Verification checks (P4)
- Reproducibility: results.json deleted and regenerated twice; byte-identical (cmp) -> PASS.
- Statsmodels cross-check (inside analysis.py, assert): replication 1 se_conv and HC1 se match statsmodels OLS bse / HC1_se -> PASS.
- sd_beta_mc vs sd_beta_exact: relative difference 0.62%, within one MC relative SE of an SD (~1/sqrt(2(R-1)) = 1.58%) -> PASS.
- Jensen: mean_se_conventional (0.1903) <= sqrt(E[s^2]/Sxx) analytic (0.1932) -> PASS.
- Positivity: sd_beta_exact, sd_beta_mc, mean_se_conventional, MC SEs all > 0 -> PASS.
- Counts: coverage*R integers (1688, 1804); n_obs=30=n_input_rows; exclusions 30-0=30 -> PASS.
- Undercoverage rule: threshold 0.95 - 3*0.004873 = 0.93538; coverage_conventional 0.844 < threshold -> flag true, consistent -> PASS.
- Magnitudes: mean_se_conventional (0.190) well below sd_beta_exact (0.268), consistent with observed undercoverage; HC1 mean SE 0.241 also below 0.268, consistent with HC1 also undercovering (0.902) -> PASS (plausible).