1[2 {"id":"C1","text":"The conventional OLS 95% interval does not attain nominal coverage under this design: estimated coverage is 0.844, more than 3 Monte Carlo SEs below 0.95.","results_keys":["coverage_conventional","conventional_ci_undercovers","mcse_at_nominal_0.95","mcse_coverage_conventional","undercover_threshold"],"status":"supported","caveat":"Conditional on this fixed design, normal errors and seed; the conclusion holds with either binomial-SE convention."},3 {"id":"C2","text":"The HC1 interval improves coverage to 0.902 but still undercovers relative to 95%.","results_keys":["coverage_hc1","mcse_coverage_hc1"],"status":"supported","caveat":"The gap is about 7 MCSE; no formal test is applied to HC1."},4 {"id":"C3","text":"The exact SD of the slope estimator is 0.268, and the MC SD (0.270) agrees within simulation error.","results_keys":["sd_beta_exact","sd_beta_mc"],"status":"supported","caveat":"The exact value is analytical given the design."},5 {"id":"C4","text":"The conventional SE is biased downward: its mean (0.190) is about 29% below the true SD.","results_keys":["mean_se_conventional","sd_beta_exact"],"status":"supported","caveat":"The mean is a Monte Carlo estimate."}6]7