Solution

Just change the model creation line to

model = LogisticRegression(C=100000, fit_intercept=False)

Analysis of the problem

By default, sklearn solves regularized LogisticRegression, with fitting strength C=1 (small C-big regularization, big C-small regularization).

This class implements regularized logistic regression using the liblinear library, newton-cg and lbfgs solvers. It can handle both dense and sparse input. Use C-ordered arrays or CSR matrices containing 64-bit floats for optimal performance; any other input format will be converted (and copied).

Thus to obtain their model you should fit

model = LogisticRegression(C=1000000)

which gives

Intercept -2.038853 # this is actually half the intercept
study_hrs  1.504643 # this is correct

Furthermore the problem also lies in the way you work with data in patsy, see the simplified, correct example

import numpy as np
from sklearn.linear_model import LogisticRegression

X = [0.5,0.75,1.0,1.25,1.5,1.75,1.75,2.0,2.25,2.5,2.75,3.0,3.25,
3.5,4.0,4.25,4.5,4.75,5.0,5.5]
y = [0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1]

X = np.array([[x] for x in X])
y = np.ravel(y)

model = LogisticRegression(C=1000000.)
model = model.fit(X,y)

print('coef', model.coef_)
print('intercept', model.intercept_)

gives

coef [[ 1.50464059]]
intercept [-4.07769916]

What is the problem exactly? When you do dmatrices it by default embeds your input data with a column of ones (biases)

X = [0.5,0.75,1.0,1.25,1.5,1.75,1.75,2.0,2.25,2.5,2.75,3.0,3.25,
3.5,4.0,4.25,4.5,4.75,5.0,5.5]
y = [0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1]

zipped = list(zip(X,y))
df = pd.DataFrame(zipped,columns = ['study_hrs','p_or_f'])

y, X = dmatrices('p_or_f ~ study_hrs',
                  df, return_type="dataframe")

print(X)

which leads to

    Intercept  study_hrs
0           1       0.50
1           1       0.75
2           1       1.00
3           1       1.25
4           1       1.50
5           1       1.75
6           1       1.75
7           1       2.00
8           1       2.25
9           1       2.50
10          1       2.75
11          1       3.00
12          1       3.25
13          1       3.50
14          1       4.00
15          1       4.25
16          1       4.50
17          1       4.75
18          1       5.00
19          1       5.50

and this is why the resulting bias is just a half of the true one - scikit learns also added a column of ones... so you now have two biases, thus optimal solution is to give each of them half of the weight which would be given to a single one.

So what you can do?

• do not use patsy in such a way
• forbid patsy to add a bias
• tell sklearn not to add bias

.

import numpy as np
import pandas as pd
from patsy import dmatrices
from sklearn.linear_model import LogisticRegression

X = [0.5,0.75,1.0,1.25,1.5,1.75,1.75,2.0,2.25,2.5,2.75,3.0,3.25,
3.5,4.0,4.25,4.5,4.75,5.0,5.5]
y = [0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1]

zipped = list(zip(X,y))
df = pd.DataFrame(zipped,columns = ['study_hrs','p_or_f'])

y, X = dmatrices('p_or_f ~ study_hrs',
                  df, return_type="dataframe")

y = np.ravel(y)

model = LogisticRegression(C=100000, fit_intercept=False)
model = model.fit(X,y)
print(pd.DataFrame(np.transpose(model.coef_),X.columns))

gives

Intercept -4.077571
study_hrs  1.504597

as desired