## 3 Results  
From the cross-validation training, the following cross-validated MSE values were obtained for the Random Forest, Gradient Boosting, and LSTE models, respectively: \(2.05\times 10^{-8}\), \(8.14\times 10^{-5}\), and \(5.88\times 10^{-3}\) with a standard deviation of \(2.18\times 10^{-8}\), \(4.56\times 10^{-6}\), and \(5.22\times 10^{-5}\). Each fold of the training ran for a varying number of epochs, a variability that shows that early stopping occurred at different times across the folds to avoid overfitting. After training on the complete training data, the following MSE values were obtained for the test set predictions, in the same order aforementioned: \(4.7\times 10^{-9}\), \(7.4\times 10^{-5}\), and \(5.6\times 10^{-3}\). The Gradient Boosting model was chosen as the model to be implemented due to its ability to capture complex, nonlinear relationships and its adaptability to smaller datasets compared to Random Forest and LSTM. During cross-validation, Gradient Boosting demonstrated competitive performance, with its mean squared error being higher than Random Forest but still reasonable. Its ability to iteratively refine errors through its sequential learning process makes it more suited to datasets with intricate patterns. Furthermore, Gradient Boosting's stepwise construction of decision trees provides valuable insights into feature importance, improving the interpretability of its predictions. Although its standard deviation was higher than that of Random Forest, the model still exhibited strong generalization on the test set. This combination of performance, interpretability, and adaptability, particularly when hyperparameters are finely tuned, makes Gradient Boosting a robust choice. As such, it will be referred to as \"the model\" throughout the remainder of this study, representing the optimal approach for predictive tool wear analysis. The first plot (Figure 5) compares actual and predicted tool wear values. This scatter plot, with a regression line, shows how closely the model's predictions align with the true values. Each point represents a prediction, and the red line represents perfect predictions, where actual equals predicted. Ideally, the points should be as close to this line as possible. In this case, the points generally follow the regression line, indicating a strong positive correlation between the actual and predicted values. However, the deviations observed at medium tool wear levels, often referred to as outliers, suggest that the model faces some difficulty in accurately predicting certain values. This does not necessarily indicate poor model performance. It is often a positive sign that the model is not overly precise, as perfect accuracy could imply overfitting. By not being excessively precise, the model demonstrates a level of flexibility, suggesting it will generalize better to new, unseen data. Balancing prediction accuracy with generalization is key to building a robust and reliable model. The second plot (Figure 6) visualizes the error distribution, showing the difference between the actual and predicted values. The distribution should ideally be centered around zero, indicating that the model's errors are balanced and not consistently over- or underestimating tool wear. The histogram shows a relatively symmetric error distribution around zero, with a narrow spread. This suggests that most of the model's predictions are close to the actual values, with a few larger errors appearing in the tails of the distribution. The third plot (Figure 7) compares the overall distribution of the actual and predicted tool wear values using density plots. The blue curve represents the actual tool wear, while the orange curve represents the predicted values. The degree of overlap between these curves shows how well the model captures the general pattern of the data.