11.81 Refer to Exercise 11.80. Now fit the following second-order model to the data:

a Interpret the value of , and test whether the data indicate that this model is useful for predicting freshman GPA. Use .

b Sketch the relationship between predicted GPA and the verbal score x1 for the following mathematics scores: .

Compare these graphs with those for the firstorder model in Exercise 11.80.

c Test to see whether the interaction term is important for the prediction of GPA. Use

. Note that this term permits the distance between three mathematics score curves for GPA versus verbal score to change as the verbal score changes.