1. [10 marks] Given the i.i.d. responses Y1, ..., Ym, n independent copies of a random variable Y, the goal is to explain how the expected value of Y behaves as a function of the p predictors Ti = (Ci, ...,Dip) , i = 1, ..., n. Assume that Y, follows a Poisson distribution with parameter i. a) What strategy would you use? Give its name. b) What is the connection between ; and the predictor n = ; 3 when using the canonical link g(A)? c) Suppose that B is the MLE and , = g (a7 3). Find the maximized log- likelihood for the model. d) Find the maximized log-likelihood In L( ) for the saturated model (which gives us a standard which to judge the value of the maximized likelihood for a simpler model). Note that when Y, = 0, Y, In Y, is replaced with zero (as its limit as y -+ 0). e) Hence, determine the deviance for the above regression model to measure lack of fit