## 3 Material and Methods
### Statistical Analysis  
Each W value will therefore be associated with a particular sensitivity factor S. The set of sensitivity factors S together with the respective associated W will be plotted as in Figure 3A As can be seen in Figure 2, a theoretical graphical representation with differentiable trend intervals is obtained. Thus, at the point on the graph where we find the beginning of an exponential interval, we will find the value of S that will be close to the optimum. Once the results of the count are obtained, the data will be fitted to a mathematical model with change of slope (SPLINE) so that the selection of the optimal point S will coincide with the \(\text{X}_{\text{R}}\) value that provides the best fit to the model in terms of R\({}^{2}\) and significance. \begin{table}
\begin{tabular}{c c} \hline \hline \(\text{S}_{\text{factor}}\) & **Number of Points** \\ \hline
0.82 & 403 \\
0.83 & 403 \\
0.84 & 471 \\
0.85 & 605 \\
0.86 & 605 \\
0.87 & 657 \\
0.88 & 708 \\
0.89 & 787 \\
0.9 & 877 \\
0.91 & 945 \\
0.92 & 966 \\
0.93 & 1001 \\
0.94 & 1087 \\
0.95 & 1182 \\
0.96 & 1279 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Number of points detected for each \(\text{S}_{\text{factor}}\). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \(\text{S}_{\text{factor}}\) & 0.81 & 0.82 & 0.83 & 0.84 & 0.85 & 0.86 & 0.87 & 0.88 & 0.89 & 0.9 & 0.91 & 0.92 & 0.93 & 0.94 & 0.95 \\ \hline NP & - & 403 & 471 & 549 & 605 & 657 & 708 & 754 & 787 & 877 & 945 & 966 & 1001 & 1087 & 1182 \\ \hline W & - & 0.460 & 0.583 & 0.752 & 0.898 & 1.056 & 1.240 & 1.436 & 1.600 & 2.182 & 2.829 & 3.086 & 3.601 & 5.661 & 12.190 \\ \hline R\({}^{2}\) & - & - & 94.10 & 95.26 & 96.46 & 97.62 & 98.64 & 99.39 & 99.56 & 98.16 & 96.06 & 94.74 & - & - & - \\ \hline Signif. & - & - & X & X & X & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model fit for choice of \(\text{S}_{\text{factor}}\) in Trial 1. The theoretical slope change equation (SPLINE) is  
\[\mathrm{Y}=\beta_{0}+\beta_{1}\mathrm{*X}+\beta_{2}\mathrm{*D}(\mathrm{X}- \mathrm{X_{R}})+\mathrm{U} \tag{5}\]  
where:  
Y = The dependent variable of the model. \(\beta_{0}\) = The independent coefficient. Represents the value of Y variable when the variable X is zero. \(\beta_{1}\) = The coefficient that accompanies the X variable. Represents the first slope of the model and measures the increase in the variable Y when the X increases one unit. \(\mathbf{X}\) = The independent variable of the model. \(\beta_{2}\) = The coefficient that accompanies the Dummy variable. Difference in the increase in the variable Y when one unit of the variable X is increased while X \(\leq\mathrm{X_{R}}\) with respect to when X \(>\mathrm{X_{R}}\). D = Dummy variable that takes a value of 0 when X \(\leq\mathrm{X_{R}}\), and a value of 1 when X \(>\mathrm{X_{R}}\). \(\mathrm{X_{R}}\) = The node from which the slope of the line will change. U = The perturbation of the model. Represents the variables that do not appear in the model and that can affect the dependent variable Y. Applied to the variables we are working with, this would be  
\[\mathrm{W}=\beta_{0}+\beta_{1}\mathrm{*S_{factor}}+\beta_{2}\mathrm{*D}( \mathrm{S_{factor}}-\mathrm{S_{factorR}})+\mathrm{U} \tag{6}\]  
where:  
\(\mathrm{W}\) = The dependent variable of the model. \(\mathrm{S_{factor}}\) = The independent variable of the model. D = Dummy variable that takes a value of 0 when \(\mathrm{S_{factor}}\leq\mathrm{S_{factorR}}\), and a value of 1 when \(\mathrm{S_{factor}}>\mathrm{S_{factorR}}\). \(\mathrm{S_{factorR}}\) = The node from which the slope of the line will change. Table 2 shows the experimental data obtained for the trial 1 and the results for the fitting model. Every pair of R2 and significance analysis were obtained using Equation (6), choosing each time the value of \(\mathrm{S_{factorR}}\) that appears in the upper part of this pair.