1[2 {"id":"C1","text":"The conventional OLS 95% interval does not attain nominal coverage: estimated coverage 0.844, more than three Monte Carlo SEs below 0.95.","results_keys":["coverage_conventional","conventional_ci_undercovers","mcse_at_nominal","undercoverage_threshold"],"status":"supported","caveat":"Specific to this fixed design, normal errors, single seed, R=2000."},3 {"id":"C2","text":"The HC1 interval covers better (0.902) but still below nominal in this n=30 sample.","results_keys":["coverage_hc1","mcse_coverage_hc1"],"status":"supported","caveat":"No formal test specified for HC1; judged by ~7 MC SEs gap."},4 {"id":"C3","text":"The exact SD of the slope estimator is 0.268, matched by the Monte Carlo SD 0.270.","results_keys":["sd_beta_exact","sd_beta_mc"],"status":"supported","caveat":"MC SD has sampling SE ~0.004."},5 {"id":"C4","text":"The conventional SE understates the true sampling SD on average (mean 0.190 vs 0.268), which explains the undercoverage.","results_keys":["mean_se_conventional","sd_beta_exact","sd_beta_homoskedastic_formula"],"status":"supported","caveat":"Mechanism inferred from SE magnitudes; heteroskedasticity is concentrated at high-leverage x."}6]7