1. Use R to make 2 2 contingency tables for each pair of variables.
(a) Examine the relationship between Traced by MedicalAid. Is there evidence that whether or not a child was traced is independent of whether the mother had medical aid? Answer this question using two di erent methods. For each method:
name the method, explain the rationale, and quote results (with appropriate p-values). Be sure to include all the necessary steps for each method. If there is evidence of association between the variables, explain in practical terms and quantify the nature of the association.
(b) Repeat part (a) to examine the relationship between Traced and Race.
(c) Repeat part (a) to examine the relationship between MedicalAid and Race.
2. Examine the Traced and MedicalAid relationship separately for each race. Indicate (with supporting evidence/quantities) whether or not the 5-year follow-up and medical aid status are independent for each race. When there is evidence of an association, quote numbers to describe the relationship.
3. Based on your conclusions from Questions 1 and 2, is there statistical evidence that medical aid is related to whether or not a child was traced? Give a complete and thorough explanation.
4. Consider tting logistic regression models to answer the question of interest.
(a) We are interested in the characteristics that result in a child being traced (as given in the Case Study description). Speci cally, we wish to determine the e ect of race and medical aid status on the probability of being traced. Identify the response and predictor variables and explain why a logistic regression model would be appropriate for this data.
(b) Fit two logistic regression models: one with an interaction term and one without an interaction. (Hint: you need to reformat/combine your data in order to the logistic models - you can use a simple `for' loop with `if' statements.) What is the deviance of the model with the interaction term? Explain why it has this value.
(c) Now, compare the two models using two di erent statistical tests. For each test: name the test, include all the necessary steps, and explain precisely what is being tested. Between the two models, which would you choose?
(d) What do you conclude from your chosen model? Is your conclusion consistent with your answer from Question 3? For a nal conclusion, give a short summary about your ndings from this case study.
Attachment:- ASTAT_Question.zip