Chapter 14, Problem 78PS

Referring to Problem 14.77, Suppose that an addition to using ERA to predict the number of wins, analytics specialist wants to include the league $(0=\text{American,}\text{1}=\text{National)}$ as an independent variable. Develop a model to predict wins based on ERA and league. For (a) through (k), do not include an interaction term.

a. State the multiple regression equation.

b. Interpret the slopes in (a).

c. Predict the mean number of wins for a team with an ERA of 4.50 in American League.

d. Perform a residual analysis on the model and determine whether the regression assumptions are valid.

e. Is there a significant relationship between wins and the two independent variables (ERA and league) at the 0.05 level of significance?

f. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this

set of data.

g. Construct a $95\%$ confidence interval estimate of the population slope for the relationship between wins and ERA.

h. Construct a $95\%$ confidence interval estimate of the population slope for the relationship between wins and league.

i. Compute and interpret the adjusted $r^2.$

j. Compute and interpret the coefficients of partial determination.

k. What assumption do you have to make about the slope of wins with ERA?

l. Add an interaction term to the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model.

m. On the basis of the result of (f) and (l), which model appropriate? Explain.