Suppose E(y) is related to two predictor variables x1 and x2 by the equation
E(y) = 3 + x1 - 2x2 + x1x2
a. Graph the relationship between E(y) and x1 when x2 = 0. Repeat for x2 = 2 and for x2 = -2.
b. Repeat the instructions of part a for the model
E(y) = 3 + x1 - 2x2
c. The equation for part a is exactly the same as the equation in part b except that we have added the term x1x2. How does the addition of the x1x2 term affect the graphs of the three lines?
d. What flexibility is added to the first-order model
E(y) = β0 + β1x1 + β2x2 by the addition of the term β3x1x2, using the model E(y) = β0 + β1x1 + β2x2 + β3x1x2?