1[2 {"id":"C1","text":"The unadjusted OLS slope of productivity growth on training hours is negative (about -0.13 pp/hour) with a 95% CI excluding zero.","results_keys":["naive_estimate","naive_ci_low","naive_ci_high"],"status":"supported","caveat":"Descriptive association only; confounded by skill."},3 {"id":"C2","text":"Adjusting for pre-programme skill_index, one extra training hour per employee raises next-year productivity growth by about 0.25 pp (95% 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 only under selection on observables given a single covariate and a linear homogeneous effect."},4 {"id":"C3","text":"The sign reversal reflects confounding: skill is positively correlated with training and strongly negatively associated with growth.","results_keys":["skill_index_coefficient","corr_skill_training","naive_estimate","effect_estimate"],"status":"supported","caveat":"Consistent with the omitted-variable-bias formula; other unobserved confounders cannot be excluded."},5 {"id":"C4","text":"The adjusted estimate is robust to excluding/including the 12 negative-hours rows, adding skill squared, and the SE type.","results_keys":["sensitivity_full_sample_estimate","sensitivity_quadratic_skill_estimate","sensitivity_conventional_se","effect_se"],"status":"supported","caveat":"Robustness to these specification choices only, not to unobserved confounding."},6 {"id":"C5","text":"The adjusted model fits much better than the unadjusted model (residual RMSE 1.98 vs 3.86 pp).","results_keys":["model_metric","baseline_metric"],"status":"supported","caveat":"In-sample fit; better fit does not establish causal validity."}7]8