Consider a sample of j = 1,...,r independent binomials yj Bin(Nj , pj ), each with

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Consider a sample of j = 1,...,r independent binomials yj ∼ Bin(Nj , pj ), each with a covariate xj . Suppose that for some cumulative distribution function F(·), pj = F(xj ).

Show that for some transformation zj = g(xj ) and parameters α and β, this logistic regression model holds:

log  pj 1 − pj



= α + βzj .

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