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What is the relation between the coefficients of linear models and the Jacobian matrix? Should the matrix of coefficients of a (generalized) linear model be thought about as the Jacobian?

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Because $\hat{\eta} = Ax$, the partial derivative of $\hat{\eta}$ on $x$ can be described by the Jacobian matrix $J = \nabla_x\hat{\eta} = A$, which is the matrix of coefficients.

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