## 4 Results and Discussion
### Effect in Difference of Test Size vs. Training Size  
To assess the accuracy and effectiveness of the machine learning model, it is crucial to evaluate it on a different subset of data that the model has not previously encountered, known as the test set. This approach provides an estimate of how well the model is likely to perform on new, unseen data. Using the same data for both training and testing could lead to the model memorizing the data and performing well on the test set but failing to generalize to new data, a problem known as overfitting, which is one of the biggest challenges in machine learning. Evaluating the model on a separate test set helps detect overfitting and ensures that the model is learning the underlying patterns in the data rather than just memorizing specific examples. Figures 9-13 were generated at different increments of test size to prevent overfitting and achieve better accuracy. The data from Figures 9-13 were then compiled into a spreadsheet for better visualization and comparison shown in Figure 14.  
Figure 8: Compiled data from different increments of \(n\). Figure 11: Data test size 0.3. Figure 12: Data test size 0.4. Figure 9: Data test size 0.1. Figure 14, which compiles parameters affecting student attrition with varying test sizes, shows that as test sizes increase, the number of influential parameters decreases, indicating an indirectly proportional relationship. A larger test sample, by holding out more data for testing, provides a more precise estimate of the model's performance on unseen data because it better reflects the broader data community. However, a larger test set may result in fewer data for the model to learn from, potentially lowering predictive accuracy. As Figure 13 demonstrates, when the test size reaches 0.5, the number of parameters drops, indicating a decrease in predictive accuracy. [PERSON] and [PERSON] support this [21], stating that while a larger test size can yield a more accurate performance estimate on unseen data, it may reduce predictive accuracy due to limited training data availability. Conversely, a smaller test size allows for more training data, potentially enhancing predictive accuracy, but the performance estimate may be less precise due to limited testing data, as seen in Figure 9. [PERSON] confirms that a smaller test size can increase predictive accuracy by providing more training data but it may lead to a less accurate performance estimation due to the smaller testing dataset [22]. Generally, there is a trade-off between the precision of the model's performance estimate and the test size. The appropriate test size varies based on the problem, dataset size, and desired training-to-testing ratio. Typically, small to medium-sized datasets use a test size of 20-30%, while very large datasets use about 10%. Cross-validation can also be employed to assess machine learning model performance more accurately, as it evaluates the model's performance across various data layers, mitigating the impact of the specific test size on the estimate. Figure 14: Compiled data from different increments of test size. Figure 13: Data test size 0.5. A line graph illustrating the number of features in the machine learning model affecting its accuracy is shown in Figure 15. The graph indicates that the initial drop in features does not impact the model's accuracy. However, after the 12 th feature is dropped, a trend of decreasing accuracy emerges. This suggests a direct relationship: as more features are fed into the machine learning model, the model's accuracy increases. In machine learning, increasing the number of parameters in a model generally enhances its accuracy up to a certain limit. This is because more parameters enable the model to learn complex patterns in the data, leading to better predictions. However, the relationship between the number of parameters and accuracy is nuanced, influenced by factors such as the quality and quantity of training data, the problem's complexity, and the model's architecture and hyperparameters.