1[2 {"id":"C1","text":"The unadjusted OLS slope of productivity growth on training hours is negative, about -0.135 pp/hour with 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 0.234-0.271), 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 with skill_index as the sole confounder and a linear homogeneous effect."},4 {"id":"C3","text":"The sign reversal is explained by confounding: skill is positively correlated with hours and negatively related to growth.","results_keys":["skill_index_coefficient","corr_skill_hours","naive_estimate","effect_estimate"],"status":"supported","caveat":"Omitted-variable identity verified numerically in checks.md."},5 {"id":"C4","text":"Adding skill_index roughly halves residual RMSE (3.86 to 1.98 pp).","results_keys":["baseline_metric","model_metric"],"status":"supported","caveat":"In-sample fit."},6 {"id":"C5","text":"The estimate is robust to excluding the 12 negative-hours rows and to a quadratic skill term.","results_keys":["sens_excl_negative_hours_estimate","sens_excl_negative_hours_n","sens_skill_quadratic_estimate","sens_skill_quadratic_sq_coef_pvalue","data_issues"],"status":"supported","caveat":"Does not address unobserved confounding."}7]8