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# OLS
OLS = LinearRegression()
OLS.fit(X, y.ravel())

# Plot
plt.figure(figsize = (10, 6))
plt.scatter(
    X,
    y,
    c = 'teal'

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# Plot
plt.figure(figsize = (10, 6))
plt.scatter(
    X,
    y,
    c = 'teal'
)
plt.title('Data')
plt.show()

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# Set auto reload
%reload_ext autoreload
%autoreload 2

# Import libraries
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

from sklearn.datasets import make_regression

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# HAC Result
# 3
lags = None
print(f'Number of lags: {lags}')

HAC = newResult.get_robustcov_results(
    cov_type = 'HAC',
    maxlags = lags
)

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# HAC Result
# 2
lags = int(df.shape[0] ** (1 / 4))
print(f'Number of lags: {lags}')

HAC = newResult.get_robustcov_results(
    cov_type = 'HAC',
    maxlags = lags
)

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# HAC Result
# 1
lags = int(4 * (df.shape[0] / 100) ** (2 / 9))
print(f'Number of lags: {lags}')

HAC = newResult.get_robustcov_results(
    cov_type = 'HAC',
    maxlags = lags
)

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# HAC Adjustment
newModel = smf.ols(
    'logitODR ~ 1 + GDP_C_lg12 + MPI_C_lg12',
    data = df
)
newResult = newModel.fit()

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# Select variables for linear regression model
X = sm.add_constant(df[['GDP_C_lg12', 'MPI_C_lg12']]) #Add intercept
y = df['logitODR']

# Linear regression model
model = sm.OLS(y, X)
result = model.fit()
print(result.summary())

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# Set auto reload
%reload_ext autoreload
%autoreload 2

# Import libraries
import warnings
import pandas as pd
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf

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# Average spending price per period
df['TotalSale'] = df['Price'] * df['Quantity'] #Calculation total sale
dfPrice = df.groupby(
    ['cohortMonth', 'cohortIndex'],
    as_index = False
)['TotalSale'].mean()

dfPrice = pd.pivot_table(
    dfPrice,
    values = 'TotalSale',