This second chapter on generalized linear models (GLMs) introduces the reader to Poisson regression, a form of regression that can be used to model categorical counts, such as word frequency data. To understand this form of regression, the reader is introduced to the Poisson distribution and the log link function. A variant of Poisson regression, negative binomial regression, is introduced to deal with cases of “overdispersion” (excess variance). In addition, “exposure variables” are introduced to dealing with situations where counts are observed for unequal exposure times. The chapter concludes with an overview of the GLM framework, discussing the three ingredients to a GLM: (1) the linear predictor, (2) the distribution of the response variable, and (3) a link function linking the linear predictor to the distribution.