Logistic regression

Foundations of Probability in Python

Alexander A. Ramírez M.

CEO @ Synergy Vision

Original data

Hours of study vs score data

Pass or Fail test plot

Where to classify animation plot

Probability calculation with model

Logistic function plot

$$ logistic(t) = logistic(slope*x + intercept) $$

slope parameter making sigmoid function steeper animation

Intercept parameter sigmoid function plot

Probability calculation with logistic model

Logistic model outcome plot

Probability calculation and miss classifications

# Import LogisticRegression
from sklearn.linear_model import LogisticRegression

# sklearn logistic model
model = LogisticRegression(C=1e9)
model.fit(hours_of_study, outcomes)

# Get parameters
beta1 = model.coef_[0][0]
beta0 = model.intercept_[0]

# Print parameters
print(beta1, beta0)

(1.3406531235010786, -15.05906237996095)

hours_of_study_test = [[10]]

outcome = model.predict(hours_of_study_test)
print(outcome)

array([False])

$$ $$

# Put value in an array
value = np.asarray(9).reshape(-1,1)
# Calculate the probability for 9 hours of study
print(model.predict_proba(value)[:,1])

array([0.04773474])

Foundations of Probability in Python