The insight turned out to be worth more than the model

🏢 The situation

Emergency sync. Max shows a chart: subscribers of the fintech product are leaving; monthly churn is 8%.

"Retaining a customer is 5× cheaper than acquiring a new one. The retention team has a budget for calls and bonuses, but we can't call all 200,000 customers. Give me a list: who will leave within the next 30 days."

Lena translates it into ML language:

"Binary classification. Target: did the customer leave within 30 days (we have historical labels). Anya assembled the features: activity, payments, support tickets, tenure. Start with logistic regression — and understand why its output is a probability. Retention needs probabilities to rank whom to call first."

🎯 Your task

1. Understand how classification differs from regression and how logistic regression works.
2. Train a churn model and obtain probabilities.
3. Deliver a ranked customer list to the business.

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📚 Theory

Why not linear regression?

The target is 0 or 1. Linear regression outputs arbitrary numbers (−0.3, 1.7), which cannot be read as probabilities. The solution is to wrap the linear combination in a sigmoid:

The sigmoid squeezes any number into (0, 1) → the output reads as the probability of class 1: P(churn | x).

The loss function — log loss

MSE works poorly for classification (a non-convex surface). We use the logistic loss (cross-entropy): it heavily punishes confident mistakes — predicting 0.99 "stays" when the customer left → a huge penalty.

The decision threshold

The model outputs a probability; the "call / don't call" decision appears after choosing a threshold:

• 0.5 is the default, but it is almost never optimal for the business;
• retention can call only the top 5000 customers → take the top N by probability, no threshold needed at all;
• choosing a threshold is a business decision about the balance of errors (details in module 6).

Interpreting the coefficients

Logistic regression coefficients act on the log-odds: a positive feature weight increases the churn probability. exp(w) — how much the odds multiply per +1 of the feature. For the business: "every negative support ticket multiplies the odds of leaving by 1.6".

Regularization

With many features the model can overfit. L2 (Ridge) — pushes weights toward zero; L1 (Lasso) — zeroes out weak features (built-in selection). In sklearn the C parameter is the inverse regularization strength: smaller C → stronger regularization.

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