import wooldridge as woo
import numpy as np
import statsmodels.formula.api as smf

wage1 = woo.dataWoo('wage1')
reg = smf.ols(formula='wage ~ educ', data=wage1)
results = reg.fit()

# obtain coefficients, predicted values and residuals:
b = results.params
wage_hat = results.fittedvalues
u_hat = results.resid

# confirm property (1):
u_hat_mean = np.mean(u_hat)
print(f'u_hat_mean: {u_hat_mean}\n')

# confirm property (2):
educ_u_cov = np.cov(wage1['educ'], u_hat)[1, 0]
print(f'educ_u_cov: {educ_u_cov}\n')

# confirm property (3):
educ_mean = np.mean(wage1['educ'])
wage_pred = b[0] + b[1] * educ_mean
print(f'wage_pred: {wage_pred}\n')

wage_mean = np.mean(wage1['wage'])
print(f'wage_mean: {wage_mean}\n')