Fan, Heckman, and Wand analyzed third- degree burn data from the University of Southern California General Hospital Burn Center.21 In the Burns data set, 435 patients (adults ages 18–85) were grouped according to the size of the third-degree burns on their body. The explanatory variable is listed as the midpoint of set intervals: ln(area in square centimeters + 1). The response in this data set is whether or not the patient survived (1 represents a survival).
a. Create a logistic regression model using area to estimate the probability of survival.
b. Calculate the observed and expected probabilities. Plot both of these probabilities against the median area. c. Interpret the model in terms of the odds ratio. Use the Wald statistic to create a 95% confidence interval for the odds ratio.
d. Test H0: β1 = 0 versus Ha: β1 ≠ 0 using both Wald’s test and the likelihood ratio test. State your conclusion based on these tests.
e. Conduct the Pearson, deviance, and Hosmer-Lemeshow goodness-of-fit tests to assess how well the model fits the data. Interpret the results.
f. Report and interpret Somers’D, Goodman-Kruskal gamma, or Kendall’s tau-a for this logistic regression model.
g. What conclusions can you draw from this study?