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

attend = woo.dataWoo('attend')
n = attend.shape[0]

reg = smf.ols(formula='stndfnl ~ atndrte*priGPA + ACT + I(priGPA**2) + I(ACT**2)',
 data=attend)
results = reg.fit()

# print regression table:
table = pd.DataFrame({'b': round(results.params, 4),
 'se': round(results.bse, 4),
 't': round(results.tvalues, 4),
 'pval': round(results.pvalues, 4)})
print(f'table: \n{table}\n')

# estimate for partial effect at priGPA=2.59:
b = results.params
partial_effect = b['atndrte'] + 2.59 * b['atndrte:priGPA']
print(f'partial_effect: {partial_effect}\n')

# F test for partial effect at priGPA=2.59:
hypotheses = 'atndrte + 2.59 * atndrte:priGPA = 0'
ftest = results.f_test(hypotheses)
fstat = ftest.statistic[0][0]
fpval = ftest.pvalue

print(f'fstat: {fstat}\n')
print(f'fpval: {fpval}\n')