QUESTION 1 A psychiatrist is interested in identifying the relationship between patient’s anxiety level (X) and the patient’s ability to focus on a certain task (Y). The higher the score for anxiety level indicates the more anxiety is the patient. The ability to focus is measured as (Y = 1 if able, Y = 0 if unable). A random sample of 27 patients was selected. The data gathered was fitted using a simple logistic regression model and produced the following results: Based on the above output, answer the followings: a) State the fitted response function. b) At 5% significance level determine by using Wald test whether patient’s anxiety level is related to the probability that the patient will be able to focus on a given task. c) Obtain exp(b1) and interpret its meaning. d) Compute the estimated probability that patients with an anxiety test score of 500 will be able to perform a given task. e) Estimate the anxiety test score for which 50 percent of the patients with this anxiety score are expected to be able to perform a given task. f) Obtain an approximate 90% confidence interval for exp(??1). Interpret your interval. QUESTION 2 A researcher conducts a study to investigate whether the people in a certain town get a booster for protection against a new emergence influenza related disease. A random sample of 159 people in the town was selected and data on whether they have gotten the booster or not was coded as Y = 1 if they have received the booster and Y = 0, otherwise. Information on their age (X1), their awareness level on the importance of receiving the booster (X2) and their gender (X3 = 1 if males, X3 = 0 if females) were also recorded. A multiple logistic regression model was fitted to the data and the following out was obtained: a) State the fitted response function. b) Obtain the estimated probability that males aged 51 with awareness index of 76 will receive an influenza like booster. c) At 5% significance level, determine whether the logistic model is a good fit for the data d) A model without variable gender was fitted and the following output was obtained a) State the estimated response function. b) Assuming that the fitted model is appropriate, determine whether gender (X3) can be dropped from the model. Use ?? = 0.05. c) Estimate the probability that 5 or fewer number of accidents happened when the drivers are males and have joined the theory only road safety programs. QUESTION 4 Discuss briefly on the followings: a) High dimensional data. b) Limitations of Least Squares Regression in analysing high dimensional data. c) Two regression methods that can be applied to high dimensional data
