Logistic regression models the relationship between one or more predictors and a binary outcome, an outcome with two categories such as alive or dead, relapsed or not, responded or not. Instead of predicting the outcome directly, it predicts the log odds of the outcome and converts each predictor's effect into an odds ratio. That is why logistic regression is the default tool whenever the thing you are trying to explain is a yes-or-no event rather than a measured quantity.
Why you cannot just use linear regression
When the outcome is binary, ordinary linear regression breaks in concrete ways: it can predict probabilities below zero and above one, and its assumptions about the residuals are violated because a two-value outcome cannot be normally distributed around a line. Logistic regression solves this with the logit link, which transforms a probability bounded between zero and one into a log-odds scale that runs from minus to plus infinity. The model is linear on that log-odds scale, which keeps predictions inside the valid probability range and gives the coefficients a clean interpretation. Choosing logistic over linear is therefore not a stylistic preference; it follows directly from the type of outcome variable you have.
Reading the output: coefficients and odds ratios
A logistic regression coefficient is on the log-odds scale, which is hard to interpret directly, so you exponentiate it to get an odds ratio. The rule of thumb is simple:
- An odds ratio of 1 means the predictor has no association with the outcome.
- An odds ratio above 1 means higher values of the predictor increase the odds of the outcome.
- An odds ratio below 1 means higher values decrease the odds.
For a binary predictor, the odds ratio compares the two groups; for a continuous predictor, it gives the change in odds for a one-unit increase. When you want to sanity-check a model's odds ratio against a simple two-by-two table, our odds ratio calculator gives the unadjusted value and its confidence interval, which is a useful baseline before you trust the adjusted estimate.
Odds ratios are not risk ratios
A persistent source of error is treating the odds ratio as if it were a relative risk. The two diverge as the outcome becomes common: an odds ratio of 2 can correspond to a much smaller increase in actual risk when the outcome is frequent. For rare outcomes the two are close, which is why case-control studies can use the odds ratio as a stand-in for risk, but for common outcomes the gap is real and reporting an odds ratio as though it were a risk overstates the effect. If your audience needs an interpretable risk, our explainer on risk ratios shows when each measure is appropriate.
Univariable, then multivariable
Most analyses move from univariable models, one predictor at a time, to a multivariable logistic regression that includes several predictors together. The multivariable model is what lets you report the effect of an exposure adjusted for confounders, the central goal of most observational analysis. Building it well means deciding in advance which variables to include based on subject knowledge rather than letting an automated stepwise procedure churn through the data, which inflates false findings. A common planning rule is to allow roughly ten outcome events per predictor so the model is not overfit.
The assumptions that actually matter
Logistic regression has fewer assumptions than linear regression, but the ones it has are easy to violate:
- Independence of observations. Clustered or repeated data need a model that accounts for the clustering, not a plain logistic regression.
- Linearity in the logit. Continuous predictors are assumed to have a linear relationship with the log odds; if they do not, the predictor may need transformation or a spline.
- No extreme multicollinearity. Predictors that are near-duplicates inflate standard errors and destabilize the coefficients.
- Adequate events per variable. Too few outcome events for the number of predictors produces unstable, overfit estimates.
Checking these is part of the analysis, not an optional extra, and skipping them is how a published odds ratio turns out to be an artifact.
Variants you will meet
When the outcome has more than two categories, multinomial logistic regression generalizes the model; when the categories are ordered, ordinal logistic regression uses that ordering. When the outcome is a count rather than a binary event, you move to Poisson or negative binomial models instead. Recognizing which member of the family fits your outcome is the same kind of design decision as converting between effect sizes when you pool results: the right tool is dictated by the data, and using the wrong one quietly biases everything downstream.
