Logistic Regression Cheat Sheet

A cheat sheet for logistic regression covering scikit-learn usage, the sigmoid function, log loss, multiclass classification, and coefficient interpretation.

1 PageBeginnerMar 8, 2026

Fitting with scikit-learn

Train a binary classifier and evaluate it.

python

from sklearn.linear_model import LogisticRegressionfrom sklearn.metrics import classification_report, roc_auc_scoremodel = LogisticRegression(C=1.0, penalty='l2', max_iter=1000)model.fit(X_train, y_train)y_pred = model.predict(X_test)y_proba = model.predict_proba(X_test)[:, 1]print(classification_report(y_test, y_pred))print('AUC:', roc_auc_score(y_test, y_proba))

Sigmoid & Log Loss

The math behind the prediction and objective function.

python

import numpy as npdef sigmoid(z):    return 1 / (1 + np.exp(-z))# Binary cross-entropy (log loss)def log_loss(y_true, y_pred):    eps = 1e-15    y_pred = np.clip(y_pred, eps, 1 - eps)    return -np.mean(y_true * np.log(y_pred) + (1 - y_true) * np.log(1 - y_pred))

Multiclass Classification

Extend logistic regression beyond two classes.

python

model = LogisticRegression(multi_class='multinomial', solver='lbfgs')model.fit(X_train, y_train)   # softmax generalizes sigmoid to K classes

Key Concepts

Core theory behind logistic regression.

Sigmoid function- Maps any real value into (0, 1), interpreted as the probability of the positive class
Decision boundary- Threshold (default 0.5) on predicted probability used to assign the final class label
Log loss (cross-entropy)- Convex loss function minimized during training via gradient-based optimization
Odds ratio- exp(coefficient) gives the multiplicative change in odds per one-unit increase in a feature
Regularization strength (C)- Inverse of regularization strength in scikit-learn; smaller C means stronger regularization
Class imbalance- Use class_weight='balanced' or resampling techniques when classes are heavily skewed

Pro Tip

Don't read raw logistic regression coefficients as changes in probability — exponentiate them to get odds ratios, since each coefficient describes a multiplicative effect on the odds of the positive class, not a direct additive effect on probability.

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