Behavioral Research: Statistical Methods

Linear regression assumes Y is continuous and roughly Normal. When Y is **binary** (admitted/rejected, saved/scored, recovered/not), OLS shatters: predictions leak outside [0, 1]; residuals can take only two values; variance is largest at p = 0.5 and smallest at the extremes; the true relationship between predictor and probability is **S-shaped**, not linear. The fix isn't to abandon regression — it's to make it model the *log-odds* of the outcome instead of the outcome directly. That's logistic regression. And logistic regression is just one member of a larger family — **Generalised Linear Models (GLMs)** — that handles any non-Normal Y by combining three parts: a distribution, a linear predictor, and a *link function* that bridges them.