## 3 Results  
After a thorough description of the methodology and development process applied in this study, the outputs achieved will now be presented. This section presents the obtained results. Figure 5 shows the result after applying RFECV, particularly the accuracy of classification based on the number of selected features for _case study 1_. It can be noted that accuracy increases, although after about nine features, it starts to vary. To know exactly which features are not important, the \(p\)-value was calculated, and features with a value greater than 0.05 were excluded. Table 3 illustrates all the variables and their corresponding \(p\)-values for _case study 1_. The values in bold are features whose \(p\)-values are less than 0.05, and these features will be included in further analyses. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Predicted Class** & \\ \hline  & & **Class = Yes** & **Class = No** \\ \hline
**Actual Class** & Class = Yes & True Positive & False Negative \\  & Class = No & False Positive & True Negative \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The possible results of the classification prediction. Figure 5: Recursive feature elimination with cross-validation. The same steps were also carried out for _case study 2_, and the final features which were used as an input to run ML models for both case studies are summarized in Table 4. The results of the implementation of ML techniques for both cases are illustrated below. Table 5 presents the results of two case studies with the following features: _Algorithm_ (RF, Extra-Trees, SVM, KNN), _Hyperparameter_ (parameters that have been adjusted for each algorithm: _RF and Extra-Trees_: Estimators, Min leaf, Max features; _SVM_: Kernels, Gammas, C; _KNN_: K, Weight, Metric. ), _Search Space_ (the set of values for each hyperparameter), _Optimal Value_ (the optimized value selected from the search space), and _Accuracy_. For comparison purposes, the same analysis was executed without weather data, and Table 6 displays the final features serving as an input, Table 7 shows the acquired results. \begin{table}
\begin{tabular}{c c} \hline
**Case Study 1** & **Case Study 2** \\ \hline B365H & B365H \\ B365D & B365D \\ B365A & B365A \\ Tmed\_Diff & Tmed\_Diff \\ Vmax\_Diff & Vmax\_Diff \\ Trange\_Home & Trange\_Home \\ Trange\_Away & Trange\_Away \\ BWA & Racha\_Away \\ \hline \end{tabular}
\end{table} 
Table 4: The final features of the proposed models including weather features. \begin{table}
\begin{tabular}{c c c c} \hline
**Variables** & **P \textgreater{} |t|l| & **Variables** & **P \textgreater{} |t|l| \\ \hline Tmax\_Home & 0.0588 & **B365D** & **0.0000** \\ Tmin\_Home & 0.1232 & **B365A** & **0.0000** \\ Tmed\_Home & 0.0981 & BWH & 0.4560 \\ Racha\_Home & 0.2068 & BWD & 0.4059 \\ Vmax\_Home & 0.8757 & **BWA** & **0.0000** \\ Tmax\_Away & 0.6878 & **Tmed\_Diff** & **0.0000** \\ Tmin\_Away & 0.4443 & **Vmax\_Diff** & **0.0098** \\ Tmed\_Away & 0.4524 & **Trange\_Home** & **0.0007** \\ Racha\_Away & 0.1619 & **Trange\_Away** & **0.0002** \\ Vmax\_Away & 0.6823 & **Trange\_Diff** & 0.2831 \\
**B365H** & **0.0000** & & \\ \hline \end{tabular}
\end{table} 
Table 3: Variables and corresponding \(p\)-values.