stat questions! Thanks a lot!!!

PART A. Basic Questions Question A.1 [4] Generalized Linear Models (GLM) provide a uniform framework for many commonly used statistical methods for regression analysis. Give one GLM model as an example for the regression models that may be considered in each of the following two settings. (Specify all the three key GLM components in the examples.) I QA.1(i) To study how a count variable Y depends on two numerical variables X , Z and their interaction. I QA.1(ii) To study how a binary variable Y depends on two categorical variables X and Z , where X has two (2) categories and Z has three (3) categories. Question A.2 [4] Table A2 is the 2 x 2 contingency table from a medical study with the case-control design, where a. is a predetermined positive integer. Table A.2 patient case health control Total en er em e 11 12 1 male N21 N22 N2" Total NH 2 a N+2 = a NLJF = 2a I QA.2(i) Justify that the study data can not be used to estimate the proportion of such patients in the population. I QA.2(ii) Show that the sample odds ratio (OR), 6}? = (N11N22)/(N12N21), is the maximum likelihood estimator (MLE) of the population OR of the disease for females vs males