Logistic Regression

Predicting yes-or-no outcomes with a linear model and a cutoff.

Also known as: logistic regression, logit model, binary classifier

Logistic regression predicts yes-or-no outcomes — churn or stay, convert or not, fraud or legitimate — by fitting a linear combination of inputs and squashing it into a probability between 0 and 1. Despite the name, it is a classifier, not a regression: the output is a probability, and a cutoff turns it into a decision.

score = w1·tenure + w2·usage + w3·tickets + …
P(churn) = 1 / (1 + e^-score)     →  predict "churn" if P > cutoff

Its strength is transparency: each coefficient says how much its input moves the log-odds, so the model explains itself to stakeholders in a way fancier models cannot. That makes it the default first model for binary business outcomes — fast to build, easy to defend, often surprisingly close to complex alternatives.

The classic mistakes:

Reading coefficients as causal effects. A positive coefficient on “contacted support” does not mean support causes churn — struggling users both contact support and leave. Coefficients describe association in the fitted data (see correlation vs causation).
Default 0.5 cutoff. The threshold should reflect the costs of each error type, not mathematical convenience. A fraud model and a marketing model need different cutoffs from identical scores.
Imbalanced classes judged by accuracy. Predicting “no churn” for everyone scores well and helps nobody. Judge with precision, recall or profit-weighted measures (see classification vs regression).
Correlated inputs left in. Highly related features split credit arbitrarily and inflate standard errors, making coefficients unstable and uninterpretable. Check correlations and simplify.
No validation. A model that fits history perfectly and fails next month is overfit. Hold out recent data and validate there (see train-test split).

When to go further: interactions and non-linearities the linear form cannot bend to, or text and image inputs — then gradient boosting or richer models, with logistic kept as the explainable baseline every complex model must beat.