1[2 {"id":"C1","text":"The OLS slope of y on x is 0.805 with intercept 1.444.","results_keys":["beta_hat","alpha_hat"],"status":"supported","caveat":"Linear projection coefficient, not causal."},3 {"id":"C2","text":"The firm-clustered 95% CI for beta is [0.658, 0.952] and excludes zero.","results_keys":["beta_ci_low","beta_ci_high","se_cluster","ci_critical_value_t_df"],"status":"supported","caveat":"Relies on independence across 50 firms and t(49) approximation."},4 {"id":"C3","text":"The firm-clustered SE is about 3.0 times the naive OLS SE, so the naive SE substantially understates uncertainty.","results_keys":["se_ols","se_cluster","se_ratio_cluster_over_ols"],"status":"supported","caveat":"Naive SE assumes independent observations, which the design rules out."},5 {"id":"C4","text":"All 2000 rows from 50 balanced firms were analysed; no data issues were detected.","results_keys":["n_analysed","n_clusters","n_input_rows","data_issues"],"status":"supported","caveat":""}6]7