## 3 Results
Thus, to overcome this difficulty, this paper proposes to replace this complex function with a mathematical function of simple expression reproducing the result of the complex model with the least possible error. The reader should assume that this is not a statistical problem but rather a problem of adjustment or approximation of a simple expression function to a complex function, so that statistical methods are not applicable. To address the fit, the set of simple variables was extended with composite variables obtained as products and ratios of simple variables. The proposed function (29) was selected from the set of fits to linear functions of composite variables. It lacks a clear physical meaning, but it allows for reproduction of the results of the model with an average relative error equal to 2.561 kWh/m\({}^{2}\)year; therefore, it is considered suitable for the study of the relative weight of the variables. Equation (29) shows the mathematical expression of this model for which the parameters \(a\), \(b\), \(c\), \(d\), \(e\), \(f\), \(g\), \(h\), \(l\), \(r\), and \(w\) have been obtained by the least squares method (Table 3), with an adjustment coefficient \(R^{2}\) = 0.993. Table 4 shows the synoptic values of the estimation errors of the model \(\varepsilon\) and \(\varepsilon_{rel}\), given by Equations (30) and (31), where \(H_{year}^{est}\) is the annual solar irradiance on the solar collectors estimated according to Equation (28) and \(H_{year}^{adj}\) is the one approximated by the model (29). The low value obtained for the mean square error means that the equation can be considered valid for the study of dependence of the annual solar irradiance with respect to the variables \(S_{col}\), \(D_{EW}\), \(D_{NS}\), and \(T\). \[H_{year}^{adj}=a+b\;S_{col}+c\;D_{EW}+\frac{d}{D_{EW}}+eD_{NS}+f\;{D_{NS}}^{2} +g\;\frac{D_{EW}}{D_{NS}}+h\left(\frac{D_{EW}}{D_{NS}}\right)^{2}+l\;\frac{S_ {col}}{D_{NS}\;D_{EW}}+r\;\frac{D_{NS}\;D_{EW}}{S_{col}}+w\;T \tag{29}\]  
\[\varepsilon=\left|H_{year}^{est}-H_{year}^{adj}\right| \tag{30}\]  
\[\varepsilon_{rel}=\frac{\left|H_{year}^{est}-H_{year}^{adj}\right|}{H_{year}^{ est}} \tag{31}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Units** & **Value** \\ \hline \(a\) & kWh/m\({}^{2}\) year & 2656.366 \\ \hline \(b\) & kWh/m\({}^{4}\) year & \(-\)0.960 \\ \hline \(c\) & kWh/m\({}^{3}\) year & 6.921 \\ \hline \(d\) & kWh/m year & \(-\)25.783 \\ \hline \(e\) & kWh/m\({}^{3}\)year & \(-\)756.012 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Values obtained for the model of Equation (29). It is important to note that the model adjusted in Equation (30) does not consider the geometric shape of the collectors itself since, given that the mean error, \(\overline{\epsilon}\), of the proposed model is 3.3 kWh/m\({}^{2}\)year (Table 4), the geometric shape would not have an explanatory capacity superior to this \(\overline{\epsilon}\). This reasoning allowed us to conclude the little influence of the shape of the collectors in facilities that follow the tracking/ back-tracking policy considered in this work. For a better interpretation of the adjusted Equation (29), we can consider it as the addition of four terms separated by parentheses in Equation (32). \[ \begin{split} H_{y}^{adj}=a+\{b\;S_{col}\}+\left\{c\;D_{EW}+ \frac{d}{D_{EW}}+eD_{NS}+f\;D_{NS}{}^{2}+g\;\frac{D_{EW}}{D_{NS}}+h\bigg{(} \frac{D_{EW}}{D_{NS}}\bigg{)}^{2}\right\}\\ +\bigg{\{}l\;\frac{S_{col}}{D_{NS}\;D_{EW}}+r\;\frac{D_{NS}\;D_{ EW}}{S_{col}}\bigg{\}}+\{wT\}\end{split}  \tag{32}\]  
The first term only depends on the collector surface \(S_{col}\). Given that \(b<0\), it was found that, as the collectors were larger, the lower the annual incident radiation. This effect was due to the greater possibility of inter-shading as the collectors had more surface area. With the cases studied, the variation interval of the final result due exclusively to this term was 24 kWh/m\({}^{2}\) year.