Lunn and McNeil show a data set comparing two methods of surgical tattoo removal.19 In addition to which method was used, the depth of the tattoo and the patient’s gender were recorded. In this data set, Removal = 1 represents a successful removal and Removal = 0 represents a poor removal.
a. Create a logistic regression model using Method, Gender, and Depth to estimate the probability that a tattoo was removed successfully. Based on Wald’s test, which variables appear to be significant? Based on the likelihood ratio test (H0: β1 = β2 = β3 = 0 versus Ha: at least one of the coefficients is not zero), can we conclude that at least one of these terms is significant?
b. Create a logistic regression model using only Gender and Depth to estimate the probability that a tattoo was removed successfully. Based on Wald’s test, which variables appear to be significant? Based on the likelihood ratio test (H0: β1 = β2 = 0 versus Ha: at least one of the coefficients is not zero), can we conclude that at least one of these terms is significant?
c. Use the drop-in-deviance test to compare the models in Parts A and B. Can you conclude that Method is related to the probability of success?
d. Construct a model using only Method to predict the probability of a successful removal. What do Wald’s test and likelihood ratio test reveal?
e. Explain why the drop-in-deviance test in Part C is better than the approach in Part D for determining if Method is related to the probability of a successful tattoo removal.