Editing Generalized linear model (section)

=== Linear regression ===

A simple, very important example of a generalized linear model (also an example of a general linear model) is [[linear regression]]. In linear regression, the use of the [[least-squares]] estimator is justified by the [[Gauss–Markov theorem]], which does not assume that the distribution is normal.

From the perspective of generalized linear models, however, it is useful to suppose that the distribution function is the normal distribution with constant variance and the link function is the identity, which is the canonical link if the variance is known.  Under these assumptions, the least-squares estimator is obtained as the maximum-likelihood parameter estimate.

For the normal distribution, the generalized linear model has a [[Closed-form expression|closed form]] expression for the maximum-likelihood estimates, which is convenient. Most other GLMs lack [[Closed-form expression|closed form]] estimates.