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 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 α = .01.

Transcribed Image Text:

The regression equation is Y = -2.55 + 3.82 x1 + 2.63 X2-1.29 X1X2 PredictorCoef SE Coef Constant 2.550 3.815 2. 630 X1 X2 X122 1.142 -2.23 0.043 0.529 7.22 0.000 0.344 7.64 0.000 -1.285 0.159 -8.06 0.000 S0.713 R-Sq 85.6% R-Sq (adj) 81.6% - Analysis of Variance Source Regression Residual Erro 11 Total DF NS 3 33.149 11.050 21.75 0.000 0.508 5.587 14 38.736