# Robust Joint Tests
# Module 8 - Robust Joint Tests
# Dataset: MODULE8_ROBUST_SE_DEMO

# Robust Joint Tests
#
# Module 8 notebook lab. This notebook uses original Ceteris Lab teaching data and does not report real empirical findings.

# Learning goal
# Test multiple restrictions with robust covariance.
#
# Dataset: MODULE8_ROBUST_SE_DEMO. Variables: observation_id, outcome, x1, x2, group, error_variance.

# %% Cell 3
import pandas as pd
import statsmodels.api as sm

df = pd.read_csv("/data/module-8/module8_robust_se_demo.csv")
X = sm.add_constant(df[["x1", "x2"]])
model = sm.OLS(df["outcome"], X).fit()
robust = model.get_robustcov_results(cov_type="HC1")
print(robust.f_test("x1 = 0, x2 = 0"))

# Reflection
# Write two sentences: one sentence explaining what the diagnostic or robust result says, and one sentence explaining a limitation or next step.