If the truth is non-linearity, regression will make inappropriate predictions, but at least regression will have a chance to detect the non-linearity. The command differs from my code in that it adds the standardized coefficients (beta coefficients) to the regression model. The first entries of the score vector are The -th entry of the score vector is The Hessian, that is, the matrix of second derivatives, can be written as a block matrix Let us compute the blocks: and Finally, Therefore, the Hessian is By the information equality, we have that But and, by the Law of Iterated Expectations, Thus, As a consequence, the asymptotic covariance matrix is Note that if the variable takes on values in (a,b) (with a
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