1[2 {"id":"C1","text":"The conventional nominal-95% OLS interval does not attain nominal coverage under this design: estimated coverage 0.844, more than 3 binomial MCSEs below 0.95.","results_keys":["coverage_conventional","conventional_ci_undercovers"],"status":"supported","caveat":"Specific to this fixed design, normal errors, R=2000, seed 20261030."},3 {"id":"C2","text":"The HC1 interval has better coverage (0.902) than the conventional one but still undercovers at n=30.","results_keys":["coverage_hc1"],"status":"supported","caveat":"MCSE about 0.0066; HC2/HC3 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":"MC SD has about 1.6% relative sampling error."},5 {"id":"C4","text":"The conventional SE is biased downward: its mean (0.190) is about 29% below the true SD of the slope, which explains the undercoverage.","results_keys":["mean_se_conventional","sd_beta_exact"],"status":"supported","caveat":"The mean SE is a Monte Carlo estimate."}6]7