Chapter 14, Problem 81PS

A baseball analysis specialist wants to determine which variable are important in predicting a team’s wins in a given season. He has collected in predicting a team’s wins in a given season. He has collected data related to wins, earned run a average (ERA), and runs scored for the 2012 season (stored in BB2012). Develop a model to predict the number of in 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 mean 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 the 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 $r^2.$

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.

n. Perform an influence analysis on your results and determine whether any observations should be deleted from the model. If necessary, reanalyse the regression model after deleting these observations and compare your results to those of the original model.