Consider the model y = b0 + b1 x1 + b2 x1 2 + b3 x2 + b4 x3 + b5 x1 x2 + b6 x1 x3 + b7 x1 2 x2 + b8 x1 2 x3 + e where x1 is a quantitative variable and

The resulting least squares prediction equation is yn = 45.6 - 4.7x1 + .07x1 2 - 3.7x2 - 5.9x3 + 3.1x1 x2

+ 2.5x1 x3 - .09x1 2 x2 - .03x1 2 x3

a. What is the response curve for E(y) when x2 = 0 and x3 = 0? When x2 = 1 and x3 = 0? When x2 = 0 and x3 = 1?

b. On the same graph, plot the least squares prediction equation associated with level 1, with level 2, and with level 3. Choose the correct graph below.

Transcribed Image Text:

X2 = {16 1 if level 2 (1 10 otherwise X3 10 if level 3 otherwise