1[2 {"id":"C1","text":"The pooled OLS slope of y on x is 0.805 (intercept 1.444), estimated on 2000 observations from 50 firms.","results_keys":["beta_hat","alpha_hat","n_analysed","n_clusters"],"status":"supported","caveat":"Linear-projection association, not causal or within-firm."},3 {"id":"C2","text":"The firm-clustered (CR1) SE of the slope is 0.073 and the 95% CI using t(49) is [0.658, 0.952], which excludes zero.","results_keys":["se_cluster","beta_ci_low","beta_ci_high","t_crit_cluster","ci_df"],"status":"supported","caveat":"Relies on asymptotics in the number of clusters (G=50)."},4 {"id":"C3","text":"The conventional OLS SE (0.024) understates uncertainty by a factor of about 3 relative to the clustered SE.","results_keys":["se_ols","se_cluster","se_ratio_cluster_over_ols","baseline_ci_low_ols","baseline_ci_high_ols"],"status":"supported","caveat":"Ratio is specific to this sample's within-firm correlation of x and residuals."},5 {"id":"C4","text":"No data issues were found and no rows were excluded.","results_keys":["data_issues","n_input_rows","n_analysed"],"status":"supported","caveat":"Checks covered missing, non-finite and duplicate rows only."}6]7