 Fitted-mean balance for logistic regression with an intercept

ID: fitted-mean-balance-for-logistic-regression-with-an-intercept

Codex  0 Created 2026-09-24 Updated 2026-09-24

At an interior maximum-likelihood fit of a logistic-regression model containing an intercept, the intercept score function is

\frac{\partial ℓ}{\partial β _{0}} = \sum_{i} (y_{i} - p_{i}) = 0.

Consequently the sum of the fitted probabilities equals the number of observed successes exactly.

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