## 2 Materials and Methods
### Analysis of Variance (ANOVA)  
This study aims to apply the ANOVA (analysis of variance) test to examine the interactions between the dependent variable, predicted _Po_, and the independent variables. It evaluates the explanatory power of machine learning algorithms to generate these predictions. ANOVA decomposes the total variance into the variance explained by the independent variables (\(SS_{B}\)) and the residual variance (\(SS_{E}\)), expressed as [28]:  
\[SS_{T}=SS_{B}+SS_{E} \tag{1}\]  
where \(SS_{T}\) is the total variance; \(SS_{B}\) represents the variance due to the independent variables; and \(SS_{E}\) accounts for the error variance. The core mechanism of ANOVA involves calculating the mean squares (_MS_) for the sources of variance and determining the F-statistic, which evaluates the model's overall significance [29]. The F-statistic is calculated as [30]:  
\[F=\frac{MS_{B}}{MS_{E}}=\frac{\frac{SS_{B}}{df_{B}}}{\frac{SS_{E}}{df_{E}}} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Feature 1** & **Feature 2** & **Correlation** & **Uncorrected \(p\)** & **FDR** \\ \hline _Nd_ (\({}^{\circ}\)) & _Wd_ (\({}^{\circ}\)) & 0.964 & 0.000 & 0.000 \\ _Po_ (MW) & _Ws_ (m/s) & 0.896 & 0.000 & 0.000 \\ _Rs_ (s\({}^{-1}\)) & _Ws_ (m/s) & 0.842 & 0.000 & 0.000 \\ _Po_ (MW) & _Rs_ (s\({}^{-1}\)) & 0.760 & 0.000 & 0.000 \\ _Po_ (MW) & \(t\) (UTC) & 0.274 & 0.000 & 0.000 \\ _Ws_ (m/s) & \(t\) (UTC) & 0.264 & 0.000 & 0.000 \\ _Rs_ (s\({}^{-1}\)) & \(t\) (UTC) & 0.229 & 0.000 & 0.000 \\ _Wd_ (\({}^{\circ}\)) & \(t\) (UTC) & 0.073 & 0.000 & 0.000 \\ _Nd_ (\({}^{\circ}\)) & \(t\) (UTC) & 0.072 & 0.000 & 0.000 \\ _Rs_ (s\({}^{-1}\)) & _Wd_ (\({}^{\circ}\)) & \(-0.046\) & 0.000 & 0.000 \\ _Nd_ (\({}^{\circ}\)) & _Rs_ (s\({}^{-1}\)) & \(-0.044\) & 0.000 & 0.000 \\ _Nd_ (\({}^{\circ}\)) & _Ws_ (m/s) & \(-0.024\) & 0.000 & 0.000 \\ _Wd_ (\({}^{\circ}\)) & _Ws_ (m/s) & \(-0.024\) & 0.000 & 0.000 \\ _Nd_ (\({}^{\circ}\)) & _Po_ (MW) & 0.002 & 0.343 & 0.367 \\ _Po_ (MW) & _Wd_ (\({}^{\circ}\)) & 0.001 & 0.744 & 0.744 \\ \hline \end{tabular}
\end{table}
Table 4: Correlation data of variables according to the Pearson test.  
where \(MS_{B}\) refers to the mean square due to the independent variables and \(MS_{E}\) is the mean square for the error. The degrees of freedom (\(df_{B}\) and \(df_{E}\)) are determined based on the number of groups and total data points. The F-value is compared with a \(p\)-value to assess whether the model is statistically significant [31].  
In this study, the effects of independent variables (\(W_{s}\), \(N_{d}\), \(R_{s}\), etc.) on the dependent variable (\(P_{o}\)) are tested individually. After ensuring ANOVA assumptions, such as independence and normality, the results are used to evaluate the model's explanatory power. If the \(p\)-value associated with the F-statistic is below a certain significance level (\(\alpha\) = 0.05), the independent variables significantly affect the model. This analysis is critical for identifying which variables are most strongly related to the predicted values and for assessing the effectiveness of the machine learning models. MINITAB, used in this study for statistical evaluation of data and analysis such as ANOVA, is common software for creating experimental design, data analysis, and regression models with powerful statistical analysis tools.