(513138} Suppose we have data in pairs (59,-, gig} for i = 1} 2, . . . ,30. Conditional on xi, Y; is Bernoulli with success probability exp(g '1' 531551;} i=Pi2=1 =. 3\" ( |$)1+BXP(30+51$=') For this question, you'll be asked to compute the maximum likelihood estimate of El : (g, 31]? Note that the log-likelihood is 30 new) = 2 [ya- Inga) + (1 ya) logo pa]- i:1 The data are given below: 1: = c(0.02, -0.48, -1.68, -1.12, 0.87, 0.86, -0.34, 0.19, 0.2, -0.79, -0.T8, -0.08, 0.07, -0.78, -1.45, 1.4, 1.34, 1.1, -0.27, -0.18, 0.48, 0.03, -0.3, 1.81, -2.26, '0.18, 1.15, -0.56, 0.88, '0.49) y CEO, 0, 0, 0, 1, 1, '3', 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, '3', '3', 0, 1, 0, 1, 0, 0, 0, 0, 1, 0) (a) Use the function opt mm to compute ,0, using the initial value (0, 0). Compare your result with the output from the R built-in logistic regression function {glm(. . . , family = ' binomial ' I). (b) Again, using the initial value (0, 0), compute ,3 by running the Newton-Raphson algorithm for 100 iterations. (Note: You'll need to nd the gradient and Hessian of the log-likelihood with respect to ,6.)