Build a logistic regression model and explain what its output means

When the dependent variable is binary, linear regression can predict probabilities below 0 or above 1. Logistic regression instead models the log odds: ln[p ÷ (1 − p)] = b0 + b1X1 + … + bkXk, estimated by maximum likelihood. To get a probability, compute the log odds and then p = 1 ÷ (1 + e raised to minus the log odds). A slope is the change in log odds for a one-unit change in the variable, so e raised to the slope is the factor by which the odds are multiplied. Joint significance uses the likelihood ratio test, −2 × (restricted log-likelihood − unrestricted log-likelihood), against a chi-square. A common slip is to confuse odds with probability.