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 in the table). Consider a straightline model relating slugging percentage (y) to elevation (x).
(a) The model was fit to the data using MINITAB, with the results shown in the accompanying printout. Locate the estimates of the model parameters on the printout.
(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 for 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) 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?
|
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
|
