Modeling Binary Outcomes

This logistic regression calculator fits a sigmoid curve to paired (x, y) data where y is 0 or 1. The fitted line is p = 1/(1+e^(−(β₀+β₁x))) — the probability of the positive outcome at every x.

Maximum-Likelihood Fitting

Coefficients are found with iteratively reweighted least squares, which converges to the maximum-likelihood estimate — the parameters under which the observed outcomes are most probable. This is the same fit a statistics package produces.

Interpreting the Model

The odds ratio e^β₁ quantifies how strongly x shifts the odds, the pseudo-R² summarizes overall fit, and the classification accuracy counts how often the fitted probability crosses 50% in the right direction. Use these together to judge the model.