1[2 {"id":"C1","text":"The OLS slope of y on x is 0.8051 with intercept 1.4440, estimated on 2000 observations from 50 firms.","results_keys":["beta_hat","alpha_hat","n_analysed","n_clusters"],"status":"supported","caveat":"Descriptive linear projection; not causal."},3 {"id":"C2","text":"The firm-clustered 95% CI for beta is [0.6581, 0.9521] and excludes zero.","results_keys":["beta_ci_low","beta_ci_high","se_cluster","t_crit_cluster_df"],"status":"supported","caveat":"CR1 with t(49) critical value; asymptotic in number of clusters."},4 {"id":"C3","text":"The naive homoskedastic SE (0.0241) understates uncertainty by a factor of about 3 relative to the firm-clustered SE (0.0731).","results_keys":["se_ols","se_cluster","se_ratio_cluster_to_ols"],"status":"supported","caveat":"Ratio depends on within-firm correlation of x and residuals in this sample."},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 exact-duplicate rows."}6]7