solution

Predicting runs scored in baseball. Refer to the study of runs scored in Major League Baseball games, Exercise 12.14 (p. 724). Multiple regression was used to model total number of runs scored 1y2 of a team during the season as a function of number of walks (x₁), number of singles (x2), number of doubles (x₃), number of triples (x₄), number of home runs (x₅), number of stolen bases (x₆), number of times caught stealing (x₇), number of strikeouts (x₈), and total number of outs (x₉). Using the b estimates given in Exercise 12.14, predict the number of runs scored by your favorite Major League Baseball team last year. [Note: You can find data on your favorite team on the Internet at www.mlb.com.] Use statistical software to form a 95% prediction interval for your prediction. Does the actual number of runs scored by your team fall within the interval?

Exercise 12.14

Predicting runs scored in baseball. Consider a multiple regression model for predicting the total number of runs scored by a Major League Baseball (MLB) team during a season. Using data on number of walks (x1), singles (x2), doubles (x3), triples (x4), home runs (x5), stolen bases (x6), times caught stealing (x7), strike outs (x8), and ground outs (x9) for each of the 30 teams during the 2014 MLB season, a first-order model for total number of runs scored (y) was fit. The results are shown in the accompanying Minitab printout.

a. Write the least squares prediction equation for y = total number of runs scored by a team during the 2014 season.

b. Give practical interpretations of the b estimates.

c. Conduct a test of H₀: ₇ = 0 against H_a: ₇ 6 0 at a = .05. Interpret the results.

d. Locate a 95% confidence interval for ₅ on the printout. Interpret the interval.

e. Predict the number of runs scored in 2014 by your favorite Major League Baseball team. How close is the predicted value to the actual number of runs scored by your team? (Note: You can find data on your favorite team on the Internet at www.mlb.com.)