# Contract (P0)

Question. Do nominal 95% t-intervals for the OLS slope achieve 95% coverage in a fixed-design, n=30, heteroskedastic linear model y = 1 + 0.5x + sigma_i*eps_i (eps iid N(0,1))? Estimands. (a) coverage of b̂ ± t.975(28)·se_conv; (b) coverage of b̂ ± t.975(28)·se_HC1 (HC0 × n/(n−2)); (c) exact SD of b̂ = sqrt(sum w_i^2 sigma_i^2), w_i=(x_i−x̄)/Sxx (analytic); (d) E[se_conv]. (a),(b),(d) by MC, R=2000, fixed seed. Meaningful under: x, sigma fixed (conditioning on design), normal errors, correct mean model. Outputs. out/results.json with keys task_id, coverage_conventional, coverage_hc1, sd_beta_exact, sd_beta_mc, mean_se_conventional, conventional_ci_undercovers, n_replications, n_obs_per_replication, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed; out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues); out/analysis.py; out/claims.json. Undercover rule. true iff coverage_conventional < 0.95 − 3·sqrt(0.95·0.05/2000) (binomial SE evaluated at nominal p, the null hypothesis value; the SE at p̂ is also reported). Information rules. Only data/design.csv; never redraw x or sigma; only eps redrawn. Invalidity. Design file malformed/not 30 rows, non-positive sigma, constant x, wrong R/n, unseeded simulation.