Chapter 13, Problem 70SE

An aeronautical engineering student carried out an experiment to study how y = lift/drag ratio related to the variables x₁ = position of a certain forward lifting surface relative to the main wing and x₂ = tail placement relative to the main wing, obtaining the following data ( Statistics for Engineering Problem Solving. p. 133):

jr, (in.)    x₂    (in.)    y

x1(in.)	x2 (in.)	y
−1.2	−1.2	.858
−1.2	0	3.156
−1.2	1.2	3.644
0	−1.2	4.281
0	0	3.481
0	1.2	3.918
1.2	−1.2	4.136
1.2	0	3.364
1.2	1.2	4.018
		$\bar{y}$ = 3.428, SST = 8.55

1. a. Fitting the first-order model gives SSE = 5.18, whereas including x₃ =x₁x₂ as a predictor results in SSE = 3.07. Calculate and interpret the coefficient of multiple determination for each model.
2. b. Carry out a test of model utility using α = .05 for each of the models described in part (a). Does either result surprise you?