Ben Derby is a highly paid scout for a professional baseball team. He attends at least five or six Major League Baseball games a week and watches as many recorded games as he can in order to evaluate potential players for his team to recruit at the end of the season. He also keeps detailed records about each perspective player. His team is now seeking to add another hitter to its roster next season. Luckily Ben has information on 144 hitters in the league who have played at least 100 games during the last season. A portion of the data is shown in the accompanying table with the following variables: the player number (Player), the number of games played (G), at bats (AB), runs (R), hits (H), homeruns (HR), runs batted in (RBI), batting average (AVG), on base percentage (OBP), and slugging percentage (SLG).

a. Perform k-means clustering to group the 144 players into three clusters. Standardize and include all the variables except the player number in the analysis. What is the size of the largest cluster? Which cluster has the highest average number of homeruns? 

b. Select only the players with at least 500 at bats (AB ≥ 500). Perform k-means clustering with k = 3. What is the size of the largest cluster? Which cluster has the highest average number of homeruns? For Analytic Solver, use the Filter option in Excel to select the observations. Copy the observations to a new worksheet. Do not alter the order of the observations.  

Transcribed Image Text:

Player G 140 127 ⠀ 129 1 2 ⠀ 144 AB 558 405 ⠀ 471 ⠀ SLG 0.497 0.451 ⠀ 0.516