1[2 {"id":"C1","text":"The unadjusted OLS slope of productivity growth on training hours is negative (-0.132 pp/hour, 95% CI [-0.160,-0.103]).","results_keys":["naive_estimate","naive_ci_low","naive_ci_high"],"status":"supported","caveat":"Association only; confounded by skill_index."},3 {"id":"C2","text":"Adjusting for pre-programme skill_index, one extra training hour raises next-year productivity growth by about 0.254 pp (95% HC1 CI [0.234,0.273]); conclusion positive_effect.","results_keys":["effect_estimate","effect_se","effect_ci_low","effect_ci_high","conclusion"],"status":"supported","caveat":"Causal interpretation requires selection on observables given skill_index alone, linearity and homogeneity; untestable."},4 {"id":"C3","text":"The sign reversal is explained by confounding: skill_index is positively correlated with training and has a strongly negative coefficient on growth (-4.62 pp per unit).","results_keys":["skill_index_coefficient","corr_skill_training","naive_estimate","effect_estimate"],"status":"supported","caveat":"OVB identity verified numerically; does not rule out other confounders."},5 {"id":"C4","text":"The adjusted model fits much better: residual RMSE 1.98 pp vs 3.86 pp unadjusted.","results_keys":["model_metric","baseline_metric"],"status":"supported","caveat":"In-sample fit; not evidence of causal validity."},6 {"id":"C5","text":"The effect estimate is robust to adding skill^2, an hours x skill interaction, and to retaining the 12 negative-hour rows.","results_keys":["robust_quadratic_skill_effect","robust_quadratic_skill_sq_pvalue","robust_interaction_coef","robust_interaction_pvalue","sens_all_rows_effect_estimate"],"status":"supported","caveat":"Only these specific alternatives were checked."},7 {"id":"C6","text":"12 rows with negative training hours were excluded, leaving 1188 of 1200 firms.","results_keys":["n_excluded_negative_hours","n_analysed","n_input_rows"],"status":"supported","caveat":"Origin of negative values unknown."}8]9