## 4 Conclusions  
A gradient descent method was used to calculate, through a characteristic equation, the relationship between several variables which can be easily computed using quantitative data. The results showed that solar radiation and daylight time are relevant in estimating the electric power, with solar radiation being the one with the most influence over the photovoltaic power generation; nonetheless, temperature, wind speed, and daylight hour affect this process, with their inclusion being fundamental in the analysis to achieve a proper electric power estimation. According to Figures 9 and 16, an acceptable approximation between the statistical simulation results and real-time power generation has achieved. This is proven both by Table 8, where 97.63% of the estimation results matches with the real data for HS and 99.66% match for MCS, and by Table 9, achieving overall error values no greater than 7% and 2% for HS and MCS, respectively. An observable  
Figure 19: The difference errors between the high and low values: (**a**) Error value when measured data is high; (**b**) Error value when measured data is low. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Location** & **Month** & **MAE** & **MAPE (Range)** \\ \hline \multirow{8}{*}{HS} & Aug & 299.7928 W & 11.9436\% \\  & Sep & 203.7386 W & 7.5643\% \\  & Oct & 267.9841 W & 9.2382\% \\  & Nov & 138.1913 W & 5.1418\% \\  & Dec & 178.9316 W & 7.0381\% \\  & Jan & 184.5001 W & 6.7978\% \\  & TOTAL & 200.0924 W & 6.8859\% \\ \hline \multirow{8}{*}{MCS} & Jul & 590.6460 W & 1.0480\% \\  & Aug & 1192.3 W & 2.0392\% \\ \cline{1-1}  & Sep & 726.2990 W & 1.2646\% \\ \cline{1-1}  & Oct & 741.8355 W & 1.2660\% \\ \cline{1-1}  & Nov & 741.4300 W & 1.3534\% \\ \cline{1-1}  & Dec & 812.8113 W & 1.7237\% \\ \cline{1-1}  & TOTAL & 1130.4 W & 1.9291\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The error values between the estimated and real data. relationship between the determination coefficient values and error results is clear, concluding that the percentage error will be lower while \(R^{2}\) is higher. Several causes could perturb the correlation, resulting in a wider dispersion, with the weather conditions as the most important for this study. Contrary to Mexico City, Hermosillo has abrupt changes in climate throughout the year, reaching temperatures around 50 \({}^{\circ}\)C and 0 \({}^{\circ}\)C in summer and winter, respectively, as well as sudden weather changes from a sunny day to a cloudy or even a rainy day within hours. However, according to the above and even if the results have a satisfactory behavior, by definition, a statistical estimation will always have an error value. Nevertheless, these error values can be reduced, increasing the gathered input data or by other alternative methods such as intelligent systems which have proven to be an efficient methodology [53; 54; 55; 56]. The above will be discussed elsewhere. Research ideas and global design: N.P.-D., J.A.R.-H., and F.A.-V.; analysis of the results: Y.M., E.F.V.-C., and E.J.H.-L.; revision of the document: R.E.C.-L. and J.H.A.-G. This research received no external funding. The authors would like to thank the University of Sonora (UNISON), Centro de Investigacion y de Estudios Avanzados (CINVESTAV) campus Zacatenco, and Consejo Nacional de Ciencia y Tecnologia (CONACYT), with the mobility scholarship 291249. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} ANN & Artificial Neural Network \\ CSP & Concentrated Solar Power Plants \\ GDO & Gradient Descent Optimization \\ HEI & Higher Education Institutions \\ HS & Hermosillo Site \\ kWh/m\({}^{2}\) & Quantity of kilowatts during an hour striking a squared meter area \\ LSR & Least Square Regression \\ MAE & Mean Absolute Error \\ MAPE & Mean Absolute Percentage Error \\ MCS & Mexico City Site \\ PV & Photovoltaic \\ SHC & Solar Heating and Cooling \\ W & Watt. It is a unit of power defined as a derived unit of 1 joule per second (J/s) \\ \end{tabular}