1. (Adapted from Dobson and Barnett, 2008) The following table tabulates the number of deaths from Leukemia and other cancers among survivors of Hiroshima during the period 1950-1959. The subjects were aged between 25 and 60 in the year 1950, and are classified by the dose of radiation they received in radons. The research question is: How does the proportion of total cancer deaths that are due to Leukemia (rather than other cancers) vary with radiation exposure? radiation midpoint | leukemia other cancer total cancers 0 0 13 378 391 1 to 9 5 5 200 205 10 to 49 29.5 5 151 156 50 to 99 74.5 3 47 50 100 to 199 149.5 4 31 200+ 249.5 18 33 35 51 In this table we converted the radiation level to a continuous predictor, coding the value as the midpoint of the range (e.g., for a radiation of 1 to 9 we use the value (1+9)/2 = 5). For the largest radiation value we choose a value of 249.5 (assuming the radiation goes from 200 to 299). (a) Produce a graphical summary of the table above that helps address the research question. In words, summarize the table and your graphical display. What does the data suggest about the relationship between radiation and the proportion of cancer deaths that are due to leukemia? (b) In R fit a logistic regression model, relating the probability of dying of leukemia (given that the individual has died of cancer) to the midpoint of the radiation dose. Summarize your fitted model. Make sure that you interpret the slope parameter in terms of changes of the odds (with an appropriate confidence interval). Hint: You will probably need to use the information in the table to construct a data set where each cancer death is a single line, with outcome variable either 1 for a Leukemia death or 0 for a death due to a different cancer. Functions c, rep, rbind, cbind may be helpful. 2. (Data taken from Agresti, 1996). In a survey of 34 patients having surgery with a general anesthetic, patients were asked whether or not they experienced a sore throat (throat=0 for no, throat=1 for yes). The duration of the surgery in minutes was also recorded. (a) Write down the a simple logistic regression model that predicts the probability of a patient that has surgery having a sore throat based on the duration of the surgery. Make sure you define all the variables used in your model. (b) Fit the model you defined in part (a) using R. Summarize your fitted model. the model output you obtain. Make sure that you interpret the slope parameter in terms of changes of the odds (with an appropriate confidence interval).