Ben Derby is a scout for a college baseball team. He attends many high school games and practices each week in order to evaluate potential players to recruit during each college recruitment season. He also keeps detailed records about each prospective player. His college team is in particular need to add another hitter to its roster next season. Luckily, Ben has information on 144 high school players who have played at least 100 games during the previous season. portion of the data is shown in the accompanying table that includes the following variables: Player’s ID (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. Conduct principal component analysis on all the variables, except the player’s ID, in the data set. Standardize the data prior to the analysis. 

b. How many principal components are computed? How many principal components must be retained to account for at least 80% of the total variance in the data? 

c. Display the weights used to compute the first principal component scores. 

d. Create a new data set that contains the players’ names and the principal components that account for at least 80% of the total variance in the data.

Transcribed Image Text:

Player G AB 1 156 621 2 142 451 ⠀ 1 ⠀ 144 144 524 SLG 0.552 0.501 I 0.573