## 3 Results
### Regressions Analysis
This is a clear case in which a higher test \(R^{2}\) does not necessarily imply a lower error in all metrics, underscoring the importance of not relying exclusively on \(R^{2}\) to assess model performance. Furthermore, the \(RMSLE\) metric, which is sensitive to the scale of the target variable, provides unique insight into this relationship. Despite having a lower test \(R^{2}\) in \"Elongation at break\", gradient boosting shows an \(RMSLE\) of 0.490, which is comparable to the \(RMSLE\) of 0.474 for Random Forest. This indicates that although Gradient Boosting may not capture all the variability of the variables, it is relatively accurate at different scales, which is an aspect that the test \(R^{2}\) alone could not reveal. Therefore, although there is a general trend in which a higher test \(R^{2}\) suggests lower errors, this relationship is neither strictly linear nor uniform. Each error metric brings an additional layer of complexity to this relationship, which makes the interpretation of \(R^{2}\) richer and more contextual. It is crucial to consider these metrics together for a more complete and nuanced assessment of model performance, especially in a sparse dataset. Then, for simplicity Figure 3 shows (a, b, c) the tensile strength prediction graphs for each of the models used. If we use the decision tree model as a reference, the random forest model has an effect on decreasing the variance of the model [92], while the gradient boosting model puts more emphasis on the reduction in bias [43; 93]. \begin{table}
\begin{tabular}{c l c c c c c c c} \hline \hline
**Predicted** & **Model Predictive** & \(R^{2}\)**Train** & \(R^{2}\)**Test** & \(MSE\) & \(RMSE\) & \(MAE\) & \(MedAE\) & \(RMSLE\) \\ \hline \multirow{3}{*}{Tensile strength} & Decision tree & 0.961 & 0.661 & 121.998 & 11.045 & 4.626 & 2.491 & 0.559 \\  & Random forest & 0.939 & 0.821 & 64.310 & 8.019 & 5.003 & 2.632 & 0.468 \\  & Gradient boosting & 0.999 & 0.778 & 79.891 & 8.938 & 5.201 & 2.162 & 0.465 \\ \hline \multirow{3}{*}{Elongation at break} & Decision tree & 0.506 & 0.276 & 588.675 & 24.263 & 17.973 & 13.945 & 0.764 \\  & Random forest & 0.931 & 0.421 & 470.787 & 21.698 & 11.035 & 4.590 & 0.474 \\  & Gradient boosting & 0.997 & 0.156 & 686.075 & 26.193 & 11.886 & 3.881 & 0.490 \\ \hline \multirow{3}{*}{Tensile strength–elongation at break} & Decision tree & 0.536 & 0.555 & 281.606 & 16.086 & 11.333 & 6.950 & 0.609 \\  & Random forest & 0.930 & 0.650 & 232.919 & 14.324 & 8.540 & 3.801 & 0.555 \\ \cline{1-1}  & Gradient boosting & 0.996 & 0.467 & 408.516 & 17.086 & 8.341 & 2.428 & 0.433 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Errors and predictive capability of the proposed regression models. Therefore, the level of fit is usually good with this type of model. For the results obtained independently of whether both dependent variables are predicted or each one is predicted separately, or the use of different models, the outliers are the most responsible for the increase in bias and the variance of the models. For example, it is no coincidence that the values farthest from the prediction line in Figure 3 are the values with the highest prediction error since they are in the last quintile. Finally, it is important to point out that the most stable model with the extracted data was the random forest model, so its use is recommended for the analysis of scarce and highly dispersed data. This model can be used to optimize the design of biodegradable polymeric materials and to support decision making in the biomaterials manufacturing industry. However, it is important to note that the study was conducted on a small scale and with a limited number of formulations and properties, so further research is needed to validate the results and extend the analysis to a larger dataset.