Student Name: Klea Lushaj Assignment: Week 9 - Monte Carlo OLS & Numerical Integration

Overall Assessment

Grade: ✅ (Pass)

A comprehensive and professional submission. The code is well-structured, using structs to store results and handling file paths robustly. The numerical integration correctly handles the parity requirement for Simpson’s rule by truncating even grids. The convergence plots and error analysis are very thorough.

Task-by-Task Check

  1. Function Definition: ✅ Correct.
  2. DGP Logic: ✅ Correct.
  3. OLS Logic: ✅ Correct.
  4. Execution: ✅ Correct.
  5. Visuals: ✅ High-quality plots with theoretical overlays.
  6. Statistics: ✅ Detailed statistics reported.
  7. Interpretation: ✅ Detailed analysis of variance reduction.
  8. Utility Function: ✅ Correct.
  9. Trapezoidal Rule: ✅ Correct.
  10. Simpson’s Rule: ✅ Correct. You handled the even/odd grid size issue by checking mod(N,2) and adjusting the grid.
  11. Grid Loop: ✅ Correct.
  12. Visuals: ✅ Excellent convergence plots (log-log scale) showing the convergence rates.
  13. Interpretation: ✅ Correct and detailed error analysis.

Technical Implementation

  • Code Quality: High. Good use of struct for data management and try-catch for saving figures.
  • Analysis: The log-log convergence plot is a great addition to verify the order of accuracy ($O(N^{-2})$ vs $O(N^{-4})$).

Suggestions for Improvement

  • None. This is a model submission.

Summary

13/13 tasks correct. Excellent work.