The biologist in the Black Spruce Seedings Case Study in Section 1.9 was also interested in the relationship between seedling growth and water table depth. The data set Watertable contains data on a sample of the seedlings. The variable binary Alive indicates 1 if the seedling was alive at the end of the second year of the study and 0 otherwise. The variable Depth gives the depth of the water table (centimeter).
(a) Find the logistic equation modeling the log-odds of a seedling being alive against water table depth. Plot the graph of the predicted probabilities against depth and add the observed data points.
(b) Interpret the slope of the regression equation (in terms of odds).
(c) For a seedling growing in soil with a water table depth of 15 cm, find the predicted probability of being alive at the end of the second year.