import wooldridge as woo
import numpy as np

ceosal1 = woo.dataWoo('ceosal1')
x = ceosal1['roe']
y = ceosal1['salary']

# ingredients to the OLS formulas:
cov_xy = np.cov(x, y)[1, 0]  # access 2. row and 1. column of covariance matrix
var_x = np.var(x, ddof=1)
x_bar = np.mean(x)
y_bar = np.mean(y)

# manual calculation of OLS coefficients:
b1 = cov_xy / var_x
b0 = y_bar - b1 * x_bar
print(f'b1: {b1}\n')
print(f'b0: {b0}\n')