# 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.

**View Solution:**## Answer to relevant Questions

MINITAB was used to fit the model to n = 15 data points. y = β0 + β1x1 + βb2x2 + β3x1x2 + ε The resulting printout is shown below. a. What is the prediction equation for the response surface? b. Describe the geometric ...Refer to the Environmental Science & Technology (Jan. 2005) study of the reliability of a commercial kit to test for arsenic in groundwater, presented in Exercise. Recall that you fit a first-order model for arsenic level ...Refer to the Development Psychology (Mar. 2003) study of the behavior of elementary school children, presented in Exercise. The researchers used a quadratic equation to model the level (y) of aggressive fantasies experienced ...Refer to the Chance (Winter 2001) study of students who paid a private tutor (or coach) to help them improve their SAT scores, presented in Exercise. Multiple regression was used to estimate the effect of coaching on ...A study of the atmospheric pollution on the slopes of the Blue Ridge Mountains (in Tennessee) was conducted. The file LEADMOSS contains the levels of lead found in 70 fern moss specimens (in micrograms of lead per gram of ...Post your question