## 3 Purposed Approaches
### Collaborative Filtering
In addition, the value for least MAE is 0.6502 for weight = 0.9, significantly greater than our model's least MAE at 0.5699. Hence, our model is a much improved method over classic regression. In addition, the weights for the regression model for highest MAE and least accuracy do not correspond, which shows that a standardized weight may not be applicable. ### Testing Whether a Student Will Pass

For this scenario, courses are recommended when the prediction is that the student will pass. The recommendation criteria are based on a minimum cutoff for the predicted grade. If the actual received grade of a student is 1, the student will fail. We chart the effect of our system for errors for different values of the cutoff grade and recommend courses only if the predicted grade is greater than the cutoff grade. The cutoff grade varies from 1.5 to 3 in steps of 0.1 shown as Figure 11.

We see that our method provides low values of error for a range of cutoff scores. Passing a course is a very important factor for a student. Hence it is essential to reduce the beta error for the students. This can be achieved by having a high cutoff grade for the recommendation system. However, this increases the alpha error of the system where we fail to recommend those courses in which the student passes. Thus we reduce the diversity of the final course selection for the student. Therefore, there is a tradeoff between probability of passing the course and selecting from a wider pool of courses. We constructed the confusion matrix where we select the cutoff grade for recommendation. According to Table 8, the fraction of courses recommended = \((208+15)/233=0.9570\) out of 113 courses for years 3 and 4 equaling \(\sim\)108 courses. To help students narrow their search pool we added a \begin{table}
\begin{tabular}{c c c c} \hline \hline
**MAE = 0.7029** & & & \\
**Folds = 5** & **AG < 3** & **AG \(\geq\) 3** & **Acc** \\
**w = 0.45** & & & \\ \hline PG < 3 & 125 & 119 & 0.7594 \\ PG \(\geq\) 3 & 47 & 399 & Total = 690 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Confusion Matrix for regression analysis with highest accuracy. Figure 10: Accuracy for a linear regression for predictions using different weights for student and course average. professor rating filter, such that it recommends only those courses where the Professor scores at least 2 points on a grade of 5. It acts as a quality assurance bar for course recommendation. If the professor has not been rated, or if the feedback information is not available, we consider just the predicted score as the basis for the recommendation without the rating filter. Now, we see that the total fraction of recommendations = \((7+208)/233=0.9227\). Hence, we recommend 113 \(\times\) 0.4171 = 47 courses such that the average student has a 92.27% probability of passing any of these courses, and the professor's rating is at least 2. Thus we ensure diversity in course selection as well as quality, while reducing the chance of failure for students. We see that the accuracy or errors of our selection are not significantly affected by the professor rating (in both cases the accuracy is above 90%). ### Checking Effects of Professor Rating Filter on Accuracy of Predictions

We compare the accuracy levels of our predictions for different minimum professor rating levels and select only those courses where the instructor secures a minimum score in the feedback report or is unrated and there is a weighted cosine analysis. We plot MAE and see the effects on the accuracy of our recommendation system using a five-fold accuracy vs. minimum professor rating threshold. The elated results are shown in Table 9, Figures 12 and 13. We see that the change in accuracy and MAE levels are not significant. The levels stay constant until a professor rating of about 1.8. The difference in best and worst accuracies is only 2%, while the difference in MAE is 0.04. Thus, the use of professor's rating will not affect our prediction model, especially if the filter operates at below 1.8 for the professor rating.