# Question: suppose the true relationship between ey and the quantitative independent...

###### Question details

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

E(y)=
4-x_{1}+2x_{2}+x_{1}x_{2}

Explain the interaction term on the mean response E(y) and answer to the questions:

a. Describe the corresponding response surface.

b. Plot the contour lines of the response surface for
x_{1}= 2,3,4 where 0< x_{2}<5.

c. Plot the contour lines of the response surface for
x_{2}= 2,3,4 where 0<x_{1}<5.

d. Use the contour lines you plotted in parts **b**
and **c** 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 changes when x_{1} is changed
from 4 to 2, and x_{2} is simultaneously changed from 1 to
2.