Verification checks (P4)
- Clean re-run: deleted out/results.json, re-ran out/analysis.py → byte-identical (cmp). PASS
- statsmodels cross-check (asserted in script): conventional and HC1 slope SE for replication 0 match statsmodels OLS / HC1. PASS
- Exact SD identity: sqrt(sum a_i^2 sigma_i^2) with a = slope row of (X'X)^-1X' equals sqrt(sum w_i^2 sigma_i^2). PASS (assert)
- sd_beta_mc (0.26965) vs sd_beta_exact (0.26798): difference ≈ 0.39 approximate SEs of an SD estimate (sd/sqrt(2(R-1))). PASS
- mean_beta_hat (0.4962) vs beta 0.5: z ≈ -0.63 (unbiasedness). PASS
- mean_se_conventional (0.19026) ≤ sqrt(E[se_conv^2]) exact (0.19318), as Jensen requires; both well below sd_beta_exact → conventional SE is downward biased. PASS
- Coverages in [0,1]; all positive keys (sd_beta_exact, sd_beta_mc, mean_se_conventional) > 0. PASS
- Undercoverage flag: 0.844 < threshold 0.95 − 3·0.004873 = 0.93538 → true; flag equals rule. PASS
- Counts: n_input_rows 30 = n analysed 30 per replication; exclusions ledger removes 0. R = 2000. PASS
- Baseline comparison: HC1 coverage (0.902) > conventional (0.844), consistent with mean_se_hc1 (0.2408) being closer to sd_beta_exact than mean_se_conventional. PASS