## 2 Methodology  
### Statistical Method  
The amount of data collected and the correlation among them are quite important to accomplish an estimation. If the total data is scarce or the correlation between any input and the output is low, the estimation will not be satisfactory. The correlation analysis is one of the most used and reported statistical methods on scientist and medical researches; its visual representation is known as a dispersion graphic. It is used to prove or reject the existence of a relation between two different variables based on the Pearson correlation coefficient described by Equation (1). \[\rho\left(a,b\right)=\frac{E\left(ab\right)}{\sigma_{a}\sigma_{b}} \tag{1}\]  
where \(E\left(ab\right)\) is the crossed correlation between \(a\) and \(b\) and where \(\sigma_{a}^{2}=E\left(a^{2}\right)\) and \(\sigma_{b}^{2}=E\left(b^{2}\right)\) are the variations of the variables \(a\) and \(b\), respectively [38]. If \"\(a\)\" and \"\(b\)\" are the two considerate variables, then a dispersion graphic shows the location of each ordered pair in a coordinated system. If most points appear to be close to a straight line, this correlation is known as linear. If most points appear to be close to a curve, the correlation is known as nonlinear. On the other hand, if a clear pattern among the ordered pairs is inexistent, then there is no relation between both variables [39]. In order to represent the curve (curve or line regression) that best fits the behavior of ordered pairs, Equation (2) is used. \begin{table}
\begin{tabular}{l l c c c c c c c c c c c c} \hline \hline
**State** & **City** & **Jan** & **Feb** & **Mar** & **Apr** & **May** & **Jun** & **Jul** & **Aug** & **Sep** & **Oct** & **Nov** & **Dec** & **Avg** \\ \hline Sonora & Hermosillo & 4.0 & 4.6 & 5.4 & 6.6 & 8.3 & 8.5 & 6.9 & 6.6 & 6.7 & 6.0 & 4.7 & 3.9 & 6.0 \\ Sonora & Guaymas & 4.5 & 5.7 & 6.5 & 7.2 & 7.3 & 6.8 & 5.9 & 5.8 & 6.3 & 5.9 & 5.0 & 5.6 & 5.9 \\ Chihuhaha & Chihuhaha & 4.1 & 4.9 & 6.0 & 7.4 & 8.2 & 8.1 & 6.8 & 6.2 & 5.7 & 5.2 & 4.6 & 3.8 & 5.9 \\ SLP & SlP & 4.3 & 5.3 & 5.8 & 6.4 & 6.3 & 6.1 & 6.4 & 6.0 & 5.5 & 4.7 & 4.2 & 3.7 & 5.4 \\ Zacatecas & Zacatecas & 4.9 & 5.7 & 6.6 & 7.5 & 7.8 & 6.2 & 6.2 & 5.9 & 5.4 & 4.8 & 4.8 & 4.1 & 5.8 \\ Guanajuato & Guanajuato & 4.4 & 5.1 & 6.1 & 6.3 & 6.6 & 6.0 & 6.0 & 5.9 & 5.8 & 5.2 & 4.8 & 4.6 & 5.6 \\ Aguascalientes & Aguascalientes & 4.5 & 5.2 & 5.9 & 6.6 & 7.2 & 6.3 & 6.1 & 5.9 & 5.7 & 5.1 & 4.8 & 4.0 & 5.6 \\ Qaxaca & Salina Cruz & 5.4 & 6.3 & 6.6 & 6.4 & 6.1 & 5.0 & 5.6 & 5.9 & 5.2 & 5.9 & 5.7 & 5.2 & 5.8 \\ Oaxaca & Oaxaca & 4.9 & 5.7 & 5.8 & 5.5 & 6.0 & 5.4 & 5.9 & 5.6 & 5.0 & 4.9 & 4.8 & 4.4 & 5.3 \\ Jalisco & Colotlan & 4.6 & 5.7 & 6.5 & 7.5 & 8.2 & 6.6 & 5.8 & 5.6 & 5.8 & 5.3 & 4.9 & 4.1 & 5.9 \\ Jalisco & Guadalajara & 4.6 & 5.5 & 6.3 & 7.4 & 7.7 & 5.9 & 5.3 & 5.3 & 5.2 & 4.9 & 4.8 & 4.0 & 5.6 \\ Durango & Durango & 4.4 & 5.4 & 6.5 & 7.0 & 7.5 & 6.8 & 6. & 5.6 & 5.7 & 5.1 & 4.8 & 3.9 & 5.7 \\ Baja California & La Paz & 4.4 & 5.5 & 6.0 & 6.6 & 6.5 & 6.6 & 6.3 & 6.2 & 5.9 & 5.8 & 4.9 & 4.2 & 5.7 \\ Baja California & San Javier & 4.2 & 4.6 & 5.3 & 6.2 & 6.5 & 7.1 & 6.4 & 6.3 & 6.4 & 5.1 & 4.7 & 3.7 & 5.5 \\ Baja California & Mexicali & 4.1 & 4.4 & 5.0 & 5.6 & 6.6 & 7.3 & 7.0 & 6.1 & 6.1 & 5.5 & 4.5 & 3.9 & 5.5 \\ Quenetaro & Quenetaro & 5.0 & 5.7 & 6.4 & 6.8 & 6.9 & 6.4 & 6.4 & 6.4 & 6.3 & 5.4 & 5.0 & 4.4 & 5.9 \\ Puebla & Puebla & 4.9 & 5.5 & 6.2 & 6.4 & 6.1 & 5.7 & 5.8 & 5.8 & 5.2 & 5.0 & 4.7 & 4.4 & 5.5 \\ Hidalgo & Pachuca & 4.6 & 5.1 & 5.6 & 6.8 & 6.0 & 5.7 & 5.9 & 5.8 & 5.3 & 4.9 & 4.6 & 4.2 & 5.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The solar radiation on select places in Mexico (data in kWh/m\({}^{2}\) per day) [37]. \[y=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+\cdots+a_{m}x^{m} \tag{2}\]  
The correlation coefficient or \(R\) requires that both a magnitude and a direction be either positive (from 0 to 1) or negative (from \(-1\) to 0).