1[2 {"id":"C1","text":"The conventional 95% OLS interval does not attain nominal coverage: estimated coverage 0.844, more than three binomial MC standard errors below 0.95.","results_keys":["coverage_conventional","conventional_ci_undercovers","undercoverage_threshold","mcse_binomial_nominal"],"status":"supported","caveat":"Specific to this fixed design, normal errors, and seed 20261030; MC SE about 0.008."},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":"Small-sample HC1 bias with high-leverage heteroskedastic points; other HC variants not evaluated."},4 {"id":"C3","text":"The exact SD of the OLS slope is 0.268, and the Monte Carlo SD (0.270) agrees with it.","results_keys":["sd_beta_exact","sd_beta_mc"],"status":"supported","caveat":"Exact SD is analytic under the stated model."},5 {"id":"C4","text":"The conventional SE is biased downward on average (mean 0.190 vs true SD 0.268), which explains the undercoverage.","results_keys":["mean_se_conventional","sd_beta_exact"],"status":"supported","caveat":"Mean of se_conv is an MC estimate."}6]7