The coach and the general manager of a team in the National Hockey League are trying to decide what kinds of players to draft. To help in making their decision, they need to know which variables are most closely related to the goals differential—the difference between the number of goals their team scores and the number of goals scored by their team’s opponents. (A positive differential means that their team wins, and a negative differential is a loss.) After some consideration, they decide that there are two important variables: The percentage of face-offs won and the penalty-minutes differential. The latter variable is the difference between the number of penalty minutes assessed against their team and the number of penalty minutes assessed against their team’s opponents. The data from 100 games were recorded.

a. Perform a regression analysis using a first-order model with interaction.

b. Is this model valid?

c. Should the interaction term be included?