# A Fuzzy Model for Reasoning and Predicting Student's Academic Performance
## 4 Result and Discussions
### Model Evalution  
As it was mentioned in the above subsections, FPM worked well on both types of datasets and performed better in predicting academic performance than linear regression. Hence, it provided a better evaluation MSR factor and showed more details about how the predicted values are convergent to the original values, as shown in Figures 8 and 9.  
An overall evaluation to our suggested model (FPM) performance is presented in Table 8. As it is shown in Table 8, the performance evaluation of the model shows that the FPM performed well in predicting the students' performance in regards to absence rate data (absenteeism), where it performed 0.115 in Mean Bias Error (MBE), \(-1.648\) in Nash-Sutcliffe efficiency (NSE), and 0.249 in Root Mean Square Error (RMSE). Our suggested model (FPM) also showed good performance when it was tested in predicting the final exam marks using the lab exam. Hence, it performed 0.211 in Mean Bias Error (MBE), \(-2.24\) in Nash-Sutcliffe efficiency (NSE), and 0.275 in Root Mean Square Error (RMSE).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{3}{*}{**No.**} & \multicolumn{3}{c}{**Test Data Set**} & \multicolumn{2}{c}{**Predicted Data Developed**} & \multicolumn{2}{c}{**Evaluation Results**} \\  & \multicolumn{2}{c}{**Actual Data (Section 2 Data)**} & \multicolumn{2}{c}{**by the Proposed FPM**} & \multicolumn{2}{c}{**(Mean Squared Error)**} \\ \cline{2-9}  & \multirow{2}{*}{\begin{tabular}{c} **Lab Exam** \\ **Out of 15** \\ \end{tabular} } & \begin{tabular}{c} **The Final** \\ **Exam Out** \\ **of 40** \\ \end{tabular} & \begin{tabular}{c} **Final Exam** \\ **Fuzzy Set/32** \\ \end{tabular} & \begin{tabular}{c} **The** \\ **Predicted** \\ **Fuzzy Set** \\ \end{tabular} & \begin{tabular}{c} **The** \\ **Predicted** \\ **Final Exam** \\ \end{tabular} & \
\begin{tabular}{c} **The** \\ **Predicted** \\ **Fuzzy Sets** \\ \end{tabular} &
\begin{tabular}{c} **Error Rate** \\ **between** \\ **Final Exam** \\ \end{tabular} \\ \hline
1 & 4 & 10 & 0.31 & 0.27 & 8.64 & 0.0018 & 1.8496 \\ \hline
2 & 4 & 13 & 0.41 & 0.27 & 8.64 & 0.0186 & 19.0096 \\ \hline
3 & 5 & 12 & 0.38 & 0.33 & 10.56 & 0.0020 & 2.0736  
To validate the effectiveness of our proposed model (FPM), we conducted a comparative study with a linear regression model (as we mentioned in Section 4.1). The comparison results showed that our proposed model provides better results than linear regression (as we explained above). However, to provide more evaluation of our suggested model (FPM), we presented in the Table 8 the results of [30], in which the authors worked on predicting the students' marks. Their system consisted of multiple inputs and four outputs; their inputs are the student scores in 4 periods, their grades, and the number of fails besides the subject ID; their outputs are the predicted term values for periods 1 to 4 of the 11 th grade. We also presented in Table 8 the results of [31], in which the authors used the variations in course grades among students based on course category, student course attendance rate, gender, high-school grade, school type, grade point average (GPA), and course delivery mode as input predictors. Their prediction results have been evaluated using RMSE, and they provided 8 values for RMSE based on input variables removed (their RMSE values are between 9.235 to 11.315). In conclusion, we can say that our comparative study demonstrated that our proposed model (FPM) outperforms the traditional linear regression model and the existing related works in terms of MSR, MBE, NSE, and RMSE. The results suggested that our model can provide more accurate predictions of student performance and can be a valuable tool for educators and administrators.