Player Team Comp Aaron Rodgers GB 154 Alex Smith KC 341 Andy Dalton CIN 297 Ben Roethlisberg. PIT 360 Blaine Gabbert ARI 95 Blake Bortles JAX 315 Brett Hundley GB 192 Brock Osweiler DEN 96 Bryce Petty NYJ 55 C.J. Beathard SF 123 Cam Newton CAR 291 Carson Palmer ARI 164 Carson Wentz PHI 265 Case Keenum MIN 325 Dak Prescott DAL 308 Derek Carr OAK 323 Deshaun Watson HOU 126 DeShone Kizer CLE 255 Drew Brees NO 386 Drew Stanton ARI 79 Eli Manning NYG 352 Jacoby Brissett IND 276 Jameis Winston TB 282 Jared Goft LA 296 Jay Cutler MIA 266 Jimmy Garoppolo SF 120 Joe Flacco BAL 352 Josh McCown NYJ 267 Kirk Cousins WAS 347 Marcus Mariota TEN 281 Matt Moore MIA 78 Matt Ryan ATL 342 Matthew Stafford DET 371 Mike Glennon CHI 93 Mitchell Trubisky CHI 196 Nick Foles PHI 57 Philip Rivers LAC 360 Russell Wilson SEA 339 Ryan Fitzpatrick TB 96 Tom Brady NE 385 Tom Savage HOU 125 Trevor Siemian DEN 206 Turod Taylor BUF 263 Att 238 505 496 561 171 523 316 172 112 224 492 267 440 481 490 515 204 476 536 159 571 469 442 477 429 178 549 397 540 453 127 529 565 140 330 101 575 553 163 581 223 349 420 Pct 64.7 67.5 59.9 64.2 55.6 60.2 60.8 55.8 49.1 54.9 59.1 61.4 60.2 67.6 62.9 62.7 61.8 53.6 72 49.7 61.6 58.8 63.8 62.1 62 67.4 64.1 67.3 64.3 62 61.4 64.7 65.7 66.4 59.4 56.4 62.6 61.3 62 63 64 65 66 Yds 1675 4042 3320 4251 1086 3687 1836 1088 544 1430 3302 1978 3296 3547 3324 3496 1699 2894 4334 894 3468 3098 3504 3804 2666 1560 3141 2926 4093 3232 861 4095 4446 833 2193 537 4515 3983 1103 4577 1412 2285 2799 Aug Yds/G 7 239.3 8 269.5 6.7 207.5 7.6 283.4 6.4 217.2 7 230.4 5.8 166.9 6.3 181.3 4.9 136 6.4 204.3 6.7 206.4 7.4 282.6 7.5 253.5 7.4 236.5 6.8 207.8 6.8 233.1 8.3 242.7 6.1 192.9 8.1 270.9 5.6 178.8 6.1 2312 6.6 193.6 7.9 269.5 8 253.6 6.2 190.4 260 5.7 196.3 7.4 225.1 7.6 255.8 7.1 215.5 6.8 215.2 7.7 255.9 7.9 277.9 6 208.2 6.6 182.8 5.3 76.7 7.9 282.2 7.2 248.9 6.8 183.8 7.9 286.1 6.3 176.5 6.5 207.7 6.7 186.6 TD 16 26 25 28 6 21 9 5 1 4 22 9 33 22 22 22 19 11 23 6 19 13 19 28 19 7 18 18 27 13 4 20 29 4 7 5 28 34 7 32 5 12 14 fe = 8 = L -- = -- -- -- -- ? 8 15 5 12 10 5 7 2 10 11 3 8 6 14 4 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 Aaron Rodgers Alex Smith 3 Tyrod Taylor Team GB KC Comp 154 341 Int 6 BUF 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 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 96 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 d. What is the principal component 1 score for the first record (Aaron Rodgers)? (Round your final answer to 4 decimal places.) The first record (Aaron Rodgers) had a score of for the first principal component. Player Team Comp Aaron Rodgers GB 154 Alex Smith KC 341 Andy Dalton CIN 297 Ben Roethlisberg. PIT 360 Blaine Gabbert ARI 95 Blake Bortles JAX 315 Brett Hundley GB 192 Brock Osweiler DEN 96 Bryce Petty NYJ 55 C.J. Beathard SF 123 Cam Newton CAR 291 Carson Palmer ARI 164 Carson Wentz PHI 265 Case Keenum MIN 325 Dak Prescott DAL 308 Derek Carr OAK 323 Deshaun Watson HOU 126 DeShone Kizer CLE 255 Drew Brees NO 386 Drew Stanton ARI 79 Eli Manning NYG 352 Jacoby Brissett IND 276 Jameis Winston TB 282 Jared Goft LA 296 Jay Cutler MIA 266 Jimmy Garoppolo SF 120 Joe Flacco BAL 352 Josh McCown NYJ 267 Kirk Cousins WAS 347 Marcus Mariota TEN 281 Matt Moore MIA 78 Matt Ryan ATL 342 Matthew Stafford DET 371 Mike Glennon CHI 93 Mitchell Trubisky CHI 196 Nick Foles PHI 57 Philip Rivers LAC 360 Russell Wilson SEA 339 Ryan Fitzpatrick TB 96 Tom Brady NE 385 Tom Savage HOU 125 Trevor Siemian DEN 206 Turod Taylor BUF 263 Att 238 505 496 561 171 523 316 172 112 224 492 267 440 481 490 515 204 476 536 159 571 469 442 477 429 178 549 397 540 453 127 529 565 140 330 101 575 553 163 581 223 349 420 Pct 64.7 67.5 59.9 64.2 55.6 60.2 60.8 55.8 49.1 54.9 59.1 61.4 60.2 67.6 62.9 62.7 61.8 53.6 72 49.7 61.6 58.8 63.8 62.1 62 67.4 64.1 67.3 64.3 62 61.4 64.7 65.7 66.4 59.4 56.4 62.6 61.3 62 63 64 65 66 Yds 1675 4042 3320 4251 1086 3687 1836 1088 544 1430 3302 1978 3296 3547 3324 3496 1699 2894 4334 894 3468 3098 3504 3804 2666 1560 3141 2926 4093 3232 861 4095 4446 833 2193 537 4515 3983 1103 4577 1412 2285 2799 Aug Yds/G 7 239.3 8 269.5 6.7 207.5 7.6 283.4 6.4 217.2 7 230.4 5.8 166.9 6.3 181.3 4.9 136 6.4 204.3 6.7 206.4 7.4 282.6 7.5 253.5 7.4 236.5 6.8 207.8 6.8 233.1 8.3 242.7 6.1 192.9 8.1 270.9 5.6 178.8 6.1 2312 6.6 193.6 7.9 269.5 8 253.6 6.2 190.4 260 5.7 196.3 7.4 225.1 7.6 255.8 7.1 215.5 6.8 215.2 7.7 255.9 7.9 277.9 6 208.2 6.6 182.8 5.3 76.7 7.9 282.2 7.2 248.9 6.8 183.8 7.9 286.1 6.3 176.5 6.5 207.7 6.7 186.6 TD 16 26 25 28 6 21 9 5 1 4 22 9 33 22 22 22 19 11 23 6 19 13 19 28 19 7 18 18 27 13 4 20 29 4 7 5 28 34 7 32 5 12 14 fe = 8 = L -- = -- -- -- -- ? 8 15 5 12 10 5 7 2 10 11 3 8 6 14 4 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 Aaron Rodgers Alex Smith 3 Tyrod Taylor Team GB KC Comp 154 341 Int 6 BUF 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 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 96 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 d. What is the principal component 1 score for the first record (Aaron Rodgers)? (Round your final answer to 4 decimal places.) The first record (Aaron Rodgers) had a score of for the first principal component