MINITAB was used to fit the model y = b0 + b1 x1 + b2 x2 + b3 x1 x2 + e to n = 15 data points. The resulting printout is shown below.

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 the graph you plotted in 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 a = .01.

Transcribed Image Text:

The regression equation is Y-2.55 + 3.82 X1 + 2.63 X2 -1.29 X1X2 Predictor Coef SE Coef T P Constant -2.550 1.142 -2.23 0.043 X1 3.815 X2 2.630 X1XZ -1.285 0.529 7.22 0.000 0.344 7.64 0.000 0.159 -8.06 0.000 S 0.713 R-Sq 85.6% R-Sq (adj) = 81.6% Analysis of Variance Source DF SS Regression 3 33.149 MS 11.050 F P 21.75 0.000 Residual Error 11 5.587 0.508 Total 14 38.736