1[2 {"id":"C1","text":"The OLS slope of y on x (with intercept) is about 0.805, with intercept about 1.444, using all 2000 observations from 50 firms.","results_keys":["beta_hat","alpha_hat","n_analysed","n_clusters"],"status":"supported","caveat":"Linear projection coefficient, not causal."},3 {"id":"C2","text":"The firm-clustered (CR1) SE of the slope is about 0.073, and the 95% CI (t with 49 df) is about [0.658, 0.952], which excludes zero.","results_keys":["se_cluster","beta_ci_low","beta_ci_high","ci_critical_value"],"status":"supported","caveat":"Asymptotic in the number of clusters (G=50)."},4 {"id":"C3","text":"The conventional OLS SE (about 0.024) is roughly 3 times smaller than the clustered SE, so ignoring within-firm dependence overstates precision.","results_keys":["se_ols","se_cluster","se_ratio_cluster_to_ols"],"status":"supported","caveat":"The variance shares quoted as the explanation come from the audit, not from results.json."},5 {"id":"C4","text":"The data have no missing values, no duplicate rows, and no exclusions.","results_keys":["data_issues","n_input_rows","n_analysed"],"status":"supported","caveat":""}6]7