Logistic Regression

Logistic Regression models a binary outcome (0/1) against one or more covariates, producing odds ratios for each predictor. The workhorse of clinical research for any yes/no outcome.

Step 1 — Provide your data

  • Outcome — binary (0 or 1)
  • Covariates — numeric or categorical predictors

Supports Excel Import (with ColumnSelector and CategoryMapper), Sample Data Selector, and Manual Entry.

Step 2 — Choose reference categories

For categorical covariates, pick the baseline. ORs are reported relative to this reference.

Step 3 — Results

Covariate table:

  • Coefficient (beta), OR = exp(beta), 95% CI, SE, Z-score, p-value

Model Fit:

  • Log-likelihood, Null/Residual deviance
  • Chi-square (LR test), df, overall p-value
  • McFadden's pseudo R-squared
  • Nagelkerke's R-squared
  • AIC, BIC

Hosmer-Lemeshow test — goodness-of-fit (10 deciles, df=8)

Predictive accuracy — classification at p=0.5 cut-off

AUC with 95% CI

Visualisations:

  • Odds Ratio Forest Plot
  • Predicted probability distributions

A UniversalChatBot is available for discussion.

Statistical methods used

Model

log(p/(1-p)) = beta0 + beta1*X1 + ... + betap*Xp

Estimation — Newton-Raphson/IRLS

  • Max iterations: 50
  • Convergence: max |score| < 1e-8
  • Ridge regularisation (1e-8) for stability

Odds Ratios with 95% CI (Wald)

OR = exp(beta), CI: exp(beta +/- 1.96 * SE)

Overall model — Likelihood Ratio Test

chi2 = 2 * (logL_full - logL_null) with df = p.

Pseudo R-squared

  • McFadden: 1 - (logL_full / logL_null)
  • Nagelkerke: Cox-Snell scaled to max 1

Hosmer-Lemeshow

10-decile goodness-of-fit. p > 0.05 indicates good calibration.

Pre-flight checks: minimum 10 observations, minimum 5 events and 5 non-events, perfect-separation detection.