Does elevation affect hitting performance in baseball? Refer to the Chance (Winter 2006) i...

Does elevation affect hitting performance in baseball? Refer to the Chance (Winter 2006) investigation of the effects of elevation on slugging percentage in Major League Baseball, Exercise.

Does elevation impact hitting performance in baseball? The Colorado Rockies play their major league home baseball games in Coors Field, Denver. Each year, the Rockies are among the leaders in team batting statistics (e.g., home runs, batting average, and slugging percentage). Many baseball experts attribute this phenomenon to the “thin air” of Denver—called the “mile-high city” due to its elevation. Chance (Winter 2006) investigated the effects of elevation on slugging percentage in Major League Baseball. Data were compiled on players’ composite slugging percentage at each of 29 cities for the 2003 season, as well as each city’s elevation (feet above sea level). The data are saved in the MLBPARKS file. (Selected observations are shown inthe next table.) Construct a scatterplot for the data. Do you detect a trend?

Data were compiled on players’ composite slugging percentages at each of 29 cities for the 2003 season, as well as on each city’s elevation (feet above sea level.) The data are saved in the MLBPARKS file. (Selected observations are shown in the table in the next column.) Consider a straight-line model relating slugging percentage ( y ) to elevation ( x ).

a. The model was fit to the data with the use of MINITAB, with the results shown in the printout below. Locate the estimates of the model parameters on the printout.

City	Slug Pct.	Elevation
Anaheim	.480	160
Arlington	.605	616
Atlanta	.530	1,050
Baltimore	.505	130
Boston	.505	20
. . .	. . .	. . .
Denver	.625	5,277
. . .	. . .	. . .
Seattle	.550	350
San Francisco	.510	63
St. Louis	.570	465
Tampa	.500	10
Toronto	.535	566

Based on Schaffer, J., and Heiny, E. L. “The effects of elevation on slugging percentage in Major League Baseball.” Chance , Vol. 19, No. 1, Winter 2006.

---

b. Is there sufficient evidence (at α = .01) of a positive linear relationship between elevation ( x ) and slugging percentage ( y )? Use the p -value shown on the printout to make the inference.

---

c. Construct a scatterplot of the data and draw the least squares line on the graph. Locate the data point for Denver on the graph. What do you observe?

---

d. Recall that the Colorado Rockies, who play their home games in Denver, are annually among the league leaders in slugging percentage. Baseball experts attribute this to the "thin air" of Denver—called the Mile High city due to its elevation. Remove the data point for Denver from the data set and refit the straight-line model to the remaining data. Repeat parts a and b. What conclusions can you draw about the “thin air” theory from this analysis?