# Question: Suppose the true relationship between E y and the quantitative

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

E(y) = 3 + x1 + 2x2 - x1 x2

a. Describe the corresponding three-dimensional response surface.

b. Plot the linear relationship between y and x2 for x2 = 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.

E(y) = 3 + x1 + 2x2 - x1 x2

a. Describe the corresponding three-dimensional response surface.

b. Plot the linear relationship between y and x2 for x2 = 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.

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