How do you interpret the coefficients of a logistic regression model?

Example Answer

In a binary logistic regression, the model is log(p/(1 − p)) = β₀ + β₁x₁ + …, where p is the probability of the outcome coded as one. For a predictor that enters only as a linear main effect, a one-unit increase changes the fitted log odds by its coefficient while the other predictors stay fixed. Exponentiating that coefficient gives the conditional odds ratio.

For example, a coefficient of log(2), about 0.693, means twice the odds. If the starting probability is 20%, the odds are 0.2/0.8 = 0.25. Doubling them gives odds of 0.5 and a new probability of 0.5/1.5, or one-third. It does not mean doubling the probability or adding 69.3 percentage points.

I would check the units and reference category, report uncertainty, and inspect interactions or nonlinear terms. With an x-by-z interaction, x's one-unit log-odds change is βx + βxz × z, so a single main-effect coefficient is incomplete. These are conditional associations unless the study and identifying assumptions support a causal interpretation.

Follow-up to prepare for

For a k-unit change in a linear main-effect predictor, the odds ratio is exp(kβ). The probability change still depends on the starting probability.