Suppose the true relationship between E(y) and the quantitative independent variables x1 and x2 is
E(y) = 3 + x1 + 2x2 - x1x2
a. Describe the corresponding three-dimensional response surface.
b. Plot the linear relationship between y and x2 for x1 = 0, 1, 2, where 0 ≤ x2 ≤ 5.
c. Explain why the lines you plotted in part b are not parallel.
d. Use the lines you plotted in part b to explain how changes in the settings of x1 and x2 affect E(y).
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.