Denise Lau is an avid football fan and religiously follows every college football game. During the current season, she meticulously keeps a record of how each quarterback has played throughout the season. Denise is making a presentation at a local college football fan club about these quarterbacks. The accompanying table shows a portion of the data that she has recorded. Variables include the player number (Player), completed passes (Comp), attempted passes (Att), completion percentage (Pct), total yards thrown (Yds), average yards per attempt (Avg), yards thrown per game (Yds/G), number of touchdowns (TD), and number of interceptions (Int). 

a. Perform agglomerative clustering to group the quarterbacks according to their performance to help Denise prepare for this presentation. Standardize the variables and use the Euclidean distance and the Ward clustering method. Cluster the data into three clusters. How many players are in the largest cluster? What is the average number of touchdowns of the largest cluster? 

b. Select only the quarterbacks with at least 150 attempted passes and repeat the cluster analysis performed in part a. Cluster the data into two clusters. How many players are in the larger cluster? What is the average number of touchdowns of the larger cluster?  

Transcribed Image Text:

Player 1 2 # 43 Comp 107 238 # 184 Att 166 353 ⠀ 294 ⠀ Int 4 4 ⠀ 3