possible outcome, rather than simply making a single optimal prediction, is one means of alleviating this issue. Setup The basic setup is the same as in logistic regression, the only difference being that the dependent variables are categorical rather than binary, i.e. there are K possible outcomes rather than just two. The following description is somewhat shortened; for more details, consult the logistic regression article. Data points Specifically, it is assumed that we have a series of N observed data points. Each data point i (ranging from 1 to N) consists of a set of M explanatory variables x1,i ... xM,i (aka independent variables, predictor variables, features, etc.), and an associated categorical outcome Yi (aka dependent variable, response variable), which can take on one of K possible values. These possible values represent logically separate categories (e.g. different political parties, blood types, etc.), and are often described mathematically by arbitrarily assigning each a number from 1 to K. The explanatory variables and outcome represent observed properties of the data points, and are often thought of as originating in the observations of N "experiments" — although an "experiment" may consist in nothing more than gathering data. The goal of multinomial logistic regression is to construct a model that explains the relationship between the explanatory variables and the outcome, so that the outcome of a new "experiment" can be correctly predicted for a new data point for which the explanatory variables, but not the outcome, are available. In the process, the model attempts to explain the relative effect of differing explanatory variables on the outcome. Some examples: The observed outcomes are different variants of a disease such as hepatitis (possibly including "no disease" and/or other related diseases) in a set of patients, and the explanatory variables might be characteristics of the patients thought to be pertinent (sex, race, age, blood pressure, outcomes of various liver-function tests, etc.). The goal is then to predict which disease is causing the observed liver-related symptoms in a new patient. The observed outcomes are the party chosen by a set of people in an election, and the explanatory variables are the demographic characteristics of each person (e.g. sex, race, age, income, etc.). The goal is then to predict the likely vote of a new voter with given characteristics. Linear predictor As in other forms of linear regression, multinomial logistic regression uses a linear predictor function to predict the