1[2 {"id": "C1", "text": "Memo's conclusion: the slope of y on x is statistically significant at the 5% level.", "results_keys": ["p_hac", "t_hac", "memo_claim_supported"], "status": "unsupported", "caveat": "Supported only under i.i.d. SEs (p_iid=0.024); with HAC SE (9 lags) p=0.120."},3 {"id": "C2", "text": "The memo's point estimate and conventional SE are reproduced: beta_hat=0.1017, se_iid=0.0448.", "results_keys": ["beta_hat", "alpha_hat", "se_iid", "t_iid", "p_iid"], "status": "supported", "caveat": ""},4 {"id": "C3", "text": "OLS residuals are strongly positively autocorrelated (rho about 0.61), so i.i.d. SEs are invalid.", "results_keys": ["rho_resid"], "status": "supported", "caveat": "Sample AR(1) coefficient of residuals; true DGP value stated as ~0.7."},5 {"id": "C4", "text": "The HAC SE (0.0654, 9 lags, Andrews AR(1) plug-in) is about 1.46 times the i.i.d. SE, and the 95% CI [-0.026, 0.230] includes zero.", "results_keys": ["se_hac", "se_iid", "hac_lags", "beta_ci_low", "beta_ci_high"], "status": "supported", "caveat": "Normal-approximation CI."},6 {"id": "C5", "text": "The non-significance at 5% holds for all HAC bandwidths from 5 to 36 lags.", "results_keys": ["hac_sensitivity"], "status": "supported", "caveat": "Only lag 0 (no autocorrelation correction) gives p<0.05."}7]8