 Generalized linear model

A generalized linear model takes independent responses from an exponential dispersion family and relates their means to linear predictors by $g({\mu }_i)=x_i^T\beta$. The response distribution, systematic component, link, dispersion, and known observation weights together specify the model.

A Generalized Linear Model (GLM) is a flexible framework for modeling a wide variety of response variables and is an extension of traditional linear regression. It generalizes linear regression to allow for response variables that have error distribution models other than a normal distribution. Here are the key components of a GLM: 1. **Random Component**: This refers to the probability distribution of the response variable \(Y\).