# Contract (P0)

Question: In the fixed-design model y_i = 1 + 0.5 x_i + sigma_i eps_i (n=30, x and sigma fixed from data/design.csv, eps iid N(0,1)), do nominal 95% OLS t-intervals for the slope achieve 95% coverage?

Estimands:

• (a) coverage_conventional: P(|beta_hat - 0.5| <= t_{.975}(28) se_conv), se_conv from s^2=RSS/(n-2). MC, R=2000.
• (b) coverage_hc1: same with se_HC1 = sqrt(n/(n-2) * sum(w_i^2 e_i^2)), w_i=(x_i-xbar)/Sxx. MC.
• (c) sd_beta_exact = sqrt(sum((x_i-xbar)^2 sigma_i^2))/Sxx (analytical; exact since design fixed and errors normal).
• (d) mean_se_conventional: MC mean of se_conv.
• Also sd_beta_mc (ddof=1), conventional_ci_undercovers = cov_conv < 0.95 - 3sqrt(0.950.05/2000). Assumptions: model as stated; coverage meaningful as frequentist long-run probability under repeated eps draws.

Outputs: out/results.json (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; plus protocol state files and out/exclusions.csv.

Information rules: Only data/design.csv; do not redraw x or sigma; constants from TASK.md. Binomial MC SE uses p=0.95 (nominal) per "binomial standard error at R=2000"; documented choice.

Invalidity: design file not 30 rows / missing or non-positive sigma; R != 2000; unseeded simulation.