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Why does logistic/poisson regression in R give z-values while linear regression gives t-values in the summary output? In general, z-test is used when the population variance is known, but I am finding it difficult to translate this to the (generalized) linear model context.

I saw somewhere (as well from the comment below) that the reason is: the dispersion parameter for the linear model is $\sigma^2$ while the dispersion parameter is 1 for the logistic/poisson regression. If this is so, I would like to understand more mathematically why the value of this dispersion parameter leads to using z-values or t-values.

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  • $\begingroup$ They're both approximations. They will often be closer to each other than either will be to the thing they're approximating. I think in R, with glm it tends to use t for choices of family where the dispersion parameter is estimated and z when the dispersion parameter is fixed, though perhaps it also depends on what arguments you use. $\endgroup$
    – Glen_b
    Commented Jul 29, 2023 at 4:01
  • $\begingroup$ Thanks for the input, I just updated the question to include that $\endgroup$
    – user344849
    Commented Jul 29, 2023 at 21:30

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