointly representation of the experimental scores with the SRM predictions in Phases B and C (Figures 4-7); (b) the determination coefficients and the residual dispersion that this coefficient represents (the lower the determination coefficient the more residual dispersion); and (c) the significant differences between the overall power parameter (\(opp\)) confidence intervals. However, the individual differences  
Figure 7: Phase C, Participant 2. ES (**left**) and SFS (**right**) scores (dots) and curves with uncertainty predicted by the stimulus response model.