1[2 {"id":"C1","text":"The conventional 95% OLS 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","undercover_threshold","conventional_ci_undercovers_using_estimated_mcse"],"status":"supported","caveat":"Specific to this fixed design, n=30, Gaussian errors, seed 20261030."},3 {"id":"C2","text":"The HC1 interval improves coverage to 0.902 but still falls short of 0.95.","results_keys":["coverage_hc1","mcse_coverage_hc1","hc1_ci_undercovers"],"status":"supported","caveat":"HC1 is known to be downward biased in small, high-leverage samples; other estimators not evaluated."},4 {"id":"C3","text":"The exact SD of the slope estimator is 0.268, and the Monte Carlo SD (0.270) agrees within Monte Carlo error.","results_keys":["sd_beta_exact","sd_beta_mc","mcse_sd_beta_mc_approx"],"status":"supported","caveat":"MC SE of the sample SD approx 0.004 (mcse_sd_beta_mc_approx)."},5 {"id":"C4","text":"The conventional SE averages 0.190, about 71% of the true SD, which explains the undercoverage.","results_keys":["mean_se_conventional","ratio_mean_se_conv_to_sd_exact","sqrt_expected_conv_variance_exact"],"status":"supported","caveat":"Attributing the undercoverage to SE bias is an interpretation, supported by the exact E[s^2] computation."}6]7