1[2 {"id":"C1","text":"The unadjusted OLS slope of productivity growth on training hours is negative (about -0.13 pp/hour, 95% CI excluding zero).","results_keys":["naive_estimate","naive_ci_low","naive_ci_high"],"status":"supported","caveat":"Descriptive association; confounded by skill_index."},3 {"id":"C2","text":"Adjusting for pre-programme skill_index, one additional training hour per employee raises next-year productivity growth by about 0.25 pp (95% CI 0.234-0.273), so conclusion = positive_effect.","results_keys":["effect_estimate","effect_se","effect_ci_low","effect_ci_high","conclusion"],"status":"supported","caveat":"Causal only under selection on observables given skill_index, linearity and homogeneity; untestable with these data."},4 {"id":"C3","text":"Skill_index is a strong negative predictor of growth and positively correlated with training, explaining the sign reversal (omitted-variable bias).","results_keys":["skill_index_coefficient","corr_skill_training","naive_estimate","effect_estimate"],"status":"supported","caveat":"OVB identity verified numerically in checks.md."},5 {"id":"C4","text":"The adjusted model fits much better than the baseline (RMSE 1.98 vs 3.86 pp).","results_keys":["model_metric","baseline_metric","adjusted_r2","naive_r2"],"status":"supported","caveat":"In-sample fit; better fit does not establish causality."},6 {"id":"C5","text":"The main estimate is robust to including the 12 negative-hours rows, to adding skill squared, and shows no evidence of heterogeneity by skill.","results_keys":["sensitivity_incl_negative_hours_estimate","sensitivity_skill_sq_estimate","sensitivity_interaction_term","sensitivity_interaction_term_p"],"status":"supported","caveat":"Only these specifications were checked; non-linearity in hours not tested."}7]8