## 4 Results and Discussion  
### Introduction  
The results of the various machine learning models, each configured with different hyperparameters, are recorded and divided into sections for thorough analysis. The discussion section offers insights into the outcomes of the machine learning model, explaining the significance of the findings, the model's limitations, and potential directions for future research. Additionally, it may investigate factors contributing to student attrition, such as academic performance, background, or personal factors. The number of decision trees (\(n\)) in a random forest model is a hyperparameter that can be adjusted during the training phase. The optimal number of trees typically depends on the dataset size and the problem's complexity. After cleaning and importing the data, hyperparameters like the number of random forest trees are set at different increments (as shown in Figures 2-7) to determine the best fit for the machine learning model, aiming to produce the most accurate predictive results. The primary hyperparameter tuned was the number of decision trees (\(n\)) in the random forest model, with values ranging from 10 to 100. Increasing the number of trees improved accuracy, but beyond 100, the returns diminished, with only marginal accuracy gains and increased computational costs. The tuning process focused on manually adjusting the number of trees rather than conducting a comprehensive exploration of other parameters. While the increased number of trees helped reduce overfitting and enhanced accuracy, we  
From Figure 8, it can be seen that as the number of decision trees (\(n\)) in the random forest model increases, the number of parameters affecting the dropout rate also rises, up to a certain point. When \(n\) is set to 10, only eight parameters impact student attrition. Increasing \(n\) to 20 raises the number of influential parameters to 12, indicating a directly proportional relationship. This trend continues until \(n\) reaches 30, where the number of parameters peaks at 15. Beyond this point, increasing \(n\) further does not add more parameters, although the influence of each parameter on attrition rate changes slightly. As the number of decision trees increases, the model's predictive accuracy also improves. This supports [PERSON]'s assertion that random forests have low bias but high variance, meaning they can overfit the training data. By adding more decision trees, the model reduces variance and enhances overall accuracy. However, beyond a certain number of trees, the model's predictive accuracy is higher.  
Figure 5: Data \(n=40\).  
Figure 6: Data \(n=50\).  
Figure 7: Data \(n=100\).  
returns diminish, and the model risks overfitting the training data. Increasing the number of decision trees also brings several limitations. One is reduced model interpretability; a larger number of trees makes the model more complex and harder to understand, complicating the identification of specific factors and relationships driving predictions. This observation is supported by [PERSON] and [PERSON], who noted that increased complexity in the model reduces its interpretability. Another limitation is increased computational time and memory requirements. Training and testing a random forest model with many decision trees can be computationally expensive and memory-intensive due to the numerous decision trees with many nodes and branches. [PERSON]'s study highlights that as tree complexity or the number of trees increases, so does computational time, which can affect the cost-efficiency of the model. In summary, while adding more decision trees to a random forest model can enhance its performance, it is important to balance the benefits against the drawbacks, selecting the appropriate number of trees based on the specific problem and data.