Student Name: Michele Nascia Assignment: Week 9 - Monte Carlo OLS & Numerical Integration

Overall Assessment

Grade: ✅ (Pass)

The submission correctly implements the Monte Carlo simulation and the structure for numerical integration. However, the manual implementation of Simpson’s rule does not account for the parity requirement (odd number of points / even intervals). For the even grid sizes specified in the homework (N=50, 200, 1000), the hardcoded formula 2:2:end-1 and 3:2:end-2 leads to points being skipped or incorrectly weighted at the end of the interval.

Task-by-Task Check

  1. Function Definition: ✅ montecarlo_ols is correctly defined.
  2. DGP Logic: ✅ Correct.
  3. OLS Logic: ✅ Correct.
  4. Execution: ✅ Correct loops.
  5. Visuals: ✅ Histograms generated.
  6. Statistics: ✅ Stats calculated.
  7. Interpretation: ✅ Correct.
  8. Utility Function: ✅ Correct.
  9. Trapezoidal Rule: ✅ Correct.
  10. Simpson’s Rule: ⚠️ Issue. The formula used assumes an odd number of points. For even N, the indexing causes the penultimate point to be skipped or the weights to misalign. You should check mod(N,2) and adjust the grid (e.g., N-1) or the method.
  11. Grid Loop: ✅ Correct.
  12. Visuals: ❌ The plot code is present but uses exportgraphics which is good.
  13. Interpretation: ✅ Correct.

Technical Implementation

  • Code Structure: Clean and readable.
  • Issue: Simpson’s rule parity logic.

Suggestions for Improvement

  • Simpson’s Rule: Add a conditional check: if mod(N,2)==0, N=N-1; end (or similar strategy) to ensure the grid size is compatible with the 1/3 rule.

Summary

11/13 tasks correct. Good work, just mind the grid parity for Simpson’s rule.