Problem 1 60.0 points possible (graded, results hidden) Consider the Poisson regression model Po (exi). Yi = Write z = i=1 xiyi and Ai = exp (oxi). (1) What is the expression for the log likelihood function, L (0)? 20 + 20 - Oz0-exp (A) (2) What is the first and second derivative of $L$, i.e. dL/de and d L/de? L' (0) = i=1 1 xi exp (xi), L" (0) L' (0) n i=1 1 xi exp (oxi), L" (0) = i=1 L' (0) = 1 xi Yi _1 *; exp (), L" (0) = - 1 L'(0) = 1 xi Yi i=1 1 xi exp (oxi), L" (0) = -i1 xi i (3) If n 10 and xi = 3+ 6i/n and z = 1551, what is the maximum likelihood estimator of 0? 0.55 1.99 2.47 3.95 (4) What is the estimated variance of ? 0.00023 0.00045 0.00225 0.17324 (5) What is the p-value obtained for the test H : 0 = 2? (Use the value rounded to two decimal places) 0.005 0.05 0.467 0.510