## 4 Analysis Results
### Prediction Model Based on Linear Regression Analysis  
Table 4 summarizes that solar radiation is the most influential factor in the correlation analysis for calculating the amount of solar power generated by the floating PV module, followed by the module temperature and ambient temperature, in sequence. The wind speed and direction have little effect on power generation. From Table 4, the correlation between the horizontal surface irradiance and slope irradiance, and that between the ambient temperature and module temperature, are 0.97 and 0.89, respectively, which means that the data are relatively similar. Thus, it is desirable to consider only the slope irradiance and module temperature.  
Table 5 summarizes the analysis results of the floating PV regression. From this table, the multiple correlation coefficient is 0.9859, which is more accurate than that of the land-based PV system. In detail, the t-statistic of irradiation is 178.63; therefore, the linear relationship between the independent variable and the dependent variable is very high. As the \(p\)-values of the module temperature and solar irradiation are 0 and the y-intercept is 0.01, whose absolute value is less than 0.05, the null hypothesis that there is no linear relationship is rejected. Therefore, the module temperature and solar irradiation coefficient can be used as the variables [26]. As a result, the formula for estimating the power generation of the floating PV module using linear regression is described in Equation (10).  
\[P_{fpv}=T_{c}\times(0.0024851)+G_{t}\times(0.0019761)+(-0.0141039), \tag{10}\]  
where \(P_{fpv}\) is the floating PV module output (kW), \(T_{c}\) is the module temperature (\({}^{\circ}\)C), and \(G\) is the solar irradiation amount (W/m\({}^{2}\)).  
Upon generating random numbers from the floating PV operating results data, 50% of the data were used for training, and the remaining 50% were used for verification, to confirm whether overfitting  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Division** & **Coefficient** & **Standard Error** & **t-Statistics** & **_p-Value_** \\ \hline Module Temperature & 0.0024851 & 0.00 & 9.88 & 0 \\ \hline Irradiation & 0.0019761 & 0.00 & 178.63 & 0 \\ \hline y-Intercept & \(-0.0141039\) & 0.01 & \(-2.75\) & 0.01 \\ \hline Multiple Correlation & & & **0.9859** \\ Coefficient & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Floating PV regression analysis results.  
occurred or not. In addition, an error function, the mean absolute percentage error (MAPE) was used to compare the accuracy, as shown in Equation (11) [27].  
\[MAPE=\frac{100}{n}\sum_{i=1}^{n}\left\lfloor\frac{E_{i}-D_{i}}{E_{i}}\right\rfloor, \tag{11}\]  
where \(D_{i}\) is the value predicted by the predictive model, \(E_{i}\) is the measured value, and \(n\) is the number of datasets.  
Figure 12 shows the results of the linear regression analysis with the learning data. The linearity can be confirmed as a result of plotting the true output and predicted output. Upon converting this into MAPE, the error showed 9.61%.  
Figure 13 shows the results obtained by entering the test data into the learning model generated from the learning data. The MAPE is 11.35%, which is greater by 1.74%, but it was confirmed that overfitting did not occur.  
Figure 12: Linear regression (LR) analysis results (train data).  
Figure 13: Linear regression (LR) analysis results (test data).