The Logistic Regression Calculator estimates the regression coefficients for a binary dependent variable (0 or 1) using gradient descent optimization. It models the probability of an event occurring as P(Y=1) = 1 / [1 + e^-(B0 + B1X1 + B2X2 + …)], where B0, B1, B2, … are coefficients. This tool is useful in predicting outcomes that have two possible states, such as success/failure or yes/no decisions.