An aeronautical engineering student carried out an experiment to study how y = lift/drag...

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):

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 α = .05 for each of the models described in part (a). Does either result surprise you?