## 3 Results
### Learning Curves
A high MSE indicates that the model has larger errors in its predictions and its estimated values deviate significantly from the true targets. A low MSE suggests that the model's predictions closely match the actual values, reflecting better accuracy. SMOTEENN consistently achieves lower MSE values for both training and test sets across all models and sample sizes compared to SMOTE. The difference in MSE between SMOTE and SMOTEENN is most significant for the test set, with SMOTEENN achieving up to 81.6% lower MSE (e.g., DTR with SMOTEENN \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Model** & **Accuracy** & **R\({}^{2}\) (Train)** & **R\({}^{2}\) (Test)** & **MSE (Train)** & **MSE (Test)** \\ \hline DTR with SMOTE & 0.89 & 1.0 & 0.93 & 0 & 0.18 \\ GBR with SMOTE & 0.89 & 0.99 & 0.96 & 0.03 & 0.12 \\ BR with SMOTE & 0.89 & 0.99 & 0.97 & 0.04 & 0.10 \\ DTR with SMOTEENN & 0.93 & 1.0 & 0.97 & 0 & 0.07 \\ GBR with SMOTEENN & 0.94 & 0.999 & 0.98 & 0.002 & 0.05 \\ BR with SMOTEENN & 0.96 & 0.995 & 0.986 & 0.113 & 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of SMOTE and SMOTEENN across a sample size of 250. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Model** & **Accuracy** & **R\({}^{2}\) (Train)** & **R\({}^{2}\) (Test)** & **MSE (Train)** & **MSE (Test)** \\ \hline DTR with SMOTE & 0.89 & 1.0 & 0.91 & 0 & 0.23 \\ GBR with SMOTE & 0.91 & 0.99 & 0.95 & 0.03 & 0.14 \\ BR with SMOTE & 0.91 & 1.0 & 0.97 & 0 & 0.09 \\ DTR with SMOTEENN & 0.97 & 1.0 & 0.96 & 0 & 0.11 \\ GBR with SMOTEENN & 0.95 & 0.997 & 0.98 & 0.009 & 0.05 \\ BR with SMOTEENN & 0.96 & 0.99 & 0.98 & 0.017 & 0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of SMOTE and SMOTEENN across a sample size of 200. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Model** & **Accuracy** & **R\({}^{2}\) (Train)** & **R\({}^{2}\) (Test)** & **MSE (Train)** & **MSE (Test)** \\ \hline DTR with SMOTE & 0.89 & 1.0 & 0.92 & 0 & 0.23 \\ GBR with SMOTE & 0.91 & 0.99 & 0.97 & 0.03 & 0.08 \\ BR with SMOTE & 0.91 & 0.99 & 0.97 & 0.04 & 0.09 \\ DTR with SMOTEENN & 0.96 & 1.0 & 0.99 & 0 & 0.04 \\ GBR with SMOTEENN & 0.96 & 0.995 & 0.98 & 0.014 & 0.04 \\ BR with SMOTEENN & 0.97 & 0.99 & 0.98 & 0.02 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of SMOTE and SMOTEENN across a sample size of 300.  
at 0.07 vs. DTR with SMOTE at 0.38 for sample size 100). As the sample size increases, the MSE values for both SMOTE and SMOTEENN generally decrease, but SMOTEENN maintains a lower MSE across all models and sample sizes. The numerical results presented in Tables 1-5 demonstrate that SMOTEENN consistently outperforms SMOTE across all three models (decision tree regression, gradient boosting regression, and Bayesian regression) and across all sampling strategies (from 100 to 300 instances). For example, at the smallest sample size of 100 instances, SMOTEENN achieved an accuracy from 0.93 to 0.96 across the three models, compared to an accuracy from 0.81 to 0.825 for SMOTE. Similarly, the MSE for SMOTEENN ranged from 0.04 to 0.07 on the test set, while SMOTE had MSE values between 0.15 and 0.38. These results highlight the superior performance of SMOTEENN in handling class imbalance and improving predictive accuracy in the context of fall risk assessment for bedridden patients.