1[2 {"id":"C1","text":"The conventional 95% interval does not attain nominal coverage: estimated coverage 0.844, more than three MC standard errors below 0.95.","results_keys":["coverage_conventional","conventional_ci_undercovers","mcse_coverage_conventional","undercoverage_threshold"],"status":"supported","caveat":"Conditional on this fixed design, normal errors and seed; MC SE about 0.008."},3 {"id":"C2","text":"The HC1 interval covers better (0.902) than the conventional interval but still falls below 95%.","results_keys":["coverage_hc1","mcse_coverage_hc1","mcse_at_nominal"],"status":"supported","caveat":"MC SE about 0.007; small-sample HC variants not evaluated."},4 {"id":"C3","text":"The exact SD of the slope estimator 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 value is analytic, given the design."},5 {"id":"C4","text":"The conventional SE is biased downward: its mean (0.190) is about 29% below the true SD of the slope estimator.","results_keys":["mean_se_conventional","sd_beta_exact","sqrt_E_s2_over_Sxx_analytic"],"status":"supported","caveat":"MC average; consistent with the analytic sqrt(E[s^2]/Sxx)."}6]7