Given a set of independent variables, discriminant analysis attempts to find linear combinations of those variables that best separate the groups of cases. These combinations are called discriminant functions, and have the following form.

F_ik = D_0k + D_1k X_i1 + ... + D_pk X_ip

F_ik is the value of the ith case of the kth function

X_ij is the value of the ith case of the jth predictor

D_jk is the value of the coefficient of the jth predictor of the kth function

The number of functions equals min(#groups-1, #predictors).

The procedure automatically chooses a first function that will separate the groups as much as possible. It then chooses a second function that provides as much more separation as possible, and is uncorrelated with the first function, continuining in this way until reaching the maximum number of functions.

The discriminant model has the following assumptions:

The predictors are not highly correlated with each other.

The mean and variance of a given predictor are not correlated.

The correlation between two predictors is constant across groups.

The values of each predictor have a normal distribution.