# Generalized linear model

The website statsoft.com offers this explanation of the **generalized linear model**:

"The Generalized Linear Model (GLZ) is a generalization of the general linear model (see, e.g., the General Linear Models, Multiple Regression, and ANOVA/MANOVA topics). In its simplest form, a linear model specifies the (linear) relationship between a dependent (or response) variable Y, and a set of predictor variables, the X's, so that

Y = b_{0} + b_{1}X_{1} + b_{2}X_{2} + ... + b_{k}X_{k}

In this equation b_{0} is the regression coefficient for the intercept and the b_{i} values are the regression coefficients (for variables 1 through k) computed from the data."^{[1]}

Whereas in classical linear models the variable Y is assumed to follow a normal distribution, generalized linear models consider more general distributions, such as a Poisson or a multinomial distribution, and are therefore applicable to a wider field of problems.