A baseball fan has been collecting data from a newspaper on the various American League teams. She wants to explain each team's winning percentage as a function of its batting average and its earned run average plus an indicator variable for whether the team fired its manager within the last 12 months (1 = Fired manager, and 0 = Did not fire manager). The data for 50 randomly selected teams over the last five seasons were recorded.

a. Perform a regression analysis using a first-order model (no interaction).

b. Do these data provide sufficient evidence that a team that fired its manager within the last 12 months wins less frequently than a team that did not fire its manager?