In this question you will program and test routines for comp

In this question you will program and test routines for computing MLEs of the parameters of the logistic regression model. The logistic regression model is a Generalized Linear Model described by the following process for i = 1,... n and x_i is a column vector with p covariates. The first coordinate of x_i is usually reserved for the intercept term and set to 1. For GLMs with the canonical link, the scoring algorithm adopts a particularly pleasant form called \"iteratively re-weighted least squares\". We start with a guess for the parameters beta^(0). Then we move from step k to step k + 1 following the rule for V_i^(k) = b\" (theta_i^(k)), mu_i^(k) = b\' (theta_i^(k)), =theta_i^(k) = x_i^T beta^(k) for I = 1, ... n. We keep iterating until convergence. Show that the Bernoulli distribution is an exponential family of the form Identify the natural parameter theta and the functions a(),6(), and c(). Use them to compute E[y] = b\'(theta) and V[y] = b\"(theta)a(Psi). Show that the canonical link is the logit function.

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