Assume that Y count variable having a Poisson() distribution where is unknown and X is a predictor (a continuous variable). (a) (3 points) Fit a Poisson regression model for this data and state the estimated Poisson regression model. (b) (4 points) With usual notation we used in class, test the null hypothesis H0 : = 0 aganist H1 : = 0. Use = 0.05. Use the likelihood ratio test. (c) (3 points) R output provides null and residual deviances for generalized linear models. In this part and the next three parts of this question we will look at how to calculate these values. Without using the values of null and residual deviances given in software out- puts, calculate the maximum likelihood (i.e. the maximum value of l()) under the saturated model. Note 1: Likelihood values are usually very small numbers and so you should give your answer in the form a 10b. Note 2: When calculating likelihood, do not ignore any constants or round o. Use all decimal places given in R outputs. (d) (3 points) Without using the values of null and residual deviances given in soft- ware outputs, calculate the maximum likelihood