## 3 Results and Discussion
### The Performances of ML Algorithms
#### 3.2.1 The Effect of Categorical Features on the Performance of Regression Problem  
The effect of considering and not considering features consisting of categorical variables on the performance of 11 ML algorithms for the regression problem is shown in Figure 4. All algorithms were trained and their performances were assessed using three metrics (MAE, RMSE and R\({}^{2}\)). The performance of the ML algorithms was determined using a 10-fold cross-validation approach. In addition, the performance of ML was gained without using the normalization technique. The performance results given as a bar graph in black color in Figure 4 were obtained as a result of 17 numerical features given as input to the algorithms. On the other hand, the results presented as bar graphs in red were obtained by using categorical features as well as numerical features. Categorical features cannot be used directly, but they are made usable with some transformation techniques. Here, the number of features increased to 56 after applying OneHotEncoder for the categorical features. The results given as a bar graph in red in Figure 4 were calculated by giving these 56 features as input to the machine learning algorithm algorithms. It can be seen that the using the categorical features generally improved the performance of ML models. An increase was observed in the performances of all algorithms except the RF algorithm. The best performance results in Figure 4 were obtained for the RF algorithm without using categorical features. These results were 0.8955, 31.2583 and 17.6274 for the R\({}^{2}\), RMSE and MAE metrics, respectively. As for the performance results for ML algorithm using categorical features, the XGBoost algorithm showed the best performance. The performance results were 0.9152, 29.5699 and 18.4419 for the R\({}^{2}\), RMSE and MAE metrics, respectively. The XGBoost algorithm made less errors using categorical features. In particular, the performances of the XGBoost and M5 Rules algorithms were boosted significantly. The performances of all algorithms except RF were enhanced after using the categorical features. There was no significant change in the performance of the RF algorithm. These results showed that boring media and boring method features are important in estimating the thickness value. No such research based on ML has been carried out before in the literature for this problem. 2.2 The Effect of Applying Normalization Techniques to Categorical Variables on Regression Problem Performance  
The performance of 11 ML algorithms on the regression problem as a result of the application of normalization techniques to the data considering categorical variables is shown in Figure 5. Within this framework, four different normalization techniques were utilized in order to observe the effect on the performance of ML algorithms. As the results were taken into consideration in Figure 5, the XGBoost algorithm showed the best performance. The performance results were 0.9152, 29.5699 and 18.4419 for the R\({}^{2}\), RMSE and MAE metrics, respectively. No change was observed for the performance of the XGBoost model as compared to the results in Figure 4, where normalization was not applied. In fact, the performances of some ML models such as KNN and SVM decreased. The R\({}^{2}\) results of KNN were found to be 0.8067, 0.7992, 0.8028, and 0.7852 for Min-Max, Z-score, Robust, and Quantile Transformer normalization methods, respectively. In Figure 4, the R\({}^{2}\) result of KNN was 0.8143 after using categorical features. The same decrease reported for the KNN was observed for the SVM algorithm. There could be several possible reasonswhy a significant increase or change was not observed in the performance when the ML algorithms were used with various normalization techniques. One of the reasons could be attributed to the dataset characteristics and its distribution. If the features in the dataset are already of similar scale (i.e., the values are very close to each other), normalization may not have an effect.