## 5 Empirical Study
### Evaluation Metrics  
We use a wide range of performance metrics in our empirical study to assess the prediction accuracy of the model. By offering distinct perspectives on model performance, each of these metrics guarantees a thorough evaluation of predictive power. To assess the accuracy of the model, the root-mean-square error (RMSE) is particularly helpful, because it measures the size of the prediction errors. The model's ability to explain the variance in the target variable was measured using the coefficient of determination (R\({}^{2}\)).  
By calculating the average magnitude of the errors, the Mean Absolute Error (MAE) provides information regarding the difference between the expected and actual values. The Mean Balanced Relative Error MBRE (Equation (5)) and Mean Inverted Balanced Relative Error (MIBE, Equation (6)) are less susceptible to bias than other similar approaches, such as MMRE, which are occasionally criticized for their bias toward underestimation [84; 85; 86; 87; 88].  
In addition to these widely used metrics, we also included the Standardized Accuracy (SA, Equation (8)) introduced by [89], which assesses the consistency of the model over time and is derived from MAE. The SA determines whether a given estimation method outperforms a random guessing baseline (P0) and overcomes interpretability issues (e.g., understanding how good the model is). A higher SA value indicates significant improvement over random guessing, whereas values approaching zero or negative suggest poor performance.  
In addition, we used the logarithmic standard deviation (LSD; Equation (7)), which measures the deviation from the optimal least-squares solution and has been used as a robust evaluation metric that accounts for the distribution of residual errors [88].  
The significance of these metrics is further supported by the findings of a systematic literature review [90] and other studies on predicting software development and assessing machine learning techniques in software development effort estimation (SDEE) [88; 91]. By integrating a diverse set of accuracy measures, our study ensures a comprehensive evaluation of model performance, mitigates potential biases, and enhances the reliability of the prediction assessments.  
Root Mean Square Error Formula (RMSE) = \(\sqrt{\frac{1}{n}{\sum_{i=1}^{n}}{\left({y_{i}-\hat{y}_{i}}\right)^{2}}}\) (2) R - Squared (\(R^{2}\)) = 1 - \(\frac{{\sum_{i=1}^{n}}{\left({y_{i}-\hat{y}_{i}}\right)^{2}}}{{\sum_{i=1}^{n} }{\left({y_{i}-\overline{y}}\right)^{2}}}\) (3) Mean Absolute Error (MAE) = \(\frac{1}{n}{\sum_{i=1}^{n}}{\left|{y_{i}-\hat{y}_{i}}\right|}\) (4) Mean Bias Relative Error (MBRE) = \(\frac{1}{n}{\sum_{i=1}^{n}}\)\(\frac{{\left|{y_{i}-\hat{y}_{i}}\right|}}{{\left|{y_{i}}\right|}}\) (5) Mean Impact Bias Relative Error (MIBRE) = \(\frac{1}{n}{\sum_{i=1}^{n}}\)\(\frac{{\left|{y_{i}-\hat{y}_{i}}\right|}}{{\left|{y_{i}}\right|}}\times{\left|{\hat{y}_{i}}\right|}\) (6) Least Square Deviation (LSD) = \(\sum_{i=1}^{n}{\left({y_{i}-\hat{y}_{i}}\right)^{2}}\) (7) Standardized Accuracy (SA) = 1 - \(\frac{\sum\left|{{\bf{y}}_{\text{test}}}-\overline{{\bf{y}}_{\text{test}}} \right|}{\sum\left|{{\bf{y}}_{\text{test}}}-{\bf{y}}_{\text{pred}}\right|}\) (8)