## 3 Results  
### Analysis of the Real Estate Market by Regression Learner  
To build regression learner models, we used Matlab, which has a very user-friendly interface [37]. Table 2 shows the results of regression learner models. For a better regression calculation, we divided the price value by one million, for example, 18,000,000 = 18 million. As an output parameter, we also set the values of the price column, and in the second case as an output parameter, we set the values of the price per square meter column. In the calculations, we used 12 forecast models. The results of the models in the table show the performance of each model on a regression task. The models are compared based on four performance metrics: RMSE, R-squared, MSE, and MAE. The data in the table suggest that the Bagged Tree model yielded the best results in terms of both RMSE and MAE for price. It also showed good performance against the price per square meter criterion, with its smallest RMSE value and a relatively high R value. The Bagged Tree model and the Fine and Medium Tree models exhibited relatively low RMSE and MAE scores for the price criterion. Additionally, they also displayed satisfactory performance when tested against the price per square meter criterion. The Boosted Tree model offered a reasonably low RMSE for the square meter price; however, its performance on the actual price was not as impressive compared to other models. The Medium Neural Network (MNN) and Wide Neural Network (WNN) models showed impressive performance in terms of accuracy when predicting the price. They had relatively low RMSE and MAE for the price criteria, and satisfactory results for the price per square meter criterion. Narrow Neural Network (NNN) and Bilayered Neural Network (BFANN) models were both fairly efficient with similar performance results. However, when it comes to the price criterion, they had a slightly increased root-mean-squared error (RMSE) and mean absolute error (MAE).  
Overall, the Bagged Tree model stands out as the best performer for both price and price per square meter criteria. However, it is always a good idea to try out multiple models and compare their performance to ensure the best possible results.  
Table 2 presents a comprehensive comparison of various regression models used to predict real estate values, analyzed based on two output parameters: the price and price per square meter criteria. The LR model shows moderate accuracy with an RMSE of 11.549 for the price criterion and 142.83 for price per square meter, indicating a lower fit for the latter. The ILR model improves upon the linear regression model, achieving a higher correlation coefficient of 0.68 and 0.4 for the two output parameters, respectively. The RLR model shows varied performance with generally lower R values compared to ILR. Decision tree models show improvements over linear models with Fine Tree providing the lowest RMSE values, indicating a better fit. The performance consistency across the tree models highlights their effectiveness in handling non-linear data relationships. Ensemble models leverage multiple learning algorithms to obtain better predictive performance, with Bagged Trees showing the best results in terms of both RMSE and R, particularly for the price criterion. The performance tends to improve with wider or more complex neural networks, as indicated by the gradual increase in R values and decrease in RMSE. Bagged Tree model shows the best overall performance for predicting price, with the lowest RMSE (7.9794) and highest R (0.81). For price per square meter, Bagged Trees again show the best performance with an RMSE of 98.46 and R of 0.69. Decision tree models generally perform well, suggesting that the data may have a non-linear structure that these models can effectively capture. Neural networks show variable performance, but the more complex models (e.g., Wide and Bilayered) generally provide better accuracy.