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\mu it's the conditional mean, not the mean |
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In a generalized linear model (GLM), each outcome '''Y''' of the [[dependent variable]]s is assumed to be generated from a particular [[probability distribution|distribution]] in an [[exponential family]], a large class of [[probability distributions]] that includes the [[normal distribution|normal]], [[binomial distribution|binomial]], [[poisson distribution|Poisson]] and [[gamma distribution|gamma]] distributions, among others. The conditional mean '''''μ''''' of the distribution depends on the independent variables '''X''' through:
: <math>\operatorname{E}(\mathbf{Y}\mid\mathbf{X}) = \boldsymbol{\mu} = g^{-1}(\mathbf{X}\boldsymbol{\beta}), </math>
where E('''Y''' | '''X''') is the [[expected value]] of '''Y''' [[conditional expectation|conditional]] on '''X'''; '''X''β''''' is the ''linear predictor'', a linear combination of unknown parameters '''''β'''''; ''g'' is the link function.
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