The Minitab printout below was obtained from fitting the model
y = β0 + β1x1 + β2x2 + β3x1x2 + ε
to n = 15 data points.
a. What is the prediction equation for the response surface?
b. Describe the geometric form of the response surface of part a.

c. Plot the prediction equation for the case when x2 = 1. Do this twice more on the same graph for the cases when x2 = 3 and x2 = 5.
d. Explain what it means to say that x1 and x2 interact. Explain why your graph of part c suggests that x1 and x2 interact.
e. Specify the null and alternative hypotheses you would use to test whether x1 and x2 interact.
f. Conduct the hypothesis test of part e using α = .01.

The regression equation is Y = -2.55 + 3.82 X1 + 2.63 X2-1.29 X1X2 Predictor Coef SE Coef Constant .550 1.142 -2.23 0.043 21 X2 X1X2 3.815 0.529 7.22 0.000 2.630 0.344 7. 64 0.000 -1.285 0.159 8.06 0.000 S-0.713 R-Sq 85.6% R-Sq (adj) = 81.64 = Analysis of Variance Source Regression Residual Error 11 5.587 0.508 Total DF HS 3 33.149 11.050 21.75 0.000 14 38.736