Glossary

Logistic Regression

Logistic regression is a generalised linear model used to predict a binary outcome from one or more predictor variables. It estimates the log-odds of the outcome using a linear combination of predictors, then transforms these log-odds into probabilities via the logistic (sigmo...

Definition

Logistic regression is a generalised linear model used to predict a binary outcome from one or more predictor variables. It estimates the log-odds of the outcome using a linear combination of predictors, then transforms these log-odds into probabilities via the logistic (sigmoid) function. The resulting odds ratios quantify how each predictor influences the likelihood of the outcome.

Why It Matters

Many research questions involve dichotomous outcomes: disease presence or absence, pass or fail, purchase or no purchase. Ordinary linear regression is inappropriate here because it can predict probabilities outside the [0, 1] range. Logistic regression provides a principled alternative that respects the binary nature of the data and produces interpretable odds ratios. It is the standard tool in epidemiology, credit scoring, and clinical prediction.

Example

A hospital develops a model to predict whether a patient will be readmitted within 30 days of discharge. Using logistic regression with age, number of comorbidities, and length of stay as predictors, the model yields an odds ratio of 2.3 for each additional comorbidity. This means that, holding other factors constant, each extra condition roughly doubles the odds of readmission, enabling clinicians to target high-risk patients for follow-up care.

Related Terms

Software Notes

  • SPSS: Analyze > Regression > Binary Logistic. Move the binary outcome to the Dependent box and predictors to the Covariates box. Check Options > CI for exp(B) for odds-ratio confidence intervals.
  • R: glm(y ~ x1 + x2, family = binomial(link = "logit"), data = df). summary(model) returns coefficients; exp(coef(model)) converts them to odds ratios. predict(model, type = "response") gives predicted probabilities.
  • Stata: logit y x1 x2 for log-odds coefficients; ologit for ordinal outcomes. or option displays odds ratios directly. margins, dydx(x1) computes average marginal effects.