Logistic Regression calculator

Fit binary logistic regression models online. Calculate log-odds, odds ratios, confidence intervals, and probabilities.

What it does

Models how predictors relate to the probability of a binary (yes/no) outcome, through the log-odds.

When to use it

Your outcome has exactly two categories (event / no event) and you want how predictors shift its probability, adjusted for other variables.

Worked example

You want to know which customers return a product. The outcome is yes/no — returned or kept — and the predictors might be the price paid, the brand, the delivery time and the postcode. The model gives the odds of a return for each factor, so you can say whether an expensive item is genuinely more likely to come back once brand and delivery are taken into account.

Alternatives

• Ordinal — the outcome has 3+ ordered categories (severity grades, Likert)
• Linear — the outcome is a continuous quantity
• Poisson / Negative Binomial — the outcome is a count of events
• penalized (Firth) logistic — you have few events per predictor, or separation (huge coefficients / non-convergence)

How to read the output

Coefficient (Estimate) — log-odds scale

Shown on the log-odds scale. The app does not convert it to an odds ratio — exponentiate it yourself, exp(b), to get the OR: the multiplicative change in odds per 1-unit increase. 'X changes the odds by b' is wrong until you exponentiate. And an OR is not a risk ratio — for a common outcome it overstates the effect (OR 3 might be RR 1.6); translate to probabilities for a typical case.

z-statistic

The Wald statistic — the GLM analogue of the t used in linear models (asymptotic, no degrees of freedom). It's labelled z, not t, on purpose; don't read it as a t-test.

95% CI

The range compatible with your data. On the odds-ratio scale, excluding 1 (equivalently, the log-odds CI excluding 0) means the direction is determined. A CI spanning 0 (log-odds) / 1 (OR) is undetermined, not evidence of no effect.

Log-Likelihood

A model-fit summary for the logistic fit — higher (closer to zero) means a better fit to the data. It is not an R²: logistic regression has no single agreed 'proportion of variance explained', so don't compare its magnitude to a linear model's R².

Huge coefficients / non-convergence

A sign of separation — a predictor nearly perfectly splits the outcome — which makes standard estimates unreliable. Watch for very large coefficients or a non-convergence note — that is separation, and the raw fit is not usable. Refit with “Penalized (Firth)”, which stays finite under separation and reports profile-likelihood intervals.

How this calculator is validated · Which statistical test should I use?