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')