Chapter 12.5, Problem 12.35LM

Suppose the true relationship between E(y) and the quantitative independent variables x₁ and x₂ is

E(y) = 3 + x₁ + 2x₂ − x₁x₂

1. a. Describe the corresponding three-dimensional response surface.
2. b. Plot the linear relationship between y and x₂ for x₁ = 0, 1, 2, where 0 ≤ x₂ ≤ 5.
3. c. Explain why the lines you plotted in part b are not parallel.
4. d. Use the lines you plotted in part b to explain how changes in the settings of x₁ and x₂ affect E(y).
5. e. Use your graph from part b to determine how much E(y) changes when x₁ is changed from 2 to 0 and x₂ is simultaneously changed from 4 to 5.