Beza Gordon-Smith is a high school senior in northern California who loves watching football. She keeps track of football results and statistics of the quarterbacks of each high school team. The accompanying table shows a portion of the data that Beza has recorded, with the following variables: the player’s number that Beza assigns to each quarterback (Player), team’s mascot (Team), completed passes (Comp), attempted pass (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. Conduct principal component analysis on all variables, except the players’ number, in the data set. Should you use the covariance matrix or the correlation matrix for the analysis in this case? Explain. 

b. Allow the maximum number of principal components to be calculated by the software. How many principal components are computed? What percent of the total variability is accounted for by the first three principal components? How many principal components must be retained in order to account for at least 80% of the total variance in the data?

c. Which original variable is given the highest weight to compute the first principal component? Which original variable is given the highest weight to compute the second principal component? 

d. What is the principal component 1 score for the first record (Player 1)?  

Transcribed Image Text:

Player 1 2 I 43 Team Albatrosses Bobcats Salamanders Comp 154 341 1 263 .... Int 65 6 5 1 4