Buckthorn is an invasive shrub that can grow to heights of 20 meters with trunk diameters of up to 10 cm and has become a significant problem on the campus of Calvin College and in much of the U.S. Midwest. Removing buckthorn from an infested area is challenging. Students and faculty at Calvin College have conducted experiments to learn how best to get rid of buckthorn. In one experiment, students cut down buckthorn plants to near ground level and painted different concentrations of glyphosate (Round Up Herbicide) on the stump to see how the concentration of glyphosate affects the proportion of plants that die. Students came back later and counted the number of new shoots growing from the old stump. Any stumps with no shoots were considered "dead". The data from 2006 are available in the buckthorn data set.
a) Fit a logistic regression model to this data and prepare a plot that shows the logistic regression fit (as a curve) and the proportion of dead plants at each concentration used (as dots).
b) Interpret the parameter estimates of the model in a way that would be useful for a biologist.
c) Do a follow-up goodness of fit test. How many degrees of freedom should you use?
d) Is there any reason to be concerned about the use of this model?
e) How might the design of the study be improved?