Crazy Dave, a well-known baseball analyst, wants to determine which variables are important in predicting a team's wins in a given season. He has collected data related to wins, earned run average (ERA), and runs scored for the 2009 season (stored in BB2009). Develop a model to predict the number of wins based on ERA and runs scored.
a. State the multiple regression equation.
b. Interpret the meaning of the slopes in this equation.
c. Predict the number of wins for a team that has an ERA of 4.50 and has scored 750 runs.
d. Perform a residual analysis on the results and determine whether the regression assumptions are valid.
e. Is there a significant relationship between number of wins and the two independent variables (ERA and runs scored) at the 0.05 level of significance?
f. Determine the p-value in (e) and interpret its meaning.
g. Interpret the meaning of the coefficient of multiple determination in this problem.
h. Determine the adjusted r2.
i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.
j. Determine the p-values in (i) and interpret their meaning.
k. Construct a 95% confidence interval estimate of the population slope between wins and ERA.
l. Compute and interpret the coefficients of partial determination.
m. Which is more important in predicting wins-pitching, as measured by ERA, or offense, as measured by runs scored? Explain.