## 2 Data and Processing
### Analysis Method  
In this paper, a multilinear regression analysis was applied to determine the causal relationship between independent variables (\(X_{i}\)), meteorological data, dependent variables (\(Y\)), and solar power generation because there were several independent variables. The regression analysis estimated the value of a dependent variable by substituting the values of independent variables. Accordingly, solar power generation can be estimated using a multilinear regression equation of the multiple meteorological variables as follows [30; 31]:  
\[(Y_{i})=\beta_{0}+\beta_{1}X_{1i}+\beta_{2}X_{2i}+\cdots+\beta_{p}X_{pi} \tag{1}\]  
Equation (1) estimates the value of the dependent variable, as well as the values of the regression coefficients, \(\beta_{0}\), \(\beta_{1}\), \(\beta_{2}\),... and \(\beta_{p}\). Each regression coefficient is interpreted as the extent to which each independent variable affects the dependent variable.  
Estimating regression coefficients requires partial differentiation of the error sum of squares (SSE) for each variable and minimizing it to estimate the regression variables. The SSE is represented as follows:  
\[\text{SSE}=\sum_{i=1}^{m}e_{i}^{2}=e_{1}^{2}+e_{2}^{2}+\cdots+e_{n}^{2}, \tag{2}\]  
where \(e_{i}\) is the deviation of the regression estimation.  
In the regression analysis, the coefficient of determination (\(R^{2}\)) is used to evaluate the goodness of fit or to know the explanatory power of the independent variables for estimating the dependent variable. The coefficient of determination is given as follows:  
\[R^{2}=\frac{\sum\left(\hat{y_{i}}-\overline{y}\right)}{\sum\left(y_{i}- \overline{y}\right)^{2}}=\frac{\text{Variation explained by the regression line}}{\text{Total variation}} \tag{3}\]  
where \(\hat{y_{i}}-\overline{y}\) indicates the difference between the estimated dependent variable value and sample mean.  
The range of \(R^{2}\) is \(0<R^{2}<1\). The closer it is to 1, the closer the regression model is to the overall variation. However, because multiple regression analysis has two or more independent variables, it is necessary to consider the adjusted coefficient of determination (Adjusted \(R^{2}\)), which compensates for the characteristic of \(R^{2}\) that increases as the number of independent variables increases. The formula for the adjusted coefficient of determination is as follows:  
\[\text{Adjusted }R^{2}=1-\frac{n-1}{(n-p-1)(1-R^{2})} \tag{4}\]  
where \((n-p-1)\) is the degree of freedom, \(n\) is the number of samples, and \(p\) is the number of independent variables.  
In addition, the \(p\)-value and multicollinearity were diagnosed to confirm statistical significance. Finally, to evaluate the accuracy of the derived regression model, we used the \(R^{2}\), adjusted \(R^{2}\), and root mean square error (RMSE) values.  
The \(p\)-value and probability of significance can determine if the null hypothesis or alternative hypothesis is adopted. To reject the null hypothesis that \"the independent variables do not affect the dependent variable,\" the \(p\)-value must be less than 0.05, and the alternative hypothesis can be adopted by rejecting the null hypothesis.  
A multicollinearity between variables exists, which overlaps with the variability between independent variables and does not bring about overlapping variability. This leads to poor interpretation of the regression analysis results and decreases its accuracy,which requires diagnosis. Methods for diagnosing multicollinearity should utilize variance inflation factors (VIFs). VIFs can be determined using Equation (5) [32].  
\[VIF_{i}=\frac{1}{1-R^{2}} \tag{5}\]  
If the VIF is greater than 10, then the variable possesses multicollinearity and should be excluded from the regression analysis.  
The RMSE is commonly used when considering the difference between the estimated and measured values, and it is suitable for expressing precision. The smaller the error, the better the performance of the regression model.