Refer to the Journal of Agricultural, Biological, and Environmental Statistics (Mar. 2005) study of the chemical composition of rainwater, presented in Exercise 12.90 (p. 704). Recall that the nitrate concentration y (milligrams per liter) in a sample of rainwater was modeled as a function of water source (groundwater, subsurface flow, or over ground flow). Now consider adding a second independent variable, silica concentration (milligrams per liter), to the model.
a. Write a first-order model for E(y) as a function of the independent variables. Assume that the rate of increase of nitrate concentration with silica concentration is the same for all three water sources. Sketch the relationships hypothesized by the model on a graph.
b. Write a first-order model for E(y) as a function of the independent variables, but now assume that the rate of increase of nitrate concentration with silica concentration differs for the three water sources. Sketch the relationships hypothesized by the model on a graph.