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  "body": "\n## Summary\n\nA generalized linear model relates the mean of a response to a linear combination of regressors through a link function.\nThe response distribution is taken from an [[exponential family|EP9VPZ0S6G]].\nIt unifies [[linear regression|41FVC4P5JB]], [[logistic regression|JN1PJ5AJJS]], [[Poisson regression|STHTW16717]] and the [[probit model|XCR3V8SJ01]] in one framework, with one fitting method and one theory of inference.\nThe framework was introduced by John Nelder and Robert Wedderburn in 1972.\nIts coefficients are estimated by [[maximum likelihood|0FREPFKNS7]], usually with iteratively reweighted least squares.\n\n## Explanations\n\n### L1 human\n\nOrdinary regression predicts a number that can be any real value, with normal noise.\nMany responses are not like that: a yes/no answer, a count, a waiting time.\nA generalized linear model keeps the simple linear formula $x^T \\beta$, but passes it through a link function that fits the range of the mean.\nIt also uses a noise distribution that suits the data.\nFor counts, for example, the logarithm of the mean is linear in the regressors and the counts are Poisson.\n",
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