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):

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 y

3.428, SST
8.55

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.

b. Carry out a test of model utility using 
.05 for each of the models described in part (a). Does either result surprise you?