Denise Lau is an avid football fan and religiously follows every game of the National Football League. During the 2017 season. she meticulously keeps a record of how each quarterback has played throughout the season. Denise is making a presentation at the local NFL fan club about these quarterbacks. The accompanying table shows a portion of the data that Denise has recorded with the following variables: the player's name (Player), team's name (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). PictureClick here for the Excel Data File Player Team Aaron Rodgers Alex Smith Comp 154 Int KC 341 Tyrod Taylor BUP 263 a. Conduct principal component analysis on all the numerical variables in the data set. Should you use the covariance matrix or the correlation matrix for the analysis in this case? Use the covariance matrix because the variables have different scales Use the covariance matrix because the variables have the same scale O Use the correlation matrix because the variables have different scales Use the correlation matrix because the variables have the same scale 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? (Show your final answer as a percentage point with 2 decimal places.) Number of principal components Percentage of total variability % Components retained for atleast 80% of total variance 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? was given the most weight to compute the first principal component was given the most weight to compute the second principal component. What is the principal component 1 score for the first record (Aaron Rodgers)? (Round your final answer to 4 decimal place The first record (Aaron Rodgers) had a score of for the first principal component B C D E Player Team Comp Att Pct Yds Avg Yds/G TD Int Aaron Rodgers GB 154 238 64.7 1675 7 239.3 16 6 Alex Smith KC 341 505 67.5 4042 8 269.5 26 5 Andy Dalton CIN 297 496 59.9 3320 6.7 207.5 25 12 Ben Roethlisberger PIT 360 561 64.2 4251 7.6 283.4 28 14 Blaine Gabbert ARI 95 171 55.6 1086 6.4 217.2 6 6 Blake Bortles JAX 315 523 60.2 3687 7 230.4. 21 13 Brett Hundley GB 192 316 60.8 1836 5.8 166.9 9 12 Brock Osweiler DEN 96 172 55.8 1088 6.3 181.3 5 S O Bryce Petty NY) 55 112 49.1 544 4.9 136 1 3 1 CJ. Beathard SF 123 224 54.9 1430 6.4 204.3 4 6 2 Cam Newton CAR 291 492 59.1 3302 6.7 206.4 22 16 13 Carson Palmer ARI 164 267 61.4 1978 7.A 282.6 9 7 14 Carson Wentz PHI 265 440 60.2 3296 7.5 253.5 33 7 15 Case Keenum MIN 325 481 67.6 3547 7A 236.5 22 7 16 Dak Prescott DAL 308 490 62.9 3324 6.8 207.8 22 13 17 Derek Carr OAK 323 515 62.7 3496 6.8 233.1 22 13 18 Deshaun Watson HOU 126 204 61.8 1699 8.3 242.7 19 8 19 DeShone Kizer CLE 255 476 53.6 2894 6.1 192.9 11 22 20 Drew Brees NO 386 536 72 4334 8.1 270.9 23 8 21 Drew Stanton ARI 79 159 49.7 894 5.6 178.8 6 5 22 Eli Manning NYG 352 571 61.6 3468 6.1 231.2 19 23 Jacoby Brissett IND 276 469 58.8 3098 6.6 193.6 13 24 Jameis Winston TB 282 442 63.8 3504 7.9 269.5 19 25 Jared Goff LA 296 477 62.1 3804 8 253.6 28 26 Jay Cutler MIA 266 429 62 2666 27 Jimmy Garoppolo SF 120 178 67.4 1560 28 Joe Flacco BAL 352 549 64.1 3141 29 Josh McCown NYJ 267 397 673 2926 30 Kirk Cousins WAS 347 540 64.3 4093 6855N 6.2 190.4 19 8.8 260 5.7 196.3 18 7.4 225.1 18 7.6 255.8 27 93960087 13 7 11 7 14 45 13 9 13 31 Marcus Mariota TEN 281 453 62 32 Matt Moore MIA 78 127 61.4 24 3232 7.1 215.5 13 15 861 6.8 215.2 4 SS 33 Matt Ryan ATL 342 529 64.7 4095 7.7 255.9 20 12 34 Matthew Stafford DET 371 565 65.7 4446 7.9 277.9 29 10 9 35 Mike Glennon CHI 93 140 66.4 833 6 208.2 4 5 36 Mitchell Trubisky CHI 196 330 59.4 2193 37 Nick Foles PHI 57 101 56.4 537 38 Philip Rivers LAC 360 575 62.6 4515 39 Russell Wilson SEA 339 553 61.3 3983 40 Ryan Fitzpatrick TB 96 163 58.9 1103 41 Tom Brady NE 385 581 66.3 4577 42 Tom Savage HOU 125 223 56.1 1412 43 Trevor Siemian DEN 206 349 59 2285 44 Tyrod Taylor BUF 263 420 62.6 2799 665566 999 6.6 5.3 79 7.2 6.3 6.4 639233 182.8 7 7 76.7 5 282.2 28 10 248.9 34 11 183.8 7 286.1 6.5 176.5 6.6 207.7 6.7 186.6 2524 14 4 2966703 8 45