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.