# Student Performance Prediction with Regression Approach and Data Generation
## 3 Experiment and Analysis of Results
### Generation and Use of Synthetic Data
* Second, the GANs should generate more dispersed data. During the training process of the GANs, it is possible that the generator generates data concentrated in a certain range of the real data distribution. The generated data are real-like but all similar, while the discriminator cannot reflect this problem. By choosing a generator that generates dispersed data, this problem can be alleviated. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Age** & **Medu** & **Fedu** & **Absences** & **G1** & **G2** & **Traveltime** & **Studytime** & **Faliures** & **Famrel** \\ \hline
18 & 0 & 2 & 5 & 14 & 12 & 1 & 1 & 0 & 5 \\
18 & 0 & 4 & 8 & 17 & 10 & 1 & 1 & 0 & 5 \\
16 & 1 & 4 & 9 & 16 & 10 & 1 & 1 & 0 & 5 \\
18 & 0 & 4 & 4 & 17 & 10 & 1 & 1 & 0 & 5 \\
19 & 0 & 4 & 0 & 18 & 12 & 1 & 1 & 0 & 5 \\
18 & 0 & 4 & 2 & 17 & 11 & 1 & 1 & 0 & 5 \\
19 & 0 & 4 & 7 & 16 & 11 & 1 & 1 & 0 & 5 \\
18 & 0 & 3 & 2 & 18 & 12 & 1 & 1 & 0 & 5 \\
19 & 0 & 4 & 1 & 17 & 11 & 1 & 1 & 0 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Sample data from abandoned GANs. Figure 2: Loss–epoch relationship of abandoned GANs. (**a**) Generator. (**b**) Discriminator. To evaluate the ability of the GANs, SVR, NN, and RF are trained again to predict student mathematics performance using a regression approach but on a dataset containing synthetic data. The training dataset contains 100 pieces of synthetic data and 70% of data randomly selected from the mathematics performance dataset collected. The other 30% of the collected data is used as the test set. The result is presented in Table 7.  
An examination of the results presented in Table 7 shows that although NN has an increase of 2.5% in accuracy, RF and SVR remain largely unaffected. This aligns with the understanding that NN is more responsive to the volume of training data. The marginal improvement in NN's accuracy suggests that the synthetic data are well matched to the distribution of the collected data. An analysis of the generated data (Table 6) shows that current synthetic data are still not sufficiently dispersed to fully cover the real data distribution. Some age values never appear in the generated data and failures are all 0. Furthermore, in the generated data, a larger student absence number occurs frequently, which does not match the collected data. As the synthetic data are concentrated, it only smoothes the distribution of the collected data a little, leading to a small improvement in NN's performance. In addition, the encoder and decoder used in this research are not capable of correctly encoding and decoding each piece of data. Although this feature is \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Age** & **Medu** & **Fedu** & **Absences** & **G1** & **G2** & **Traveltime** & **Studytime** & **Faliures** & **Famrel** \\ \hline
16 & 0 & 0 & 4 & 13 & 11 & 3 & 3 & 0 & 3 \\
15 & 1 & 4 & 0 & 7 & 8 & 1 & 1 & 0 & 5 \\
19 & 0 & 0 & 16 & 12 & 8 & 3 & 2 & 0 & 4 \\
15 & 4 & 4 & 10 & 8 & 6 & 2 & 2 & 0 & 5 \\
15 & 4 & 4 & 27 & 13 & 7 & 1 & 2 & 0 & 5 \\
15 & 2 & 4 & 7 & 13 & 10 & 1 & 2 & 0 & 5 \\
15 & 4 & 4 & 6 & 14 & 8 & 1 & 3 & 0 & 5 \\
16 & 1 & 2 & 10 & 15 & 11 & 1 & 3 & 0 & 5 \\
15 & 4 & 4 & 5 & 17 & 13 & 1 & 4 & 0 & 5 \\
17 & 0 & 1 & 4 & 6 & 6 & 2 & 2 & 0 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Sample data from chosen GANs. Figure 3: Loss–epoch relationship of chosen GANs. (**a**) Generator. (**b**) Discriminator. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **SVR** & **NN** & **RF** \\ \hline Performance & 81.5\% & 75.9\% & 79.0\% \\ Comparing to Classification Approach 1 & +21.9\% & +15.6\% & +6.6\% \\ Comparing to Regression Approach 2 & +0\% & +2.5\% & +0.8\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance of regression approach with synthetic data. used as random noise, it also makes data generation more uncertain. It is expected that a better auto-encoder with more collected data can help GANs achieve better performance.