BANA703
Bhuwaneshwari Iyer
- Data set
PGA.csvcontains statistics of performance and winnings for 196 PGA tour participants during 2004 season [https://www.pgatour.com/]. Here is the list of variable: Name, Age, Average Drive (Yards), Driving accuracy (percent), Greens on regulation (%), Average # of putts, Save Percent, Money Rank, # Events, Total Winnings ($), Average winnings ($). Please read PGA data (PGA.csv) into R.
PGA <- read.csv("C:/Users/bhuvi iyer/Downloads/PGA.csv",h=T)
PGA## Name Age AverageDrive DrivingAccuracy GreensonRegulation
## 1 Aaron Baddeley 23 288.0 53.1 58.2
## 2 Adam Scott 24 295.4 57.7 65.6
## 3 Alex Cejka 34 285.8 64.2 63.8
## 4 Andre Stolz 34 297.9 59.0 63.0
## 5 Arjun Atwal 31 289.4 60.5 62.5
## 6 Arron Oberholser 29 284.6 68.8 67.0
## 7 Bart Bryant 42 282.1 74.2 68.9
## 8 Ben Crane 28 283.8 64.4 64.2
## 9 Ben Curtis 27 282.1 64.3 63.4
## 10 Bernhard Langer 47 282.2 62.6 65.3
## 11 Billy Andrade 40 283.5 59.7 64.4
## 12 Billy Mayfair 38 285.2 70.1 66.0
## 13 Blaine McCalliste 46 280.9 63.4 63.6
## 14 Bo Van Pelt 29 294.4 65.1 67.7
## 15 Bob Burns 36 276.1 67.2 62.3
## 16 Bob Estes 38 278.2 63.9 64.2
## 17 Bob Tway 45 278.2 63.7 64.8
## 18 Brad Faxon 43 273.7 61.6 61.4
## 19 Brenden Pappas 34 298.9 50.1 63.0
## 20 Brent Geiberger 36 291.3 64.8 64.9
## 21 Brett Quigley 35 294.3 57.2 65.8
## 22 Brian Bateman 31 292.2 66.1 66.6
## 23 Brian Gay 33 279.7 64.8 61.5
## 24 Brian Kortan 33 292.4 63.0 62.0
## 25 Briny Baird 32 289.4 65.0 70.6
## 26 Cameron Beckman 34 291.2 66.5 67.0
## 27 Carl Pettersson 27 290.8 61.1 64.5
## 28 Carlos Franco 39 290.6 59.3 67.8
## 29 Chad Campbell 30 288.0 63.9 67.7
## 30 Charles Howell II 25 288.5 64.3 66.1
## 31 Chris Couch 31 302.1 56.2 60.8
## 32 Chris DiMarco 36 277.3 68.6 67.1
## 33 Chris Riley 31 277.3 61.8 62.5
## 34 Chris Smith 35 304.0 59.5 70.4
## 35 Cliff Kresge 36 283.4 62.8 60.5
## 36 Corey Pavin 45 268.2 71.9 62.1
## 37 Craig Barlow 32 291.0 67.8 67.7
## 38 Craig Bowden 36 270.8 76.1 62.9
## 39 Craig Parry 38 276.9 63.5 60.7
## 40 Craig Perks 37 289.4 54.4 63.0
## 41 D.J. Brigman 28 290.7 63.9 65.8
## 42 Dan Forsman 46 281.9 64.3 63.1
## 43 Dan Olsen 37 296.0 51.5 60.7
## 44 Daniel Chopra 30 295.9 58.6 63.9
## 45 Danny Briggs 44 283.8 65.5 68.1
## 46 Danny Ellis 34 286.7 62.9 63.9
## 47 Darren Clarke 36 289.0 62.3 64.0
## 48 David Branshaw 35 285.8 66.6 66.2
## 49 David Frost 45 273.6 66.1 63.7
## 50 David Gossett 25 283.8 54.4 54.7
## 51 David Morland IV 35 272.8 69.4 60.1
## 52 David Peoples 44 281.3 63.7 64.0
## 53 David Toms 37 285.3 63.4 68.5
## 54 Davis Love III 40 300.1 60.1 63.4
## 55 Dean Wilson 34 282.2 63.0 62.0
## 56 Deane Pappas 37 295.3 60.1 63.4
## 57 Dennis Paulson 42 300.1 60.4 63.0
## 58 Dicky Pride 35 280.5 68.3 62.6
## 59 Dudley Hart 36 285.6 63.1 64.2
## 60 Duffy Waldorf 42 285.4 68.6 69.0
## 61 Ernie Els 35 298.0 55.5 65.6
## 62 Esteban Toledo 42 275.2 67.8 60.1
## 63 Frank Lickliter I 35 287.3 66.6 64.8
## 64 Fred Couples 45 294.5 58.8 66.3
## 65 Fred Funk 48 271.9 77.2 65.5
## 66 Fredrik Jacobson 30 287.9 55.6 64.4
## 67 Gene Sauers 42 280.2 66.2 62.0
## 68 Geoff Ogilvy 27 303.3 63.2 66.9
## 69 Glen Day 39 286.1 65.6 61.8
## 70 Grant Waite 40 288.3 59.4 62.8
## 71 Greg Chalmers 31 287.3 61.7 60.6
## 72 Guy Boros 40 281.1 66.3 60.3
## 73 Hank Kuehne 29 314.4 49.9 62.9
## 74 Harrison Frazar 33 298.8 64.3 65.2
## 75 Heath Slocum 30 280.1 71.3 67.1
## 76 Hidemichi Tanaka 33 281.0 72.3 66.1
## 77 Hirofumi Miyase 33 279.7 70.6 60.4
## 78 Hunter Mahan 22 293.0 62.2 63.7
## 79 J.J. Henry 29 301.3 64.5 66.6
## 80 J.L. Lewis 44 288.3 65.5 65.8
## 81 J.P. Hayes 39 280.7 67.7 63.6
## 82 Jason Bohn 31 293.3 65.8 66.8
## 83 Jason Dufner 27 290.7 62.5 65.3
## 84 Jay Delsing 44 288.8 62.1 64.5
## 85 Jay Haas 51 274.5 65.4 66.9
## 86 Jay Williamson 37 288.1 69.3 65.4
## 87 Jeff Brehaut 41 290.9 71.3 66.2
## 88 Jeff Maggert 40 281.2 69.2 67.5
## 89 Jeff Sluman 47 279.6 67.9 68.8
## 90 Jerry Kelly 38 278.1 70.4 68.0
## 91 Jesper Parnevik 39 287.9 60.0 66.1
## 92 Joe Durant 40 287.2 75.1 73.3
## 93 Joe Ogilvie 30 288.8 61.3 62.5
## 94 Joey Sindelar 46 291.5 65.6 67.6
## 95 John Cook 47 270.2 73.4 66.5
## 96 John Daly 38 306.0 53.0 66.4
## 97 John Huston 43 286.4 65.9 68.8
## 98 John Riegger 41 285.0 61.4 67.1
## 99 John Rollins 29 286.7 69.1 62.5
## 100 John Senden 33 296.6 65.6 70.5
## 101 Jonathan Byrd 26 295.8 62.1 61.4
## 102 Jonathan Kaye 34 290.9 64.7 66.5
## 103 Jose Coceres 41 279.4 74.3 63.3
## 104 Jose Maria Olazab 38 277.7 57.0 62.5
## 105 Justin Leonard 32 282.9 67.4 66.1
## 106 Justin Rose 24 290.7 61.5 67.7
## 107 K.J. Choi 34 285.0 61.2 65.9
## 108 Ken Duke 35 284.3 59.0 61.9
## 109 Kenny Perry 44 295.9 62.5 68.6
## 110 Kent Jones 37 286.4 69.8 67.4
## 111 Kevin Muncrief 28 290.7 56.1 59.1
## 112 Kevin Na 21 280.1 68.7 63.4
## 113 Kevin Sutherland 40 286.1 67.1 63.0
## 114 Kirk Triplett 42 279.1 72.1 67.7
## 115 Kris Cox 31 299.1 59.0 62.0
## 116 Lee Janzen 40 286.1 62.2 67.8
## 117 Len Mattiace 37 278.0 67.2 59.1
## 118 Loren Roberts 49 269.1 69.8 66.6
## 119 Lucas Glover 25 303.4 64.4 67.5
## 120 Luke Donald 27 279.8 69.6 69.4
## 121 Mark Brooks 43 273.8 66.8 59.8
## 122 Mark Calcavecchia 44 291.3 64.5 64.1
## 123 Mark Hensby 33 284.6 67.7 63.3
## 124 Mark O'Meara 47 272.9 67.0 62.5
## 125 Mark Wilson 30 282.1 72.0 68.9
## 126 Mathias Gronberg 34 292.1 58.5 63.2
## 127 Matt Gogel 33 285.6 68.5 63.2
## 128 Matt Kuchar 26 287.3 64.4 65.3
## 129 Michael Allen 45 291.1 56.5 64.2
## 130 Mike Heinen 37 305.2 62.7 62.8
## 131 Mike Weir 34 282.1 64.1 65.1
## 132 Neal Lancaster 42 291.6 57.6 65.2
## 133 Nick Price 47 272.8 68.3 59.1
## 134 Niclas Fasth 32 289.1 61.6 61.5
## 135 Notah Begay III 32 285.8 69.5 66.2
## 136 Olin Browne 45 281.9 73.5 68.9
## 137 Omar Uresti 36 272.2 73.1 62.6
## 138 Pat Bates 35 275.5 69.9 66.3
## 139 Pat Perez 28 291.4 65.0 66.2
## 140 Patrick Sheehan 35 290.3 63.0 64.9
## 141 Paul Azinger 44 285.1 57.6 63.0
## 142 Peter Lonard 37 291.4 61.5 62.9
## 143 Phil Mickelson 34 295.4 62.9 69.5
## 144 Retief Goosen 35 294.2 62.5 68.7
## 145 Rich Barcelo 29 293.1 59.0 64.4
## 146 Rich Beem 34 296.7 61.7 63.7
## 147 Richard S. Johnso 28 283.4 69.3 64.5
## 148 Robert Allenby 33 294.9 65.0 70.3
## 149 Robert Damron 32 277.2 70.0 63.8
## 150 Robert Gamez 36 288.1 65.2 65.7
## 151 Rocco Mediate 41 283.4 69.9 65.5
## 152 Rod Pampling 35 292.1 59.8 66.1
## 153 Roger Tambellini 29 297.8 59.2 63.2
## 154 Roland Thatcher 27 293.1 64.8 68.0
## 155 Rory Sabbatini 28 292.2 59.2 64.9
## 156 Russ Cochran 46 280.3 65.4 63.6
## 157 Ryan Palmer 28 295.6 63.2 65.5
## 158 Scott Hend 31 312.6 54.1 62.7
## 159 Scott Hoch 49 280.4 68.8 68.6
## 160 Scott McCarron 39 294.1 64.9 65.4
## 161 Scott Simpson 49 278.7 70.7 62.0
## 162 Scott Verplank 40 278.0 77.1 68.5
## 163 Sergio Garcia 24 295.1 58.5 70.8
## 164 Shaun Micheel 35 287.5 63.1 67.0
## 165 Shigeki Maruyama 35 280.1 63.7 64.6
## 166 Skip Kendall 40 281.3 68.2 62.7
## 167 Spike McRoy 36 281.5 67.1 64.9
## 168 Stephen Ames 40 287.9 65.0 68.4
## 169 Stephen Leaney 35 282.3 64.8 64.8
## 170 Steve Allan 31 301.2 59.3 66.8
## 171 Steve Elkington 42 287.1 68.2 66.1
## 172 Steve Flesch 37 279.9 65.8 65.8
## 173 Steve Lowery 44 288.8 58.3 63.9
## 174 Steve Pate 43 283.5 64.8 65.1
## 175 Steve Stricker 37 281.8 52.7 59.3
## 176 Stewart Cink 31 290.5 58.7 66.4
## 177 Stuart Appleby 33 293.2 62.5 65.1
## 178 Tag Ridings 30 301.0 56.4 64.2
## 179 Ted Purdy 31 289.2 70.1 67.4
## 180 Tiger Woods 28 301.9 56.1 66.9
## 181 Tim Clark 28 278.8 72.0 65.8
## 182 Tim Herron 34 293.8 58.0 65.1
## 183 Tim Petrovic 38 287.2 63.6 63.4
## 184 Todd Fischer 35 280.1 61.7 63.9
## 185 Todd Hamilton 39 283.5 58.7 62.7
## 186 Tom Byrum 44 272.6 74.7 63.7
## 187 Tom Carter 36 296.5 55.1 62.9
## 188 Tom Lehman 45 287.2 69.7 71.4
## 189 Tom Pernice, Jr. 45 286.0 68.2 66.8
## 190 Tommy Armour III 45 290.5 62.4 64.3
## 191 Tommy Tolles 38 287.8 54.0 61.9
## 192 Tripp Isenhour 36 286.2 61.7 62.1
## 193 Vaughn Taylor 28 292.5 65.1 68.4
## 194 Vijay Singh 41 300.8 60.4 73.0
## 195 Woody Austin 40 291.3 63.3 68.1
## 196 Zach Johnson 28 285.6 71.9 67.9
## AverageNumofPutts SavePercent MoneyRank NumEvents TotalWinnings
## 1 1.767 50.9 123 27 632878
## 2 1.757 59.3 7 16 3724984
## 3 1.795 50.7 54 24 1313484
## 4 1.787 47.7 101 20 808373
## 5 1.766 43.5 146 30 486053
## 6 1.780 50.9 52 23 1355433
## 7 1.777 40.4 80 23 962167
## 8 1.740 53.8 75 27 1036958
## 9 1.809 42.2 141 20 500818
## 10 1.777 47.7 83 15 943589
## 11 1.773 50.5 124 31 631143
## 12 1.829 49.7 140 32 503252
## 13 1.808 42.3 198 27 162701
## 14 1.768 43.1 39 30 1553826
## 15 1.769 51.9 130 30 581421
## 16 1.756 44.8 74 23 1046064
## 17 1.788 46.9 79 26 966554
## 18 1.749 52.9 76 28 1016899
## 19 1.759 55.6 137 34 524907
## 20 1.775 49.3 57 31 1259780
## 21 1.780 52.7 97 31 836382
## 22 1.766 48.5 86 24 919256
## 23 1.737 52.2 122 32 645196
## 24 1.844 52.1 200 24 159939
## 25 1.780 42.1 69 30 1156517
## 26 1.771 47.3 107 30 779189
## 27 1.733 52.9 51 28 1367963
## 28 1.798 47.1 29 27 1955395
## 29 1.799 46.1 24 28 2264985
## 30 1.802 48.9 33 30 1703485
## 31 1.796 34.2 217 24 100283
## 32 1.752 50.6 12 27 2971843
## 33 1.766 51.6 56 23 1292732
## 34 1.811 33.2 115 33 692785
## 35 1.802 45.7 175 33 258061
## 36 1.762 57.4 89 23 881938
## 37 1.787 52.9 128 25 595820
## 38 1.791 53.1 143 30 494569
## 39 1.797 55.3 55 16 1308586
## 40 1.815 50.5 152 27 423749
## 41 1.810 49.6 160 27 356943
## 42 1.811 62.3 165 28 315540
## 43 1.778 41.4 207 31 135731
## 44 1.748 52.2 108 33 763253
## 45 1.792 45.6 157 28 397606
## 46 1.757 54.0 144 26 490414
## 47 1.745 46.2 28 16 2009819
## 48 1.796 43.2 169 30 293617
## 49 1.802 60.1 155 26 402589
## 50 1.847 47.7 245 25 21250
## 51 1.786 49.2 197 27 164435
## 52 1.779 50.0 147 26 479465
## 53 1.758 55.7 22 24 2357531
## 54 1.753 51.9 10 24 3075094
## 55 1.755 52.4 133 33 561341
## 56 1.776 44.1 161 22 346632
## 57 1.774 61.1 117 21 677035
## 58 1.842 41.5 184 23 230329
## 59 1.784 45.6 92 23 854638
## 60 1.770 41.3 46 26 1487912
## 61 1.740 47.9 2 16 5787225
## 62 1.795 51.8 211 36 115185
## 63 1.759 40.8 58 27 1259235
## 64 1.781 47.1 50 16 1396109
## 65 1.769 54.6 25 29 2103732
## 66 1.750 43.9 59 24 1259048
## 67 1.788 42.7 170 30 287150
## 68 1.752 61.0 61 26 1236909
## 69 1.749 47.5 138 33 519935
## 70 1.808 43.8 180 29 239319
## 71 1.726 57.7 156 22 402380
## 72 1.810 42.5 208 24 130783
## 73 1.765 59.3 99 30 816889
## 74 1.748 51.7 48 25 1446765
## 75 1.788 54.3 72 31 1066838
## 76 1.780 41.6 104 27 795206
## 77 1.823 43.9 199 27 162120
## 78 1.775 45.8 100 30 813089
## 79 1.788 41.7 93 30 848823
## 80 1.769 49.1 102 32 807344
## 81 1.776 46.2 174 27 260816
## 82 1.778 42.0 131 29 567931
## 83 1.790 52.5 164 28 317770
## 84 1.797 51.3 193 26 190184
## 85 1.758 56.1 27 23 2071626
## 86 1.776 56.3 120 33 660038
## 87 1.810 46.4 149 34 448914
## 88 1.789 49.5 43 20 1527883
## 89 1.777 45.9 77 28 1007635
## 90 1.763 52.8 17 29 2496223
## 91 1.759 51.9 40 24 1550135
## 92 1.798 41.7 81 26 952548
## 93 1.755 47.7 49 32 1443363
## 94 1.811 35.1 41 31 1536882
## 95 1.789 50.0 189 19 210448
## 96 1.736 54.8 21 22 2359507
## 97 1.804 55.9 90 20 874280
## 98 1.773 38.9 153 17 423263
## 99 1.764 46.1 109 29 737957
## 100 1.791 50.6 114 28 698203
## 101 1.760 56.0 70 27 1133166
## 102 1.803 42.2 34 25 1695333
## 103 1.754 61.7 106 20 779197
## 104 1.745 51.2 142 17 495051
## 105 1.769 54.0 42 25 1531023
## 106 1.762 49.4 62 22 1236765
## 107 1.770 45.8 26 24 2077775
## 108 1.785 47.9 166 30 301308
## 109 1.776 45.8 30 23 1952043
## 110 1.776 46.5 119 32 674910
## 111 1.823 47.0 244 21 21660
## 112 1.775 49.7 87 32 901159
## 113 1.799 53.7 85 27 928759
## 114 1.752 49.3 38 24 1566426
## 115 1.808 41.9 190 26 205171
## 116 1.781 51.5 96 25 837482
## 117 1.792 60.2 188 25 213707
## 118 1.738 59.3 78 22 998677
## 119 1.797 48.4 134 30 557454
## 120 1.791 52.2 35 21 1646267
## 121 1.796 43.5 173 31 264076
## 122 1.765 52.3 112 24 717876
## 123 1.738 54.0 15 29 2718765
## 124 1.768 53.7 135 17 543866
## 125 1.788 48.1 167 19 300317
## 126 1.811 43.9 132 32 565013
## 127 1.749 53.3 98 25 817117
## 128 1.795 46.6 139 28 509258
## 129 1.763 48.9 88 28 882872
## 130 1.790 31.8 195 17 166185
## 131 1.749 53.7 14 22 2761537
## 132 1.781 52.4 113 33 701240
## 133 1.746 58.7 103 15 796086
## 134 1.806 40.7 172 22 265424
## 135 1.771 44.2 129 23 583537
## 136 1.775 47.8 127 30 597034
## 137 1.813 56.8 163 28 345798
## 138 1.803 45.0 168 32 299385
## 139 1.780 51.1 111 32 723724
## 140 1.759 43.0 63 33 1234345
## 141 1.745 51.7 126 23 601438
## 142 1.819 47.1 118 23 675189
## 143 1.759 56.4 3 22 5784823
## 144 1.743 54.6 6 16 3885573
## 145 1.797 35.3 186 26 223597
## 146 1.814 56.4 183 28 230499
## 147 1.758 50.8 148 32 461184
## 148 1.798 46.5 44 26 1513537
## 149 1.792 49.4 84 28 933389
## 150 1.767 48.3 110 31 725369
## 151 1.800 45.0 176 19 257692
## 152 1.763 58.9 31 26 1737725
## 153 1.796 49.3 181 28 234164
## 154 1.811 42.3 177 23 247987
## 155 1.792 48.9 16 26 2500397
## 156 1.791 45.7 194 25 185108
## 157 1.768 51.3 37 33 1592344
## 158 1.806 49.0 136 29 531263
## 159 1.786 50.0 60 17 1239360
## 160 1.772 49.7 105 27 790720
## 161 1.800 51.2 192 18 190986
## 162 1.743 47.1 20 24 2365594
## 163 1.790 48.1 9 18 3239216
## 164 1.793 47.2 82 27 949919
## 165 1.746 49.4 23 26 2301693
## 166 1.767 48.3 64 29 1206440
## 167 1.810 45.8 159 33 374187
## 168 1.755 54.5 8 27 3303207
## 169 1.805 55.3 68 24 1166560
## 170 1.795 48.9 121 33 648480
## 171 1.796 49.0 179 20 243239
## 172 1.763 49.0 18 31 2461789
## 173 1.769 43.8 66 28 1191245
## 174 1.797 48.5 191 24 199569
## 175 1.745 48.8 151 27 440906
## 176 1.723 56.1 5 28 4450272
## 177 1.764 51.4 13 25 2949234
## 178 1.751 49.4 125 18 623262
## 179 1.769 46.6 36 35 1636876
## 180 1.724 53.5 4 19 5365472
## 181 1.764 53.3 71 26 1108190
## 182 1.787 47.8 32 26 1727577
## 183 1.776 49.2 65 32 1193355
## 184 1.769 46.7 94 33 847996
## 185 1.774 44.6 11 27 3063780
## 186 1.776 52.5 91 25 873140
## 187 1.790 42.7 158 35 395782
## 188 1.778 44.0 53 19 1343278
## 189 1.778 55.4 47 31 1475273
## 190 1.807 43.6 95 28 844636
## 191 1.776 43.5 201 25 151852
## 192 1.795 43.8 218 22 90699
## 193 1.761 41.9 67 27 1176435
## 194 1.757 50.9 1 29 10905167
## 195 1.775 46.9 45 29 1495982
## 196 1.751 45.3 19 30 2417685
## AverageWinnings
## 1 23440
## 2 232812
## 3 54729
## 4 40419
## 5 16202
## 6 58932
## 7 41833
## 8 38406
## 9 25041
## 10 62906
## 11 20359
## 12 15727
## 13 6026
## 14 51794
## 15 19381
## 16 45481
## 17 37175
## 18 36318
## 19 15438
## 20 40638
## 21 26980
## 22 38302
## 23 20162
## 24 6664
## 25 38551
## 26 25973
## 27 48856
## 28 72422
## 29 80892
## 30 56783
## 31 4178
## 32 110068
## 33 56206
## 34 20993
## 35 7820
## 36 38345
## 37 23833
## 38 16486
## 39 81787
## 40 15694
## 41 13220
## 42 11269
## 43 4378
## 44 23129
## 45 14200
## 46 18862
## 47 125614
## 48 9787
## 49 15484
## 50 850
## 51 6090
## 52 18441
## 53 98230
## 54 128129
## 55 17010
## 56 15756
## 57 32240
## 58 10014
## 59 37158
## 60 57227
## 61 361702
## 62 3200
## 63 46638
## 64 87257
## 65 72542
## 66 52460
## 67 9572
## 68 47573
## 69 15756
## 70 8252
## 71 18290
## 72 5449
## 73 27230
## 74 57871
## 75 34414
## 76 29452
## 77 6004
## 78 27103
## 79 28294
## 80 25230
## 81 9660
## 82 19584
## 83 11349
## 84 7315
## 85 90071
## 86 20001
## 87 13203
## 88 76394
## 89 35987
## 90 86077
## 91 64589
## 92 36636
## 93 45105
## 94 49577
## 95 11076
## 96 107250
## 97 43714
## 98 24898
## 99 25447
## 100 24936
## 101 41969
## 102 67813
## 103 38960
## 104 29121
## 105 61241
## 106 56217
## 107 86574
## 108 10044
## 109 84871
## 110 21091
## 111 1031
## 112 28161
## 113 34398
## 114 65268
## 115 7891
## 116 33499
## 117 8548
## 118 45394
## 119 18582
## 120 78394
## 121 8519
## 122 29912
## 123 93751
## 124 31992
## 125 15806
## 126 17657
## 127 32685
## 128 18188
## 129 31531
## 130 9776
## 131 125524
## 132 21250
## 133 53072
## 134 12065
## 135 25371
## 136 19901
## 137 12350
## 138 9356
## 139 22616
## 140 37404
## 141 26149
## 142 29356
## 143 262947
## 144 242848
## 145 8600
## 146 8232
## 147 14412
## 148 58213
## 149 33335
## 150 23399
## 151 13563
## 152 66836
## 153 8363
## 154 10782
## 155 96169
## 156 7404
## 157 48253
## 158 18319
## 159 72904
## 160 29286
## 161 10610
## 162 98566
## 163 179956
## 164 35182
## 165 88527
## 166 41601
## 167 11339
## 168 122341
## 169 48607
## 170 19651
## 171 12162
## 172 79413
## 173 42544
## 174 8315
## 175 16330
## 176 158938
## 177 117969
## 178 34626
## 179 46768
## 180 282393
## 181 42623
## 182 66445
## 183 37292
## 184 25697
## 185 113473
## 186 34926
## 187 11308
## 188 70699
## 189 47589
## 190 30166
## 191 6074
## 192 4123
## 193 43572
## 194 376040
## 195 51586
## 196 80590- Visualize the data concisely using scatter plots and histograms. For example, you can use R functions such as
pairs(),hist(), andpairs.panels()in the R packagepsych. Briefly describe the visualization results, e.g., outliers, skewness, strong correlations, clusters, and so on.
hist(PGA$Age)
We can infer that most of the players are in age range 30-40
hist(PGA$DrivingAccuracy)
The driving accuracy of most players is between 60-65%
Some correalted scatter plots-
plot(PGA$AverageDrive,PGA$AverageWinnings,pch=2,col="purple")
plot(PGA$MoneyRank,PGA$AverageWinnings,pch=2,col="blue")
Pairs between all the variables to get an idea about the correlation between the variables
pairs (PGA,pch=20)
plot(~PGA$AverageWinnings + PGA$Age + PGA$AverageDrive + PGA$DrivingAccuracy + PGA$GreensonRegulation + PGA$AverageNumofPutts + PGA$SavePercent + PGA$NumEvents,data = PGA,pch=2,col="purple")
Box plot of average winnings
boxplot(PGA$AverageWinnings,
main = "Box plot of AverageWinnings",
xlab = "",
ylab = "AverageWinnings",
col = "orange",
border = "brown",
horizontal = TRUE,
notch = TRUE
)
- Fit a multiple linear regression to the data. Use Average winnings as the response variable and use Age, Average Drive (Yards), Driving Accuracy (percent), Greens on Regulation (%), Average # of Putts, Save Percent, and # Events as covariates. Based on the regression results, which covariate has the largest estimated slope (in absolute value)? Which covariates are important in terms of the association with the response variable?
Model1 testing all variables given
model_pga <- lm(AverageWinnings~Age+AverageDrive+DrivingAccuracy+NumEvents+AverageNumofPutts+SavePercent+GreensonRegulation, data = PGA)
summary(model_pga)##
## Call:
## lm(formula = AverageWinnings ~ Age + AverageDrive + DrivingAccuracy +
## NumEvents + AverageNumofPutts + SavePercent + GreensonRegulation,
## data = PGA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -71690 -22176 -6735 17147 247928
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 945579.88 305886.59 3.091 0.00230 **
## Age -587.13 519.32 -1.131 0.25968
## AverageDrive -94.76 567.42 -0.167 0.86755
## DrivingAccuracy -2360.57 854.02 -2.764 0.00628 **
## NumEvents -3159.22 644.24 -4.904 2.03e-06 ***
## AverageNumofPutts -694226.49 138155.99 -5.025 1.17e-06 ***
## SavePercent 1395.67 587.54 2.375 0.01853 *
## GreensonRegulation 8466.04 1303.87 6.493 7.30e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 41430 on 188 degrees of freedom
## Multiple R-squared: 0.4527, Adjusted R-squared: 0.4323
## F-statistic: 22.21 on 7 and 188 DF, p-value: < 2.2e-16model_pga$coefficients## (Intercept) Age AverageDrive
## 945579.87536 -587.12529 -94.76127
## DrivingAccuracy NumEvents AverageNumofPutts
## -2360.56944 -3159.22407 -694226.48514
## SavePercent GreensonRegulation
## 1395.66667 8466.03572model_pga$residuals## 1 2 3 4 5 6
## -7763.9747 97689.0095 18807.2522 -13861.9772 -9996.6673 -10123.5373
## 7 8 9 10 11 12
## -10593.3840 -37173.6736 -2773.3291 -18942.3176 -20839.4118 27672.1374
## 13 14 15 16 17 18
## 6716.3936 -6323.1582 2725.7362 -14906.6410 4107.5204 -3653.2150
## 19 20 21 22 23 24
## -45992.2552 8699.3642 -32095.3714 -35056.5710 -13121.5366 15249.8967
## 25 26 27 28 29 30
## -33339.7647 -24059.8661 -37421.4212 11044.5512 30938.3846 22924.2846
## 31 32 33 34 35 36
## -1724.2369 36729.1197 -1490.0068 -15622.6725 37749.1317 4362.8128
## 37 38 39 40 41 42
## -42754.7836 28856.1308 41657.2840 -10844.6481 -21974.1088 -4259.7446
## 43 44 45 46 47 48
## -9257.9100 -34539.0808 -31703.1139 -45557.6648 31286.8330 -10083.6707
## 49 50 51 52 53 54
## -11745.0047 56807.9479 18445.9081 -18721.6214 -10321.2893 59960.8572
## 55 56 57 58 59 60
## -8555.3835 -34093.4117 -38398.3564 36324.2744 -7269.3055 -5590.4775
## 61 62 63 64 65 66
## 232199.2639 47168.6227 6947.4691 -5262.6742 52121.0984 -32741.4274
## 67 68 69 70 71 72
## 23037.6870 -57314.2402 3999.9073 7676.3741 -62050.8333 29050.8108
## 73 74 75 76 77 78
## -48928.0964 -19887.4571 -3343.6799 3901.8448 51215.7962 -7146.9241
## 79 80 81 82 83 84
## -5434.5448 -8989.9523 -11286.3346 -22873.0401 -38276.7524 -26465.1308
## 85 86 87 88 89 90
## 3265.3484 -8021.1939 26322.9736 8910.1620 -19645.6910 21502.2450
## 91 92 93 94 95 96
## -24251.3500 -29365.3351 12970.9630 47369.3486 -38816.9649 -25859.1838
## 97 98 99 100 101 102
## -38830.2985 -62455.8766 9942.7136 -53967.5365 -4558.1357 31272.7256
## 103 104 105 106 107 108
## -21836.0891 -68733.7925 -7544.2305 -51916.3028 15199.1644 -5701.3114
## 109 110 111 112 113 114
## 1616.8938 -12325.7656 -2154.7779 10860.3905 23713.4904 -8858.4922
## 115 116 117 118 119 120
## 2057.3635 -45133.3295 8338.2777 -51681.1838 -28254.4647 -11216.9956
## 121 122 123 124 125 126
## 49603.4630 -24508.8090 41242.9350 -24949.7821 -64606.1785 19828.5734
## 127 128 129 130 131 132
## -21016.6829 -16156.4183 -26059.0851 -16828.4227 35569.8657 -20516.1260
## 133 134 135 136 137 138
## -595.7606 3890.8253 -30281.2924 -22037.1769 24101.4668 4118.3974
## 139 140 141 142 143 144
## -20425.7380 4537.9770 -52040.9725 15498.7974 137343.9149 95996.1593
## 145 146 147 148 149 150
## -17720.0318 -13839.7705 -19699.4015 -16311.3946 21483.9410 -18829.6178
## 151 152 153 154 155 156
## -23783.0006 -25101.2803 -20795.4087 -43026.8762 42963.4547 -10106.8893
## 157 158 159 160 161 162
## 1835.8322 -5548.3888 -11886.5715 -19900.7317 -2777.1531 25013.4668
## 163 164 165 166 167 168
## 47529.0397 -16705.4165 18814.8420 27237.8741 19402.2220 29490.7733
## 169 170 171 172 173 174
## 6413.2172 -22592.4810 -38539.1967 33810.3306 2220.9333 -27671.1562
## 175 176 177 178 179 180
## -29840.6902 41821.4188 47803.7822 -71689.6767 15280.5052 130114.7662
## 181 182 183 184 185 186
## -14835.7644 10452.0349 19998.4811 -959.9942 80010.9178 16713.9600
## 187 188 189 190 191 192
## 6158.3642 -28237.4473 5941.8382 23542.8129 -35284.3437 -18784.1037
## 193 194 195 196
## -33901.0125 247928.2363 -11605.1512 20538.1655model_pga$fitted.values## 1 2 3 4 5 6
## 31203.9747 135122.9905 35921.7478 54280.9772 26198.6673 69055.5373
## 7 8 9 10 11 12
## 52426.3840 75579.6736 27814.3291 81848.3176 41198.4118 -11945.1374
## 13 14 15 16 17 18
## -690.3936 58117.1582 16655.2638 60387.6410 33067.4796 39971.2150
## 19 20 21 22 23 24
## 61430.2552 31938.6358 59075.3714 73358.5710 33283.5366 -8585.8967
## 25 26 27 28 29 30
## 71890.7647 50032.8661 86277.4212 61377.4488 49953.6154 33858.7154
## 31 32 33 34 35 36
## 5902.2369 73338.8803 57696.0068 36615.6725 -29929.1317 33982.1872
## 37 38 39 40 41 42
## 66587.7836 -12370.1308 40129.7160 26538.6481 35194.1088 15528.7446
## 43 44 45 46 47 48
## 13635.9100 57668.0808 45903.1139 64419.6648 94327.1670 19870.6707
## 49 50 51 52 53 54
## 27229.0047 -55957.9479 -12355.9081 37162.6214 108551.2893 68168.1428
## 55 56 57 58 59 60
## 25565.3835 49849.4117 70638.3564 -26310.2744 44427.3055 62817.4775
## 61 62 63 64 65 66
## 129502.7361 -43968.6227 39690.5309 92519.6742 20420.9016 85201.4274
## 67 68 69 70 71 72
## -13465.6870 104887.2402 11756.0927 575.6259 80340.8333 -23601.8108
## 73 74 75 76 77 78
## 76158.0964 77758.4571 37757.6799 25550.1552 -45211.7962 34249.9241
## 79 80 81 82 83 84
## 33728.5448 34219.9523 20946.3346 42457.0401 49625.7524 33780.1308
## 85 86 87 88 89 90
## 86805.6516 28022.1939 -13119.9736 67483.8380 55632.6910 64574.7550
## 91 92 93 94 95 96
## 88840.3500 66001.3351 32134.0370 2207.6514 49892.9649 133109.1838
## 97 98 99 100 101 102
## 82544.2985 87353.8766 15504.2864 78903.5365 46527.1357 36540.2744
## 103 104 105 106 107 108
## 60796.0891 97854.7925 68785.2305 108133.3028 71374.8356 15745.3114
## 109 110 111 112 113 114
## 83254.1062 33416.7656 3185.7779 17300.6095 10684.5096 74126.4922
## 115 116 117 118 119 120
## 5833.6365 78632.3295 209.7223 97075.1838 46836.4647 89610.9956
## 121 122 123 124 125 126
## -41084.4630 54420.8090 52508.0650 56941.7821 80412.1785 -2171.5734
## 127 128 129 130 131 132
## 53701.6829 34344.4183 57590.0851 26604.4227 89954.1343 41766.1260
## 133 134 135 136 137 138
## 53667.7606 8174.1747 55652.2924 41938.1769 -11751.4668 5237.6026
## 139 140 141 142 143 144
## 43041.7380 32866.0230 78189.9725 13857.2026 125603.0851 146851.8407
## 145 146 147 148 149 150
## 26320.0318 22071.7705 34111.4015 74524.3946 11851.0590 42228.6178
## 151 152 153 154 155 156
## 37346.0006 91937.2803 29158.4087 53808.8762 53205.5453 17510.8893
## 157 158 159 160 161 162
## 46417.1678 23867.3888 84790.5715 49186.7317 13387.1531 73552.5332
## 163 164 165 166 167 168
## 132426.9603 51887.4165 69712.1580 14363.1259 -8063.2220 92850.2267
## 169 170 171 172 173 174
## 42193.7828 42243.4810 50701.1967 45602.6694 40323.0667 35986.1562
## 175 176 177 178 179 180
## 46170.6902 117116.5812 70165.2178 106315.6767 31487.4948 152278.2338
## 181 182 183 184 185 186
## 57458.7644 55992.9651 17293.5189 26656.9942 33462.0822 18212.0400
## 187 188 189 190 191 192
## 5149.6358 98936.4473 41647.1618 6623.1871 41358.3437 22907.1037
## 193 194 195 196
## 77473.0125 128111.7637 63191.1512 60051.8345summary(model_pga)$coef## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 945579.87536 305886.5949 3.0912760 2.296050e-03
## Age -587.12529 519.3241 -1.1305567 2.596820e-01
## AverageDrive -94.76127 567.4194 -0.1670039 8.675464e-01
## DrivingAccuracy -2360.56944 854.0207 -2.7640660 6.276772e-03
## NumEvents -3159.22407 644.2424 -4.9037814 2.026906e-06
## AverageNumofPutts -694226.48514 138155.9949 -5.0249465 1.167423e-06
## SavePercent 1395.66667 587.5388 2.3754460 1.853368e-02
## GreensonRegulation 8466.03572 1303.8682 6.4930148 7.300592e-10Here DrivingAccuracy,GreensonRegulation,AverageNumofPutts,NumEvents and Age have the highest slopes and they are the major factors that affect the reponse variable.
reduced = lm(PGA$AverageWinnings ~ PGA$MoneyRank + PGA$NumEvents, data=PGA) # Reducedodel
full = model_pga # full model
anova(reduced, model_pga)## Warning in anova.lmlist(object, ...): models with response
## '"AverageWinnings"' removed because response differs from model 1## Analysis of Variance Table
##
## Response: PGA$AverageWinnings
## Df Sum Sq Mean Sq F value Pr(>F)
## PGA$MoneyRank 1 2.9254e+11 2.9254e+11 220.083 < 2.2e-16 ***
## PGA$NumEvents 1 4.0588e+10 4.0588e+10 30.535 1.052e-07 ***
## Residuals 193 2.5654e+11 1.3292e+09
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Here P value is less than 0.05 hence we do not reject the null hypothesis.
- Based on the fitted regression, is AverageDrive a covariate with statistically significant nonzero slope? State your conclusion and reasons.
summary(model_pga)##
## Call:
## lm(formula = AverageWinnings ~ Age + AverageDrive + DrivingAccuracy +
## NumEvents + AverageNumofPutts + SavePercent + GreensonRegulation,
## data = PGA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -71690 -22176 -6735 17147 247928
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 945579.88 305886.59 3.091 0.00230 **
## Age -587.13 519.32 -1.131 0.25968
## AverageDrive -94.76 567.42 -0.167 0.86755
## DrivingAccuracy -2360.57 854.02 -2.764 0.00628 **
## NumEvents -3159.22 644.24 -4.904 2.03e-06 ***
## AverageNumofPutts -694226.49 138155.99 -5.025 1.17e-06 ***
## SavePercent 1395.67 587.54 2.375 0.01853 *
## GreensonRegulation 8466.04 1303.87 6.493 7.30e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 41430 on 188 degrees of freedom
## Multiple R-squared: 0.4527, Adjusted R-squared: 0.4323
## F-statistic: 22.21 on 7 and 188 DF, p-value: < 2.2e-16Based on the summary the p value of averagedrive is 0.87 which greate than 0.05 and hence we conclude that it has a zero slope.
- If you run a simple linear regression of
lm(AverageWinnings ~ AverageDrive, data=d), is AverageDrive a covariate with statistically significant nonzero slope in this case? State your conclusion and reasons.
model_pga_1 <- lm(PGA$AverageWinnings ~ PGA$AverageDrive,data = PGA)
summary(model_pga_1)##
## Call:
## lm(formula = PGA$AverageWinnings ~ PGA$AverageDrive, data = PGA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -62001 -28630 -13234 10847 311571
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -331133.4 134365.6 -2.464 0.01459 *
## PGA$AverageDrive 1315.2 467.7 2.812 0.00543 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 54040 on 194 degrees of freedom
## Multiple R-squared: 0.03916, Adjusted R-squared: 0.03421
## F-statistic: 7.907 on 1 and 194 DF, p-value: 0.005429In this case AverageDrive is a covariate with significant non zero slope as the p value is way less than 0.05.This specific regressor affects the response variable according to the t-test.
- If you run a multiple linear regression similar to the one in question 3 except you remove Driving Accuracy as a covariate, is AverageDrive a significant covariate with nonzero slope in this case? Are these results consistent or contradicted with the results in questions 4 and 5? State your conclusion and reasons.
model_pga_6 <- lm(PGA$AverageWinnings ~ PGA$Age + PGA$AverageDrive + PGA$GreensonRegulation + PGA$AverageNumofPutts + PGA$SavePercent + PGA$MoneyRank + PGA$NumEvents,data = PGA)
summary(model_pga_6)##
## Call:
## lm(formula = PGA$AverageWinnings ~ PGA$Age + PGA$AverageDrive +
## PGA$GreensonRegulation + PGA$AverageNumofPutts + PGA$SavePercent +
## PGA$MoneyRank + PGA$NumEvents, data = PGA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -50234 -19322 -6841 9506 260123
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 82492.68 266149.64 0.310 0.75694
## PGA$Age -25.19 449.10 -0.056 0.95533
## PGA$AverageDrive 1032.87 350.65 2.946 0.00363 **
## PGA$GreensonRegulation 727.16 1146.28 0.634 0.52661
## PGA$AverageNumofPutts -151065.82 136788.06 -1.104 0.27084
## PGA$SavePercent 537.86 514.19 1.046 0.29689
## PGA$MoneyRank -536.39 61.88 -8.668 2.02e-15 ***
## PGA$NumEvents -3128.68 552.88 -5.659 5.61e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 35730 on 188 degrees of freedom
## Multiple R-squared: 0.5931, Adjusted R-squared: 0.5779
## F-statistic: 39.14 on 7 and 188 DF, p-value: < 2.2e-16If we remove driving accuracy as a covariate it is noticed that AverageDrive acts as a significant covariate in the model which differs from the result obtained in 3.
- Based on regression results, is the fitted regression model in question 3 a significant model (at least one nonzero slope)? What a bout the fitted regression models in question 5 and 6? State your conclusion and reasons.
Based on the regression analysis the model in question 3 is overfitted for example since drivingaccuracy and averagedrive are strongly related to each other the impact of either of those covariates can not be observed if both are present in the model.
8.1 Using the fitted regression in question 3, obtain the prediction of the response variable for a new player with Age = 35, AverageDrive = 287, DrivingAccuracy = 64, GreensonRegulation = 64.9, AverageNumofPutts = 1.778, SavePercent = 48, NumEvents = 26. Provide a prediction interval and explain what it means.
observations_for_pred_1 <- data.frame(Age = 35, AverageDrive = 287, DrivingAccuracy = 64, GreensonRegulation = 64.9, AverageNumofPutts = 1.778, SavePercent = 48, NumEvents = 26)
y_pred_data8 <- predict(model_pga, newdata = observations_for_pred_1, interval = 'confidence', level = 0.95, type = 'response')
y_pred_data8## fit lwr upr
## 1 46720.76 40657.8 52783.72This means that 95% of predicted data lies between lower bound and upper bound.
8.2 Similarly, make another prediction for the case of Age = 42, AverageDrive = 295, DrivingAccuracy = 69, GreensonRegulation = 67.7, AverageNumofPutts = 1.80, SavePercent = 54, NumEvents = 30.
observations_for_pred_2=data.frame(Age=c(42), AverageDrive=c(295),DrivingAccuracy=c(69),
GreensonRegulation= c(67.7),AverageNumofPutts = c(1.80), SavePercent =c(54) , NumEvents= c(30))
observations_for_pred_2## Age AverageDrive DrivingAccuracy GreensonRegulation AverageNumofPutts
## 1 42 295 69 67.7 1.8
## SavePercent NumEvents
## 1 54 30y_pred_8_2 <- predict(model_pga, newdata = observations_for_pred_2, interval = 'confidence', level = 0.95, type = 'response')
y_pred_8_2## fit lwr upr
## 1 34218.97 14565.55 53872.398.3 Make a third prediction for the case of Age = 45, AverageDrive = 320, DrivingAccuracy = 70, GreensonRegulation = 67.7, AverageNumofPutts = 1.80, SavePercent = 54, NumEvents = 30.
observations_for_pred_3=data.frame(Age=c(45), AverageDrive=c(320),DrivingAccuracy=c(70),
GreensonRegulation= c(67.7),AverageNumofPutts = c(1.80), SavePercent =c(54) , NumEvents= c(30))
observations_for_pred_3## Age AverageDrive DrivingAccuracy GreensonRegulation AverageNumofPutts
## 1 45 320 70 67.7 1.8
## SavePercent NumEvents
## 1 54 30y_pred_8_3 <- predict(model_pga, newdata = observations_for_pred_3, interval = 'confidence', level = 0.95, type = 'response')
y_pred_8_3## fit lwr upr
## 1 27727.99 -17967.85 73423.83- Compare the predictions from previous questions, what do you observe? For example, which prediction interval is wider? which prediction dosen’t make sense? Among these predictions, which one is extrapolation? State your conclusion and reasons.
y_pred_data8## fit lwr upr
## 1 46720.76 40657.8 52783.72y_pred_8_2## fit lwr upr
## 1 34218.97 14565.55 53872.39y_pred_8_3## fit lwr upr
## 1 27727.99 -17967.85 73423.83The range of Average Winning in prediction 1 is the least and in prediction 3 is the highest also it doesn’t make sense since average winning cannot have a negative value and in our 3 prediction in the lower bound we have got -17967.
model_pga <- lm(AverageWinnings~Age+AverageDrive+DrivingAccuracy+NumEvents+AverageNumofPutts+SavePercent+GreensonRegulation, data = PGA)
cbind(PGA, leverage=hatvalues(model_pga))## Name Age AverageDrive DrivingAccuracy GreensonRegulation
## 1 Aaron Baddeley 23 288.0 53.1 58.2
## 2 Adam Scott 24 295.4 57.7 65.6
## 3 Alex Cejka 34 285.8 64.2 63.8
## 4 Andre Stolz 34 297.9 59.0 63.0
## 5 Arjun Atwal 31 289.4 60.5 62.5
## 6 Arron Oberholser 29 284.6 68.8 67.0
## 7 Bart Bryant 42 282.1 74.2 68.9
## 8 Ben Crane 28 283.8 64.4 64.2
## 9 Ben Curtis 27 282.1 64.3 63.4
## 10 Bernhard Langer 47 282.2 62.6 65.3
## 11 Billy Andrade 40 283.5 59.7 64.4
## 12 Billy Mayfair 38 285.2 70.1 66.0
## 13 Blaine McCalliste 46 280.9 63.4 63.6
## 14 Bo Van Pelt 29 294.4 65.1 67.7
## 15 Bob Burns 36 276.1 67.2 62.3
## 16 Bob Estes 38 278.2 63.9 64.2
## 17 Bob Tway 45 278.2 63.7 64.8
## 18 Brad Faxon 43 273.7 61.6 61.4
## 19 Brenden Pappas 34 298.9 50.1 63.0
## 20 Brent Geiberger 36 291.3 64.8 64.9
## 21 Brett Quigley 35 294.3 57.2 65.8
## 22 Brian Bateman 31 292.2 66.1 66.6
## 23 Brian Gay 33 279.7 64.8 61.5
## 24 Brian Kortan 33 292.4 63.0 62.0
## 25 Briny Baird 32 289.4 65.0 70.6
## 26 Cameron Beckman 34 291.2 66.5 67.0
## 27 Carl Pettersson 27 290.8 61.1 64.5
## 28 Carlos Franco 39 290.6 59.3 67.8
## 29 Chad Campbell 30 288.0 63.9 67.7
## 30 Charles Howell II 25 288.5 64.3 66.1
## 31 Chris Couch 31 302.1 56.2 60.8
## 32 Chris DiMarco 36 277.3 68.6 67.1
## 33 Chris Riley 31 277.3 61.8 62.5
## 34 Chris Smith 35 304.0 59.5 70.4
## 35 Cliff Kresge 36 283.4 62.8 60.5
## 36 Corey Pavin 45 268.2 71.9 62.1
## 37 Craig Barlow 32 291.0 67.8 67.7
## 38 Craig Bowden 36 270.8 76.1 62.9
## 39 Craig Parry 38 276.9 63.5 60.7
## 40 Craig Perks 37 289.4 54.4 63.0
## 41 D.J. Brigman 28 290.7 63.9 65.8
## 42 Dan Forsman 46 281.9 64.3 63.1
## 43 Dan Olsen 37 296.0 51.5 60.7
## 44 Daniel Chopra 30 295.9 58.6 63.9
## 45 Danny Briggs 44 283.8 65.5 68.1
## 46 Danny Ellis 34 286.7 62.9 63.9
## 47 Darren Clarke 36 289.0 62.3 64.0
## 48 David Branshaw 35 285.8 66.6 66.2
## 49 David Frost 45 273.6 66.1 63.7
## 50 David Gossett 25 283.8 54.4 54.7
## 51 David Morland IV 35 272.8 69.4 60.1
## 52 David Peoples 44 281.3 63.7 64.0
## 53 David Toms 37 285.3 63.4 68.5
## 54 Davis Love III 40 300.1 60.1 63.4
## 55 Dean Wilson 34 282.2 63.0 62.0
## 56 Deane Pappas 37 295.3 60.1 63.4
## 57 Dennis Paulson 42 300.1 60.4 63.0
## 58 Dicky Pride 35 280.5 68.3 62.6
## 59 Dudley Hart 36 285.6 63.1 64.2
## 60 Duffy Waldorf 42 285.4 68.6 69.0
## 61 Ernie Els 35 298.0 55.5 65.6
## 62 Esteban Toledo 42 275.2 67.8 60.1
## 63 Frank Lickliter I 35 287.3 66.6 64.8
## 64 Fred Couples 45 294.5 58.8 66.3
## 65 Fred Funk 48 271.9 77.2 65.5
## 66 Fredrik Jacobson 30 287.9 55.6 64.4
## 67 Gene Sauers 42 280.2 66.2 62.0
## 68 Geoff Ogilvy 27 303.3 63.2 66.9
## 69 Glen Day 39 286.1 65.6 61.8
## 70 Grant Waite 40 288.3 59.4 62.8
## 71 Greg Chalmers 31 287.3 61.7 60.6
## 72 Guy Boros 40 281.1 66.3 60.3
## 73 Hank Kuehne 29 314.4 49.9 62.9
## 74 Harrison Frazar 33 298.8 64.3 65.2
## 75 Heath Slocum 30 280.1 71.3 67.1
## 76 Hidemichi Tanaka 33 281.0 72.3 66.1
## 77 Hirofumi Miyase 33 279.7 70.6 60.4
## 78 Hunter Mahan 22 293.0 62.2 63.7
## 79 J.J. Henry 29 301.3 64.5 66.6
## 80 J.L. Lewis 44 288.3 65.5 65.8
## 81 J.P. Hayes 39 280.7 67.7 63.6
## 82 Jason Bohn 31 293.3 65.8 66.8
## 83 Jason Dufner 27 290.7 62.5 65.3
## 84 Jay Delsing 44 288.8 62.1 64.5
## 85 Jay Haas 51 274.5 65.4 66.9
## 86 Jay Williamson 37 288.1 69.3 65.4
## 87 Jeff Brehaut 41 290.9 71.3 66.2
## 88 Jeff Maggert 40 281.2 69.2 67.5
## 89 Jeff Sluman 47 279.6 67.9 68.8
## 90 Jerry Kelly 38 278.1 70.4 68.0
## 91 Jesper Parnevik 39 287.9 60.0 66.1
## 92 Joe Durant 40 287.2 75.1 73.3
## 93 Joe Ogilvie 30 288.8 61.3 62.5
## 94 Joey Sindelar 46 291.5 65.6 67.6
## 95 John Cook 47 270.2 73.4 66.5
## 96 John Daly 38 306.0 53.0 66.4
## 97 John Huston 43 286.4 65.9 68.8
## 98 John Riegger 41 285.0 61.4 67.1
## 99 John Rollins 29 286.7 69.1 62.5
## 100 John Senden 33 296.6 65.6 70.5
## 101 Jonathan Byrd 26 295.8 62.1 61.4
## 102 Jonathan Kaye 34 290.9 64.7 66.5
## 103 Jose Coceres 41 279.4 74.3 63.3
## 104 Jose Maria Olazab 38 277.7 57.0 62.5
## 105 Justin Leonard 32 282.9 67.4 66.1
## 106 Justin Rose 24 290.7 61.5 67.7
## 107 K.J. Choi 34 285.0 61.2 65.9
## 108 Ken Duke 35 284.3 59.0 61.9
## 109 Kenny Perry 44 295.9 62.5 68.6
## 110 Kent Jones 37 286.4 69.8 67.4
## 111 Kevin Muncrief 28 290.7 56.1 59.1
## 112 Kevin Na 21 280.1 68.7 63.4
## 113 Kevin Sutherland 40 286.1 67.1 63.0
## 114 Kirk Triplett 42 279.1 72.1 67.7
## 115 Kris Cox 31 299.1 59.0 62.0
## 116 Lee Janzen 40 286.1 62.2 67.8
## 117 Len Mattiace 37 278.0 67.2 59.1
## 118 Loren Roberts 49 269.1 69.8 66.6
## 119 Lucas Glover 25 303.4 64.4 67.5
## 120 Luke Donald 27 279.8 69.6 69.4
## 121 Mark Brooks 43 273.8 66.8 59.8
## 122 Mark Calcavecchia 44 291.3 64.5 64.1
## 123 Mark Hensby 33 284.6 67.7 63.3
## 124 Mark O'Meara 47 272.9 67.0 62.5
## 125 Mark Wilson 30 282.1 72.0 68.9
## 126 Mathias Gronberg 34 292.1 58.5 63.2
## 127 Matt Gogel 33 285.6 68.5 63.2
## 128 Matt Kuchar 26 287.3 64.4 65.3
## 129 Michael Allen 45 291.1 56.5 64.2
## 130 Mike Heinen 37 305.2 62.7 62.8
## 131 Mike Weir 34 282.1 64.1 65.1
## 132 Neal Lancaster 42 291.6 57.6 65.2
## 133 Nick Price 47 272.8 68.3 59.1
## 134 Niclas Fasth 32 289.1 61.6 61.5
## 135 Notah Begay III 32 285.8 69.5 66.2
## 136 Olin Browne 45 281.9 73.5 68.9
## 137 Omar Uresti 36 272.2 73.1 62.6
## 138 Pat Bates 35 275.5 69.9 66.3
## 139 Pat Perez 28 291.4 65.0 66.2
## 140 Patrick Sheehan 35 290.3 63.0 64.9
## 141 Paul Azinger 44 285.1 57.6 63.0
## 142 Peter Lonard 37 291.4 61.5 62.9
## 143 Phil Mickelson 34 295.4 62.9 69.5
## 144 Retief Goosen 35 294.2 62.5 68.7
## 145 Rich Barcelo 29 293.1 59.0 64.4
## 146 Rich Beem 34 296.7 61.7 63.7
## 147 Richard S. Johnso 28 283.4 69.3 64.5
## 148 Robert Allenby 33 294.9 65.0 70.3
## 149 Robert Damron 32 277.2 70.0 63.8
## 150 Robert Gamez 36 288.1 65.2 65.7
## 151 Rocco Mediate 41 283.4 69.9 65.5
## 152 Rod Pampling 35 292.1 59.8 66.1
## 153 Roger Tambellini 29 297.8 59.2 63.2
## 154 Roland Thatcher 27 293.1 64.8 68.0
## 155 Rory Sabbatini 28 292.2 59.2 64.9
## 156 Russ Cochran 46 280.3 65.4 63.6
## 157 Ryan Palmer 28 295.6 63.2 65.5
## 158 Scott Hend 31 312.6 54.1 62.7
## 159 Scott Hoch 49 280.4 68.8 68.6
## 160 Scott McCarron 39 294.1 64.9 65.4
## 161 Scott Simpson 49 278.7 70.7 62.0
## 162 Scott Verplank 40 278.0 77.1 68.5
## 163 Sergio Garcia 24 295.1 58.5 70.8
## 164 Shaun Micheel 35 287.5 63.1 67.0
## 165 Shigeki Maruyama 35 280.1 63.7 64.6
## 166 Skip Kendall 40 281.3 68.2 62.7
## 167 Spike McRoy 36 281.5 67.1 64.9
## 168 Stephen Ames 40 287.9 65.0 68.4
## 169 Stephen Leaney 35 282.3 64.8 64.8
## 170 Steve Allan 31 301.2 59.3 66.8
## 171 Steve Elkington 42 287.1 68.2 66.1
## 172 Steve Flesch 37 279.9 65.8 65.8
## 173 Steve Lowery 44 288.8 58.3 63.9
## 174 Steve Pate 43 283.5 64.8 65.1
## 175 Steve Stricker 37 281.8 52.7 59.3
## 176 Stewart Cink 31 290.5 58.7 66.4
## 177 Stuart Appleby 33 293.2 62.5 65.1
## 178 Tag Ridings 30 301.0 56.4 64.2
## 179 Ted Purdy 31 289.2 70.1 67.4
## 180 Tiger Woods 28 301.9 56.1 66.9
## 181 Tim Clark 28 278.8 72.0 65.8
## 182 Tim Herron 34 293.8 58.0 65.1
## 183 Tim Petrovic 38 287.2 63.6 63.4
## 184 Todd Fischer 35 280.1 61.7 63.9
## 185 Todd Hamilton 39 283.5 58.7 62.7
## 186 Tom Byrum 44 272.6 74.7 63.7
## 187 Tom Carter 36 296.5 55.1 62.9
## 188 Tom Lehman 45 287.2 69.7 71.4
## 189 Tom Pernice, Jr. 45 286.0 68.2 66.8
## 190 Tommy Armour III 45 290.5 62.4 64.3
## 191 Tommy Tolles 38 287.8 54.0 61.9
## 192 Tripp Isenhour 36 286.2 61.7 62.1
## 193 Vaughn Taylor 28 292.5 65.1 68.4
## 194 Vijay Singh 41 300.8 60.4 73.0
## 195 Woody Austin 40 291.3 63.3 68.1
## 196 Zach Johnson 28 285.6 71.9 67.9
## AverageNumofPutts SavePercent MoneyRank NumEvents TotalWinnings
## 1 1.767 50.9 123 27 632878
## 2 1.757 59.3 7 16 3724984
## 3 1.795 50.7 54 24 1313484
## 4 1.787 47.7 101 20 808373
## 5 1.766 43.5 146 30 486053
## 6 1.780 50.9 52 23 1355433
## 7 1.777 40.4 80 23 962167
## 8 1.740 53.8 75 27 1036958
## 9 1.809 42.2 141 20 500818
## 10 1.777 47.7 83 15 943589
## 11 1.773 50.5 124 31 631143
## 12 1.829 49.7 140 32 503252
## 13 1.808 42.3 198 27 162701
## 14 1.768 43.1 39 30 1553826
## 15 1.769 51.9 130 30 581421
## 16 1.756 44.8 74 23 1046064
## 17 1.788 46.9 79 26 966554
## 18 1.749 52.9 76 28 1016899
## 19 1.759 55.6 137 34 524907
## 20 1.775 49.3 57 31 1259780
## 21 1.780 52.7 97 31 836382
## 22 1.766 48.5 86 24 919256
## 23 1.737 52.2 122 32 645196
## 24 1.844 52.1 200 24 159939
## 25 1.780 42.1 69 30 1156517
## 26 1.771 47.3 107 30 779189
## 27 1.733 52.9 51 28 1367963
## 28 1.798 47.1 29 27 1955395
## 29 1.799 46.1 24 28 2264985
## 30 1.802 48.9 33 30 1703485
## 31 1.796 34.2 217 24 100283
## 32 1.752 50.6 12 27 2971843
## 33 1.766 51.6 56 23 1292732
## 34 1.811 33.2 115 33 692785
## 35 1.802 45.7 175 33 258061
## 36 1.762 57.4 89 23 881938
## 37 1.787 52.9 128 25 595820
## 38 1.791 53.1 143 30 494569
## 39 1.797 55.3 55 16 1308586
## 40 1.815 50.5 152 27 423749
## 41 1.810 49.6 160 27 356943
## 42 1.811 62.3 165 28 315540
## 43 1.778 41.4 207 31 135731
## 44 1.748 52.2 108 33 763253
## 45 1.792 45.6 157 28 397606
## 46 1.757 54.0 144 26 490414
## 47 1.745 46.2 28 16 2009819
## 48 1.796 43.2 169 30 293617
## 49 1.802 60.1 155 26 402589
## 50 1.847 47.7 245 25 21250
## 51 1.786 49.2 197 27 164435
## 52 1.779 50.0 147 26 479465
## 53 1.758 55.7 22 24 2357531
## 54 1.753 51.9 10 24 3075094
## 55 1.755 52.4 133 33 561341
## 56 1.776 44.1 161 22 346632
## 57 1.774 61.1 117 21 677035
## 58 1.842 41.5 184 23 230329
## 59 1.784 45.6 92 23 854638
## 60 1.770 41.3 46 26 1487912
## 61 1.740 47.9 2 16 5787225
## 62 1.795 51.8 211 36 115185
## 63 1.759 40.8 58 27 1259235
## 64 1.781 47.1 50 16 1396109
## 65 1.769 54.6 25 29 2103732
## 66 1.750 43.9 59 24 1259048
## 67 1.788 42.7 170 30 287150
## 68 1.752 61.0 61 26 1236909
## 69 1.749 47.5 138 33 519935
## 70 1.808 43.8 180 29 239319
## 71 1.726 57.7 156 22 402380
## 72 1.810 42.5 208 24 130783
## 73 1.765 59.3 99 30 816889
## 74 1.748 51.7 48 25 1446765
## 75 1.788 54.3 72 31 1066838
## 76 1.780 41.6 104 27 795206
## 77 1.823 43.9 199 27 162120
## 78 1.775 45.8 100 30 813089
## 79 1.788 41.7 93 30 848823
## 80 1.769 49.1 102 32 807344
## 81 1.776 46.2 174 27 260816
## 82 1.778 42.0 131 29 567931
## 83 1.790 52.5 164 28 317770
## 84 1.797 51.3 193 26 190184
## 85 1.758 56.1 27 23 2071626
## 86 1.776 56.3 120 33 660038
## 87 1.810 46.4 149 34 448914
## 88 1.789 49.5 43 20 1527883
## 89 1.777 45.9 77 28 1007635
## 90 1.763 52.8 17 29 2496223
## 91 1.759 51.9 40 24 1550135
## 92 1.798 41.7 81 26 952548
## 93 1.755 47.7 49 32 1443363
## 94 1.811 35.1 41 31 1536882
## 95 1.789 50.0 189 19 210448
## 96 1.736 54.8 21 22 2359507
## 97 1.804 55.9 90 20 874280
## 98 1.773 38.9 153 17 423263
## 99 1.764 46.1 109 29 737957
## 100 1.791 50.6 114 28 698203
## 101 1.760 56.0 70 27 1133166
## 102 1.803 42.2 34 25 1695333
## 103 1.754 61.7 106 20 779197
## 104 1.745 51.2 142 17 495051
## 105 1.769 54.0 42 25 1531023
## 106 1.762 49.4 62 22 1236765
## 107 1.770 45.8 26 24 2077775
## 108 1.785 47.9 166 30 301308
## 109 1.776 45.8 30 23 1952043
## 110 1.776 46.5 119 32 674910
## 111 1.823 47.0 244 21 21660
## 112 1.775 49.7 87 32 901159
## 113 1.799 53.7 85 27 928759
## 114 1.752 49.3 38 24 1566426
## 115 1.808 41.9 190 26 205171
## 116 1.781 51.5 96 25 837482
## 117 1.792 60.2 188 25 213707
## 118 1.738 59.3 78 22 998677
## 119 1.797 48.4 134 30 557454
## 120 1.791 52.2 35 21 1646267
## 121 1.796 43.5 173 31 264076
## 122 1.765 52.3 112 24 717876
## 123 1.738 54.0 15 29 2718765
## 124 1.768 53.7 135 17 543866
## 125 1.788 48.1 167 19 300317
## 126 1.811 43.9 132 32 565013
## 127 1.749 53.3 98 25 817117
## 128 1.795 46.6 139 28 509258
## 129 1.763 48.9 88 28 882872
## 130 1.790 31.8 195 17 166185
## 131 1.749 53.7 14 22 2761537
## 132 1.781 52.4 113 33 701240
## 133 1.746 58.7 103 15 796086
## 134 1.806 40.7 172 22 265424
## 135 1.771 44.2 129 23 583537
## 136 1.775 47.8 127 30 597034
## 137 1.813 56.8 163 28 345798
## 138 1.803 45.0 168 32 299385
## 139 1.780 51.1 111 32 723724
## 140 1.759 43.0 63 33 1234345
## 141 1.745 51.7 126 23 601438
## 142 1.819 47.1 118 23 675189
## 143 1.759 56.4 3 22 5784823
## 144 1.743 54.6 6 16 3885573
## 145 1.797 35.3 186 26 223597
## 146 1.814 56.4 183 28 230499
## 147 1.758 50.8 148 32 461184
## 148 1.798 46.5 44 26 1513537
## 149 1.792 49.4 84 28 933389
## 150 1.767 48.3 110 31 725369
## 151 1.800 45.0 176 19 257692
## 152 1.763 58.9 31 26 1737725
## 153 1.796 49.3 181 28 234164
## 154 1.811 42.3 177 23 247987
## 155 1.792 48.9 16 26 2500397
## 156 1.791 45.7 194 25 185108
## 157 1.768 51.3 37 33 1592344
## 158 1.806 49.0 136 29 531263
## 159 1.786 50.0 60 17 1239360
## 160 1.772 49.7 105 27 790720
## 161 1.800 51.2 192 18 190986
## 162 1.743 47.1 20 24 2365594
## 163 1.790 48.1 9 18 3239216
## 164 1.793 47.2 82 27 949919
## 165 1.746 49.4 23 26 2301693
## 166 1.767 48.3 64 29 1206440
## 167 1.810 45.8 159 33 374187
## 168 1.755 54.5 8 27 3303207
## 169 1.805 55.3 68 24 1166560
## 170 1.795 48.9 121 33 648480
## 171 1.796 49.0 179 20 243239
## 172 1.763 49.0 18 31 2461789
## 173 1.769 43.8 66 28 1191245
## 174 1.797 48.5 191 24 199569
## 175 1.745 48.8 151 27 440906
## 176 1.723 56.1 5 28 4450272
## 177 1.764 51.4 13 25 2949234
## 178 1.751 49.4 125 18 623262
## 179 1.769 46.6 36 35 1636876
## 180 1.724 53.5 4 19 5365472
## 181 1.764 53.3 71 26 1108190
## 182 1.787 47.8 32 26 1727577
## 183 1.776 49.2 65 32 1193355
## 184 1.769 46.7 94 33 847996
## 185 1.774 44.6 11 27 3063780
## 186 1.776 52.5 91 25 873140
## 187 1.790 42.7 158 35 395782
## 188 1.778 44.0 53 19 1343278
## 189 1.778 55.4 47 31 1475273
## 190 1.807 43.6 95 28 844636
## 191 1.776 43.5 201 25 151852
## 192 1.795 43.8 218 22 90699
## 193 1.761 41.9 67 27 1176435
## 194 1.757 50.9 1 29 10905167
## 195 1.775 46.9 45 29 1495982
## 196 1.751 45.3 19 30 2417685
## AverageWinnings leverage
## 1 23440 0.06765323
## 2 232812 0.07569896
## 3 54729 0.01220045
## 4 40419 0.03121853
## 5 16202 0.02459782
## 6 58932 0.02556188
## 7 41833 0.04866769
## 8 38406 0.03167885
## 9 25041 0.05470490
## 10 62906 0.04770781
## 11 20359 0.02889132
## 12 15727 0.04591929
## 13 6026 0.03498565
## 14 51794 0.02667187
## 15 19381 0.02271467
## 16 45481 0.03069602
## 17 37175 0.02627037
## 18 36318 0.04715286
## 19 15438 0.07102347
## 20 40638 0.01489144
## 21 26980 0.03000198
## 22 38302 0.01733760
## 23 20162 0.04470833
## 24 6664 0.06968808
## 25 38551 0.04239473
## 26 25973 0.01504469
## 27 48856 0.03469607
## 28 72422 0.03269389
## 29 80892 0.02641874
## 30 56783 0.03429403
## 31 4178 0.07928766
## 32 110068 0.02636335
## 33 56206 0.03652633
## 34 20993 0.08466298
## 35 7820 0.03123447
## 36 38345 0.04603761
## 37 23833 0.02329137
## 38 16486 0.04828451
## 39 81787 0.05598839
## 40 15694 0.05224930
## 41 13220 0.02766524
## 42 11269 0.07774519
## 43 4378 0.05698599
## 44 23129 0.03404614
## 45 14200 0.02734458
## 46 18862 0.01264314
## 47 125614 0.04822055
## 48 9787 0.01636739
## 49 15484 0.06007581
## 50 850 0.13431286
## 51 6090 0.03620472
## 52 18441 0.01579862
## 53 98230 0.03049683
## 54 128129 0.04947630
## 55 17010 0.03044149
## 56 15756 0.02572464
## 57 32240 0.08421527
## 58 10014 0.05704812
## 59 37158 0.01113865
## 60 57227 0.03251449
## 61 361702 0.05567596
## 62 3200 0.05574320
## 63 46638 0.03245205
## 64 87257 0.05010584
## 65 72542 0.05508160
## 66 52460 0.05025898
## 67 9572 0.02951163
## 68 47573 0.07161132
## 69 15756 0.04733781
## 70 8252 0.02634473
## 71 18290 0.05747809
## 72 5449 0.03961344
## 73 27230 0.10355671
## 74 57871 0.04061021
## 75 34414 0.03964263
## 76 29452 0.03332022
## 77 6004 0.05355895
## 78 27103 0.03332971
## 79 28294 0.03857441
## 80 25230 0.02897816
## 81 9660 0.01388453
## 82 19584 0.02233485
## 83 11349 0.02317171
## 84 7315 0.02318974
## 85 90071 0.05621779
## 86 20001 0.03836965
## 87 13203 0.05535820
## 88 76394 0.02380104
## 89 35987 0.03742927
## 90 86077 0.02633955
## 91 64589 0.01821352
## 92 36636 0.06807228
## 93 45105 0.02748229
## 94 49577 0.06552961
## 95 11076 0.04554186
## 96 107250 0.06629376
## 97 43714 0.05422951
## 98 24898 0.05921234
## 99 25447 0.04149314
## 100 24936 0.03642065
## 101 41969 0.04744006
## 102 67813 0.01843541
## 103 38960 0.07627636
## 104 29121 0.06870084
## 105 61241 0.01718929
## 106 56217 0.04277243
## 107 86574 0.02038899
## 108 10044 0.02250979
## 109 84871 0.03391176
## 110 21091 0.02257480
## 111 1031 0.06440164
## 112 28161 0.05783999
## 113 34398 0.02589408
## 114 65268 0.02877628
## 115 7891 0.03707119
## 116 33499 0.02383478
## 117 8548 0.05574351
## 118 45394 0.06457473
## 119 18582 0.04776536
## 120 78394 0.06834212
## 121 8519 0.04776020
## 122 29912 0.03131524
## 123 93751 0.03548708
## 124 31992 0.04552209
## 125 15806 0.05010905
## 126 17657 0.02932617
## 127 32685 0.03178440
## 128 18188 0.02443970
## 129 31531 0.03753065
## 130 9776 0.15685474
## 131 125524 0.02190023
## 132 21250 0.04356508
## 133 53072 0.09249627
## 134 12065 0.03672110
## 135 25371 0.02615576
## 136 19901 0.03807609
## 137 12350 0.05593074
## 138 9356 0.03903217
## 139 22616 0.02282782
## 140 37404 0.03035121
## 141 26149 0.03793656
## 142 29356 0.02893077
## 143 262947 0.03756535
## 144 242848 0.04965602
## 145 8600 0.04551817
## 146 8232 0.05113048
## 147 14412 0.03380865
## 148 58213 0.03199906
## 149 33335 0.02323735
## 150 23399 0.01311527
## 151 13563 0.03298612
## 152 66836 0.03068827
## 153 8363 0.02261160
## 154 10782 0.04181068
## 155 96169 0.02073970
## 156 7404 0.02248460
## 157 48253 0.02739446
## 158 18319 0.07816247
## 159 72904 0.04929838
## 160 29286 0.02015055
## 161 10610 0.06294613
## 162 98566 0.05929367
## 163 179956 0.09450444
## 164 35182 0.01505545
## 165 88527 0.02428352
## 166 41601 0.02200566
## 167 11339 0.02767923
## 168 122341 0.02388072
## 169 48607 0.03134658
## 170 19651 0.03501101
## 171 12162 0.02701870
## 172 79413 0.02176129
## 173 42544 0.03340142
## 174 8315 0.01570780
## 175 16330 0.07205770
## 176 158938 0.04749653
## 177 117969 0.01169064
## 178 34626 0.04638184
## 179 46768 0.03857345
## 180 282393 0.06301145
## 181 42623 0.03710438
## 182 66445 0.01435472
## 183 37292 0.01640281
## 184 25697 0.03562706
## 185 113473 0.02631816
## 186 34926 0.03577614
## 187 11308 0.04576552
## 188 70699 0.05330045
## 189 47589 0.03755191
## 190 30166 0.03190169
## 191 6074 0.04094986
## 192 4123 0.02177832
## 193 43572 0.03380616
## 194 376040 0.07498445
## 195 51586 0.01903929
## 196 80590 0.04742997x_new <- c(1,35,287,64,26,1.778,48,64.9)
X=model.matrix(model_pga)
leaverage1 <- t(x_new)%*%solve(t(X)%*%X)%*%x_new
leaverage1## [,1]
## [1,] 0.005502717x_new2 <- c(1,42,295,69,30,1.80,54,67.7)
leaverage2 <- t(x_new2)%*%solve(t(X)%*%X)%*%x_new2
leaverage2## [,1]
## [1,] 0.05782079x_new3 <- c(1,45,320,70,30,1.80,54,67.7)
leaverage3 <- t(x_new3)%*%solve(t(X)%*%X)%*%x_new3
leaverage3## [,1]
## [1,] 0.3125799Here Hmax is 0.1568 and the residual of the third prediction is greater than that hence the point is extrapolation.
- Obtain the standardized regression coefficients and compare the influence of all variables.
transform the data using unit normal scaling
Pga_Data <- PGA[,2:11]
Pga_Normalized=as.data.frame(apply(Pga_Data,1,function(x){(x-mean(x))/sd(x)}))
Pga_Normalized## V1 V2 V3 V4 V5
## Age -0.3293061 -0.3377119 -0.3307247 -0.3336203 -0.3280857
## AverageDrive -0.3279773 -0.3374803 -0.3301162 -0.3325833 -0.3263990
## DrivingAccuracy -0.3291552 -0.3376832 -0.3306517 -0.3335220 -0.3278932
## GreensonRegulation -0.3291296 -0.3376764 -0.3306527 -0.3335063 -0.3278801
## AverageNumofPutts -0.3294126 -0.3377309 -0.3308026 -0.3337468 -0.3282765
## SavePercent -0.3291662 -0.3376818 -0.3306844 -0.3335664 -0.3280041
## MoneyRank -0.3288047 -0.3377264 -0.3306764 -0.3333570 -0.3273350
## NumEvents -0.3292861 -0.3377187 -0.3307489 -0.3336753 -0.3280922
## TotalWinnings 2.8441202 2.8405020 2.8435965 2.8425164 2.8444931
## AverageWinnings -0.2118825 -0.1390923 -0.1985389 -0.1749390 -0.2225272
## V6 V7 V8 V9 V10
## Age -0.3313503 -0.3313545 -0.3291897 -0.3337642 -0.3391437
## AverageDrive -0.3307516 -0.3305622 -0.3284069 -0.3321462 -0.3383513
## DrivingAccuracy -0.3312571 -0.3312483 -0.3290783 -0.3335276 -0.3390912
## GreensonRegulation -0.3312613 -0.3312657 -0.3290789 -0.3335333 -0.3390821
## AverageNumofPutts -0.3314140 -0.3314872 -0.3292701 -0.3339240 -0.3392961
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## MoneyRank -0.3312964 -0.3312291 -0.3290459 -0.3330412 -0.3390224
## NumEvents -0.3313643 -0.3314172 -0.3291928 -0.3338086 -0.3392515
## TotalWinnings 2.8433772 2.8433804 2.8441152 2.8425248 2.8397451
## AverageWinnings -0.1933833 -0.1934563 -0.2117420 -0.1751118 -0.1273654
## V11 V12 V13 V14 V15
## Age -0.3276005 -0.3273296 -0.3297529 -0.3278733 -0.3280062
## AverageDrive -0.3263766 -0.3257714 -0.3251692 -0.3273315 -0.3266961
## DrivingAccuracy -0.3275015 -0.3271273 -0.3294134 -0.3277996 -0.3278360
## GreensonRegulation -0.3274778 -0.3271531 -0.3294094 -0.3277943 -0.3278627
## AverageNumofPutts -0.3277926 -0.3275576 -0.3306152 -0.3279289 -0.3281930
## SavePercent -0.3275477 -0.3272559 -0.3298251 -0.3278445 -0.3279195
## MoneyRank -0.3271783 -0.3266867 -0.3267869 -0.3278529 -0.3274933
## NumEvents -0.3276457 -0.3273674 -0.3301236 -0.3278713 -0.3280390
## TotalWinnings 2.8445893 2.8446829 2.8441599 2.8444821 2.8444905
## AverageWinnings -0.2254686 -0.2284339 -0.2130642 -0.2221858 -0.2224446
## V16 V17 V18 V19 V20
## Age -0.3313513 -0.3296320 -0.3286929 -0.3267055 -0.3275107
## AverageDrive -0.3306223 -0.3288663 -0.3279730 -0.3251048 -0.3268679
## DrivingAccuracy -0.3312727 -0.3295706 -0.3286349 -0.3266082 -0.3274382
## GreensonRegulation -0.3312718 -0.3295670 -0.3286355 -0.3265303 -0.3274380
## AverageNumofPutts -0.3314613 -0.3297739 -0.3288216 -0.3269003 -0.3275969
## SavePercent -0.3313307 -0.3296258 -0.3286620 -0.3265750 -0.3274772
## MoneyRank -0.3312421 -0.3295204 -0.3285899 -0.3260831 -0.3274579
## NumEvents -0.3313969 -0.3296944 -0.3287397 -0.3267055 -0.3275233
## TotalWinnings 2.8433792 2.8439634 2.8442517 2.8448396 2.8445832
## AverageWinnings -0.1934300 -0.2077132 -0.2155023 -0.2336268 -0.2252730
## V21 V22 V23 V24 V25
## Age -0.3275701 -0.3307815 -0.3272808 -0.3316159 -0.3278988
## AverageDrive -0.3265866 -0.3298795 -0.3260679 -0.3264650 -0.3271928
## DrivingAccuracy -0.3274859 -0.3306603 -0.3271244 -0.3310202 -0.3278083
## GreensonRegulation -0.3274533 -0.3306585 -0.3271406 -0.3310400 -0.3277929
## AverageNumofPutts -0.3276961 -0.3308824 -0.3274345 -0.3322346 -0.3279817
## SavePercent -0.3275030 -0.3307210 -0.3271864 -0.3312366 -0.3278711
## MoneyRank -0.3273349 -0.3305915 -0.3268432 -0.3282998 -0.3277973
## NumEvents -0.3275853 -0.3308056 -0.3272857 -0.3317946 -0.3279043
## TotalWinnings 2.8445863 2.8435997 2.8446794 2.8436502 2.8444838
## AverageWinnings -0.2253712 -0.1986193 -0.2283160 -0.1999436 -0.2222364
## V26 V27 V28 V29 V30
## Age -0.3279577 -0.3287052 -0.3291092 -0.3286620 -0.3278720
## AverageDrive -0.3269105 -0.3280933 -0.3287008 -0.3283006 -0.3273813
## DrivingAccuracy -0.3278254 -0.3286261 -0.3290762 -0.3286146 -0.3277988
## GreensonRegulation -0.3278234 -0.3286182 -0.3290624 -0.3286092 -0.3277955
## AverageNumofPutts -0.3280889 -0.3287638 -0.3291695 -0.3287015 -0.3279152
## SavePercent -0.3279036 -0.3286451 -0.3290960 -0.3286395 -0.3278275
## MoneyRank -0.3276605 -0.3286496 -0.3291254 -0.3286704 -0.3278571
## NumEvents -0.3279740 -0.3287029 -0.3291286 -0.3286648 -0.3278627
## TotalWinnings 2.8444872 2.8442497 2.8441116 2.8442476 2.8444816
## AverageWinnings -0.2223432 -0.2154454 -0.2116435 -0.2153848 -0.2221716
## V31 V32 V33 V34 V35
## Age -0.3322480 -0.3290965 -0.3313461 -0.3269354 -0.3272794
## AverageDrive -0.3236597 -0.3288389 -0.3307412 -0.3257038 -0.3242379
## DrivingAccuracy -0.3314497 -0.3290617 -0.3312705 -0.3268232 -0.3269499
## GreensonRegulation -0.3313039 -0.3290633 -0.3312688 -0.3267733 -0.3269782
## AverageNumofPutts -0.3331732 -0.3291331 -0.3314179 -0.3270873 -0.3276998
## SavePercent -0.3321466 -0.3290809 -0.3312955 -0.3269436 -0.3271601
## MoneyRank -0.3263556 -0.3291221 -0.3312847 -0.3265691 -0.3255706
## NumEvents -0.3324697 -0.3291061 -0.3313658 -0.3269445 -0.3273162
## TotalWinnings 2.8436798 2.8441103 2.8433774 2.8447611 2.8447780
## AverageWinnings -0.2008733 -0.2116076 -0.1933868 -0.2309810 -0.2315859
## V36 V37 V38 V39 V40
## Age -0.3313542 -0.3303095 -0.3280553 -0.3377447 -0.3293593
## AverageDrive -0.3305507 -0.3289297 -0.3265490 -0.3371645 -0.3274689
## DrivingAccuracy -0.3312574 -0.3301188 -0.3277981 -0.3376828 -0.3292290
## GreensonRegulation -0.3312927 -0.3301193 -0.3278828 -0.3376896 -0.3291646
## AverageNumofPutts -0.3315099 -0.3304705 -0.3282748 -0.3378326 -0.3296228
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## MoneyRank -0.3311958 -0.3297981 -0.3273689 -0.3377034 -0.3284980
## NumEvents -0.3314334 -0.3303468 -0.3280938 -0.3377982 -0.3294342
## TotalWinnings 2.8433813 2.8437987 2.8444931 2.8405080 2.8441277
## AverageWinnings -0.1934777 -0.2035078 -0.2225246 -0.1391895 -0.2120927
## V41 V42 V43 V44 V45
## Age -0.3295053 -0.3289573 -0.3284673 -0.3269364 -0.3288867
## AverageDrive -0.3271695 -0.3265847 -0.3224108 -0.3258314 -0.3269727
## DrivingAccuracy -0.3291861 -0.3287733 -0.3281282 -0.3268176 -0.3287151
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## AverageNumofPutts -0.3297382 -0.3294018 -0.3292909 -0.3270538 -0.3292235
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## NumEvents -0.3295142 -0.3291384 -0.3286076 -0.3269240 -0.3290144
## TotalWinnings 2.8441315 2.8442713 2.8446305 2.8447600 2.8442654
## AverageWinnings -0.2122040 -0.2160767 -0.2269564 -0.2309448 -0.2159002
## V46 V47 V48 V49 V50
## Age -0.3298252 -0.3377216 -0.3282675 -0.3298128 -0.3386931
## AverageDrive -0.3281897 -0.3373215 -0.3255571 -0.3280105 -0.2998867
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## TotalWinnings 2.8439729 2.8405047 2.8445039 2.8439773 2.8439426
## AverageWinnings -0.2079681 -0.1391354 -0.2228766 -0.2080867 -0.2149864
## V51 V52 V53 V54 V55
## Age -0.3299344 -0.3297686 -0.3306844 -0.3306726 -0.3269877
## AverageDrive -0.3253432 -0.3281977 -0.3303500 -0.3304041 -0.3255852
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## MoneyRank -0.3268067 -0.3290867 -0.3307046 -0.3307035 -0.3264283
## NumEvents -0.3300889 -0.3298877 -0.3307019 -0.3306891 -0.3269933
## TotalWinnings 2.8441589 2.8439734 2.8435937 2.8435928 2.8447635
## AverageWinnings -0.2130297 -0.2079814 -0.1984711 -0.1984510 -0.2310622
## V56 V57 V58 V59 V60
## Age -0.3323030 -0.3328262 -0.3318610 -0.3313875 -0.3296060
## AverageDrive -0.3299365 -0.3316155 -0.3284761 -0.3304602 -0.3290869
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## NumEvents -0.3324404 -0.3329247 -0.3320265 -0.3314358 -0.3296402
## TotalWinnings 2.8431506 2.8428500 2.8434138 2.8433815 2.8439604
## AverageWinnings -0.1882878 -0.1817901 -0.1942714 -0.1934826 -0.2076327
## V61 V62 V63 V64 V65
## Age -0.3376948 -0.3270331 -0.3291462 -0.3377279 -0.3282205
## AverageDrive -0.3375504 -0.3206087 -0.3285103 -0.3371599 -0.3278828
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## NumEvents -0.3377052 -0.3271984 -0.3291663 -0.3377940 -0.3282492
## TotalWinnings 2.8405009 2.8450124 2.8441138 2.8405077 2.8443706
## AverageWinnings -0.1390753 -0.2400342 -0.2117038 -0.1391838 -0.2188914
## V66 V67 V68 V69 V70
## Age -0.3307345 -0.3281980 -0.3296631 -0.3269834 -0.3287120
## AverageDrive -0.3300843 -0.3255657 -0.3289542 -0.3254759 -0.3254192
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## MoneyRank -0.3306614 -0.3267835 -0.3295759 -0.3263794 -0.3268554
## NumEvents -0.3307496 -0.3283306 -0.3296657 -0.3270200 -0.3288578
## TotalWinnings 2.8435967 2.8445042 2.8439617 2.8447645 2.8444003
## AverageWinnings -0.1985440 -0.2228862 -0.2076683 -0.2310981 -0.2198115
## V71 V72 V73 V74 V75
## Age -0.3322939 -0.3316490 -0.3279708 -0.3301543 -0.3275464
## AverageDrive -0.3302711 -0.3257935 -0.3268623 -0.3295712 -0.3268027
## DrivingAccuracy -0.3320516 -0.3310102 -0.3278896 -0.3300856 -0.3274236
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## AverageNumofPutts -0.3325249 -0.3325765 -0.3280765 -0.3302229 -0.3276303
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## MoneyRank -0.3313073 -0.3275688 -0.3276989 -0.3301214 -0.3274215
## NumEvents -0.3323649 -0.3320376 -0.3279669 -0.3301718 -0.3275434
## TotalWinnings 2.8431464 2.8436621 2.8444868 2.8437892 2.8445842
## AverageWinnings -0.1881892 -0.2002824 -0.2223296 -0.2032652 -0.2253063
## V76 V77 V78 V79 V80
## Age -0.3292188 -0.3299922 -0.3279866 -0.3279565 -0.3271997
## AverageDrive -0.3282291 -0.3251611 -0.3269292 -0.3269388 -0.3262399
## DrivingAccuracy -0.3290620 -0.3292559 -0.3278297 -0.3278239 -0.3271153
## GreensonRegulation -0.3290867 -0.3294557 -0.3278239 -0.3278160 -0.3271141
## AverageNumofPutts -0.3293434 -0.3306028 -0.3280655 -0.3280582 -0.3273657
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## MoneyRank -0.3289355 -0.3267415 -0.3276822 -0.3277173 -0.3269719
## NumEvents -0.3292428 -0.3301097 -0.3279554 -0.3279528 -0.3272469
## TotalWinnings 2.8441178 2.8441598 2.8444865 2.8444863 2.8446772
## AverageWinnings -0.2118150 -0.2130621 -0.2223203 -0.2223136 -0.2282441
## V81 V82 V83 V84 V85
## Age -0.3295501 -0.3284364 -0.3291220 -0.3301911 -0.3312857
## AverageDrive -0.3266086 -0.3269709 -0.3264884 -0.3261044 -0.3309432
## DrivingAccuracy -0.3292008 -0.3282420 -0.3287675 -0.3298889 -0.3312636
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## AverageNumofPutts -0.3300031 -0.3285997 -0.3293738 -0.3308956 -0.3313611
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## NumEvents -0.3296961 -0.3284476 -0.3291120 -0.3304916 -0.3313286
## TotalWinnings 2.8441404 2.8443807 2.8442701 2.8440024 2.8433750
## AverageWinnings -0.2124613 -0.2191952 -0.2160459 -0.2088091 -0.1933312
## V86 V87 V88 V89 V90
## Age -0.3269447 -0.3267192 -0.3335285 -0.3286872 -0.3282270
## AverageDrive -0.3257380 -0.3249535 -0.3330271 -0.3279547 -0.3279218
## DrivingAccuracy -0.3267895 -0.3265051 -0.3334678 -0.3286213 -0.3281858
## GreensonRegulation -0.3268082 -0.3265411 -0.3334714 -0.3286185 -0.3281888
## AverageNumofPutts -0.3271140 -0.3269961 -0.3336080 -0.3288296 -0.3282730
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## MoneyRank -0.3265459 -0.3259561 -0.3335223 -0.3285927 -0.3282537
## NumEvents -0.3269639 -0.3267686 -0.3335701 -0.3287470 -0.3282384
## TotalWinnings 2.8447618 2.8448422 2.8425098 2.8442520 2.8443699
## AverageWinnings -0.2310056 -0.2337216 -0.1748059 -0.2155105 -0.2188733
## V91 V92 V93 V94 V95
## Age -0.3307012 -0.3296574 -0.3271623 -0.3274724 -0.3348736
## AverageDrive -0.3301915 -0.3288337 -0.3265936 -0.3269657 -0.3315033
## DrivingAccuracy -0.3306582 -0.3295404 -0.3270935 -0.3274320 -0.3344749
## GreensonRegulation -0.3306457 -0.3295464 -0.3270909 -0.3274278 -0.3345791
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## MoneyRank -0.3306992 -0.3295208 -0.3271205 -0.3274827 -0.3327294
## NumEvents -0.3307319 -0.3297040 -0.3271579 -0.3275034 -0.3352964
## TotalWinnings 2.8435955 2.8439638 2.8446730 2.8445821 2.8421772
## AverageWinnings -0.1985153 -0.2077247 -0.2281065 -0.2252396 -0.1683359
## V96 V97 V98 V99 V100
## Age -0.3319718 -0.3335797 -0.3367047 -0.3283764 -0.3288040
## AverageDrive -0.3316112 -0.3326955 -0.3348726 -0.3272684 -0.3276060
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## TotalWinnings 2.8431247 2.8425156 2.8411656 2.8443773 2.8442559
## AverageWinnings -0.1876985 -0.1749234 -0.1500596 -0.2190906 -0.2156242
## V101 V102 V103 V104 V105
## Age -0.3291858 -0.3301357 -0.3336075 -0.3366742 -0.3301485
## AverageDrive -0.3284302 -0.3296547 -0.3326357 -0.3351354 -0.3296283
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## AverageNumofPutts -0.3292536 -0.3301959 -0.3337675 -0.3369069 -0.3302111
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## MoneyRank -0.3290625 -0.3301357 -0.3333426 -0.3360065 -0.3301277
## NumEvents -0.3291830 -0.3301525 -0.3336931 -0.3368090 -0.3301630
## TotalWinnings 2.8441146 2.8437882 2.8425174 2.8411606 2.8437888
## AverageWinnings -0.2117265 -0.2032404 -0.1749594 -0.1499701 -0.2032545
## V106 V107 V108 V109 V110
## Age -0.3320433 -0.3306912 -0.3282426 -0.3312992 -0.3272605
## AverageDrive -0.3313586 -0.3303078 -0.3256172 -0.3308895 -0.3260883
## DrivingAccuracy -0.3319471 -0.3306497 -0.3279898 -0.3312691 -0.3271063
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## AverageNumofPutts -0.3321004 -0.3307405 -0.3285924 -0.3313679 -0.3274260
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## NumEvents -0.3320485 -0.3307065 -0.3282952 -0.3313333 -0.3272840
## TotalWinnings 2.8431281 2.8435940 2.8445027 2.8433753 2.8446791
## AverageWinnings -0.1877751 -0.1984791 -0.2228365 -0.1933390 -0.2283055
## V111 V112 V113 V114 V115
## Age -0.3408664 -0.3272511 -0.3291722 -0.3306954 -0.3303093
## AverageDrive -0.3022003 -0.3263391 -0.3283313 -0.3302149 -0.3261608
## DrivingAccuracy -0.3367304 -0.3270832 -0.3290796 -0.3306344 -0.3298760
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## AverageNumofPutts -0.3447193 -0.3273188 -0.3293028 -0.3307770 -0.3307610
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## NumEvents -0.3418967 -0.3272124 -0.3292167 -0.3307319 -0.3303867
## TotalWinnings 2.8430835 2.8446759 2.8441164 2.8435955 2.8439979
## AverageWinnings -0.1932378 -0.2282007 -0.2117763 -0.1985144 -0.2086848
## V116 V117 V118 V119 V120
## Age -0.3301982 -0.3307246 -0.3320017 -0.3280898 -0.3327405
## AverageDrive -0.3292654 -0.3271440 -0.3313019 -0.3265053 -0.3322528
## DrivingAccuracy -0.3301140 -0.3302760 -0.3319356 -0.3278656 -0.3326583
## GreensonRegulation -0.3300928 -0.3303963 -0.3319458 -0.3278479 -0.3326587
## AverageNumofPutts -0.3303430 -0.3312477 -0.3321520 -0.3282219 -0.3327891
## SavePercent -0.3301546 -0.3303800 -0.3319690 -0.3279566 -0.3326919
## MoneyRank -0.3299859 -0.3284812 -0.3319095 -0.3274694 -0.3327251
## NumEvents -0.3302550 -0.3309029 -0.3320876 -0.3280613 -0.3327521
## TotalWinnings 2.8437939 2.8438272 2.8431305 2.8444914 2.8428398
## AverageWinnings -0.2033851 -0.2042745 -0.1878275 -0.2224735 -0.1815713
## V121 V122 V123 V124 V125
## Age -0.3278486 -0.3307800 -0.3282294 -0.3366076 -0.3348686
## AverageDrive -0.3250755 -0.3296864 -0.3279358 -0.3352876 -0.3322014
## DrivingAccuracy -0.3275626 -0.3306893 -0.3281889 -0.3364907 -0.3344242
## GreensonRegulation -0.3276467 -0.3306911 -0.3281941 -0.3365170 -0.3344570
## AverageNumofPutts -0.3283437 -0.3309668 -0.3282659 -0.3368719 -0.3351671
## SavePercent -0.3278426 -0.3307433 -0.3282049 -0.3365684 -0.3346771
## MoneyRank -0.3262866 -0.3304793 -0.3282504 -0.3360934 -0.3334191
## NumEvents -0.3279928 -0.3308684 -0.3282341 -0.3367829 -0.3349850
## TotalWinnings 2.8446054 2.8436030 2.8443697 2.8411588 2.8421585
## AverageWinnings -0.2260063 -0.1986983 -0.2188661 -0.1499393 -0.1679590
## V126 V127 V128 V129 V130
## Age -0.3273097 -0.3302276 -0.3289155 -0.3287071 -0.3372788
## AverageDrive -0.3258606 -0.3292464 -0.3272872 -0.3278226 -0.3321480
## DrivingAccuracy -0.3271721 -0.3300897 -0.3286762 -0.3286657 -0.3367872
## GreensonRegulation -0.3271457 -0.3301103 -0.3286706 -0.3286381 -0.3367853
## AverageNumofPutts -0.3274904 -0.3303490 -0.3290663 -0.3288625 -0.3379524
## SavePercent -0.3272541 -0.3301487 -0.3287871 -0.3286930 -0.3373783
## MoneyRank -0.3267595 -0.3299751 -0.3282113 -0.3285525 -0.3342562
## NumEvents -0.3273209 -0.3302587 -0.3289030 -0.3287682 -0.3376615
## TotalWinnings 2.8446809 2.8437941 2.8442600 2.8442531 2.8412147
## AverageWinnings -0.2283680 -0.2033886 -0.2157427 -0.2155435 -0.1509669
## V131 V132 V133 V134 V135
## Age -0.3319681 -0.3269044 -0.3391662 -0.3324695 -0.3314900
## AverageDrive -0.3316829 -0.3257754 -0.3382645 -0.3293931 -0.3301090
## DrivingAccuracy -0.3319335 -0.3268338 -0.3390812 -0.3321153 -0.3312859
## GreensonRegulation -0.3319324 -0.3267994 -0.3391179 -0.3321165 -0.3313039
## AverageNumofPutts -0.3320052 -0.3270863 -0.3393470 -0.3328308 -0.3316544
## SavePercent -0.3319455 -0.3268573 -0.3391195 -0.3323654 -0.3314236
## MoneyRank -0.3319911 -0.3265832 -0.3389426 -0.3307943 -0.3309622
## NumEvents -0.3319819 -0.3269451 -0.3392940 -0.3325891 -0.3315389
## TotalWinnings 2.8431240 2.8447610 2.8397484 2.8431589 2.8433873
## AverageWinnings -0.1876835 -0.2309761 -0.1274154 -0.1884850 -0.1936193
## V136 V137 V138 V139 V140
## Age -0.3279651 -0.3290003 -0.3275388 -0.3272815 -0.3268427
## AverageDrive -0.3267062 -0.3268326 -0.3249903 -0.3261270 -0.3261867
## DrivingAccuracy -0.3278136 -0.3286598 -0.3271690 -0.3271193 -0.3267707
## GreensonRegulation -0.3278381 -0.3287562 -0.3272072 -0.3271140 -0.3267658
## AverageNumofPutts -0.3281948 -0.3293141 -0.3278906 -0.3273964 -0.3269281
## SavePercent -0.3279502 -0.3288094 -0.3274329 -0.3271802 -0.3268221
## MoneyRank -0.3275293 -0.3278348 -0.3261294 -0.3269177 -0.3267707
## NumEvents -0.3280448 -0.3290738 -0.3275706 -0.3272639 -0.3268478
## TotalWinnings 2.8444906 2.8442683 2.8446925 2.8446782 2.8447564
## AverageWinnings -0.2224484 -0.2159873 -0.2287636 -0.2282783 -0.2308218
## V141 V142 V143 V144 V145
## Age -0.3314202 -0.3314316 -0.3319529 -0.3377027 -0.3302504
## AverageDrive -0.3301474 -0.3302353 -0.3318095 -0.3374907 -0.3265007
## DrivingAccuracy -0.3313484 -0.3313164 -0.3319371 -0.3376802 -0.3298245
## GreensonRegulation -0.3313199 -0.3313098 -0.3319334 -0.3376751 -0.3297478
## AverageNumofPutts -0.3316433 -0.3315970 -0.3319706 -0.3377299 -0.3306366
## SavePercent -0.3313795 -0.3313841 -0.3319406 -0.3376867 -0.3301610
## MoneyRank -0.3309873 -0.3310507 -0.3319699 -0.3377264 -0.3280213
## NumEvents -0.3315311 -0.3314974 -0.3319595 -0.3377182 -0.3302930
## TotalWinnings 2.8433869 2.8433849 2.8431225 2.8405020 2.8439936
## AverageWinnings -0.1936098 -0.1935627 -0.1876489 -0.1390920 -0.2085584
## V146 V147 V148 V149 V150
## Age -0.3292679 -0.3274163 -0.3296245 -0.3287398 -0.3275922
## AverageDrive -0.3256505 -0.3256595 -0.3290753 -0.3279062 -0.3264896
## DrivingAccuracy -0.3288865 -0.3271322 -0.3295574 -0.3286106 -0.3274645
## GreensonRegulation -0.3288589 -0.3271653 -0.3295463 -0.3286317 -0.3274623
## AverageNumofPutts -0.3297111 -0.3275968 -0.3296899 -0.3288425 -0.3277419
## SavePercent -0.3289595 -0.3272595 -0.3295962 -0.3286806 -0.3275384
## MoneyRank -0.3272162 -0.3265909 -0.3296014 -0.3285630 -0.3272686
## NumEvents -0.3293505 -0.3273888 -0.3296392 -0.3287534 -0.3276141
## TotalWinnings 2.8442809 2.8446841 2.8439602 2.8442525 2.8445877
## AverageWinnings -0.2163798 -0.2284748 -0.2076300 -0.2155246 -0.2254162
## V151 V152 V153 V154 V155
## Age -0.3348341 -0.3296100 -0.3293013 -0.3319219 -0.3295979
## AverageDrive -0.3318452 -0.3291405 -0.3256579 -0.3285143 -0.3292625
## DrivingAccuracy -0.3344778 -0.3295647 -0.3288920 -0.3314378 -0.3295583
## GreensonRegulation -0.3345320 -0.3295532 -0.3288378 -0.3313969 -0.3295510
## AverageNumofPutts -0.3353175 -0.3296707 -0.3296701 -0.3322445 -0.3296311
## SavePercent -0.3347848 -0.3295664 -0.3290262 -0.3317260 -0.3295713
## MoneyRank -0.3331695 -0.3296173 -0.3272411 -0.3300010 -0.3296131
## NumEvents -0.3351054 -0.3296264 -0.3293149 -0.3319731 -0.3296004
## TotalWinnings 2.8421654 2.8439595 2.8442794 2.8434107 2.8439581
## AverageWinnings -0.1680993 -0.2076103 -0.2163382 -0.1941952 -0.2075723
## V156 V157 V158 V159 V160
## Age -0.3306800 -0.3268344 -0.3284630 -0.3364966 -0.3292047
## AverageDrive -0.3266609 -0.3263014 -0.3267811 -0.3359033 -0.3281809
## DrivingAccuracy -0.3303472 -0.3267643 -0.3283250 -0.3364459 -0.3291007
## GreensonRegulation -0.3303781 -0.3267598 -0.3282736 -0.3364464 -0.3290987
## AverageNumofPutts -0.3314384 -0.3268867 -0.3286373 -0.3366177 -0.3293541
## SavePercent -0.3306852 -0.3267880 -0.3283555 -0.3364941 -0.3291617
## MoneyRank -0.3281413 -0.3268165 -0.3278358 -0.3364684 -0.3289398
## NumEvents -0.3310403 -0.3268245 -0.3284749 -0.3365787 -0.3292529
## TotalWinnings 2.8438339 2.8447552 2.8443820 2.8411446 2.8441182
## AverageWinnings -0.2044625 -0.2307794 -0.2192358 -0.1496936 -0.2118246
## V161 V162 V163 V164 V165
## Age -0.3358901 -0.3306800 -0.3353865 -0.3291819 -0.3295928
## AverageDrive -0.3320673 -0.3303607 -0.3351206 -0.3283383 -0.3292549
## DrivingAccuracy -0.3355289 -0.3306303 -0.3353527 -0.3290880 -0.3295533
## GreensonRegulation -0.3356737 -0.3306418 -0.3353406 -0.3290750 -0.3295520
## AverageNumofPutts -0.3366756 -0.3307314 -0.3354083 -0.3292928 -0.3296387
## SavePercent -0.3358534 -0.3306705 -0.3353629 -0.3291411 -0.3295730
## MoneyRank -0.3335102 -0.3307069 -0.3354012 -0.3290249 -0.3296094
## NumEvents -0.3364060 -0.3307015 -0.3353924 -0.3292086 -0.3296052
## TotalWinnings 2.8417362 2.8435936 2.8416712 2.8441160 2.8439583
## AverageWinnings -0.1601310 -0.1984706 -0.1589060 -0.2117655 -0.2075791
## V166 V167 V168 V169 V170
## Age -0.3282662 -0.3271102 -0.3290914 -0.3307368 -0.3269731
## AverageDrive -0.3276316 -0.3250290 -0.3288532 -0.3300638 -0.3256515
## DrivingAccuracy -0.3281920 -0.3268466 -0.3290674 -0.3306557 -0.3268347
## GreensonRegulation -0.3282065 -0.3268652 -0.3290641 -0.3306557 -0.3267980
## AverageNumofPutts -0.3283668 -0.3274001 -0.3291281 -0.3308271 -0.3271160
## SavePercent -0.3282444 -0.3270271 -0.3290775 -0.3306815 -0.3268856
## MoneyRank -0.3282031 -0.3260675 -0.3291221 -0.3306470 -0.3265329
## NumEvents -0.3282951 -0.3271357 -0.3291039 -0.3307667 -0.3269634
## TotalWinnings 2.8443731 2.8447699 2.8441101 2.8435975 2.8447618
## AverageWinnings -0.2189674 -0.2312886 -0.2116024 -0.1985632 -0.2310066
## V171 V172 V173 V174 V175
## Age -0.3339760 -0.3274649 -0.3286779 -0.3312527 -0.3293358
## AverageDrive -0.3307746 -0.3271519 -0.3280259 -0.3274258 -0.3275737
## DrivingAccuracy -0.3336338 -0.3274278 -0.3286398 -0.3309058 -0.3292228
## GreensonRegulation -0.3336612 -0.3274278 -0.3286249 -0.3309011 -0.3291753
## AverageNumofPutts -0.3345011 -0.3275103 -0.3287904 -0.3319083 -0.3295896
## SavePercent -0.3338845 -0.3274494 -0.3286785 -0.3311652 -0.3292508
## MoneyRank -0.3321865 -0.3274894 -0.3286193 -0.3288977 -0.3285152
## NumEvents -0.3342633 -0.3274726 -0.3287206 -0.3315550 -0.3294078
## TotalWinnings 2.8425512 2.8445804 2.8442507 2.8436390 2.8441264
## AverageWinnings -0.1756701 -0.2251864 -0.2154733 -0.1996272 -0.2120555
## V176 V177 V178 V179 V180
## Age -0.3286387 -0.3301122 -0.3355697 -0.3262314 -0.3343857
## AverageDrive -0.3284537 -0.3298322 -0.3341881 -0.3257312 -0.3342235
## DrivingAccuracy -0.3286189 -0.3300805 -0.3354351 -0.3261556 -0.3343690
## GreensonRegulation -0.3286135 -0.3300777 -0.3353953 -0.3261609 -0.3343627
## AverageNumofPutts -0.3286596 -0.3301458 -0.3357137 -0.3262880 -0.3344012
## SavePercent -0.3286208 -0.3300924 -0.3354708 -0.3262012 -0.3343706
## MoneyRank -0.3286572 -0.3301338 -0.3350854 -0.3262217 -0.3343999
## NumEvents -0.3286408 -0.3301208 -0.3356309 -0.3262236 -0.3343910
## TotalWinnings 2.8442461 2.8437863 2.8416872 2.8448994 2.8421206
## AverageWinnings -0.2153429 -0.2031908 -0.1591982 -0.2356858 -0.1672170
## V181 V182 V183 V184 V185
## Age -0.3296684 -0.3296095 -0.3271647 -0.3268889 -0.3290912
## AverageDrive -0.3289502 -0.3291322 -0.3265024 -0.3259722 -0.3288380
## DrivingAccuracy -0.3295424 -0.3295654 -0.3270967 -0.3267891 -0.3290708
## GreensonRegulation -0.3295602 -0.3295524 -0.3270972 -0.3267808 -0.3290667
## AverageNumofPutts -0.3297436 -0.3296687 -0.3272610 -0.3270132 -0.3291298
## SavePercent -0.3295960 -0.3295842 -0.3271350 -0.3268452 -0.3290854
## MoneyRank -0.3295453 -0.3296132 -0.3270930 -0.3266683 -0.3291202
## NumEvents -0.3296742 -0.3296242 -0.3271807 -0.3268964 -0.3291036
## TotalWinnings 2.8439622 2.8439595 2.8446742 2.8447589 2.8441102
## AverageWinnings -0.2076819 -0.2076097 -0.2281435 -0.2309048 -0.2116045
## V186 V187 V188 V189 V190
## Age -0.3301771 -0.3264943 -0.3344177 -0.3274812 -0.3287143
## AverageDrive -0.3293460 -0.3244067 -0.3338449 -0.3269630 -0.3277920
## DrivingAccuracy -0.3300655 -0.3263412 -0.3343593 -0.3274313 -0.3286490
## GreensonRegulation -0.3301054 -0.3262787 -0.3343553 -0.3274344 -0.3286418
## AverageNumofPutts -0.3303306 -0.3267684 -0.3345199 -0.3275742 -0.3288766
## SavePercent -0.3301462 -0.3264406 -0.3344201 -0.3274589 -0.3287196
## MoneyRank -0.3300062 -0.3255166 -0.3343988 -0.3274769 -0.3285265
## NumEvents -0.3302461 -0.3265023 -0.3344792 -0.3275113 -0.3287782
## TotalWinnings 2.8437934 2.8449124 2.8421266 2.8445825 2.8442536
## AverageWinnings -0.2033703 -0.2361634 -0.1673316 -0.2252512 -0.2155555
## V191 V192 V193 V194 V195
## Age -0.3309581 -0.3335532 -0.3291737 -0.3282025 -0.3282505
## AverageDrive -0.3257342 -0.3247864 -0.3284602 -0.3281269 -0.3277175
## DrivingAccuracy -0.3306235 -0.3326527 -0.3290736 -0.3281968 -0.3282011
## GreensonRegulation -0.3304583 -0.3326387 -0.3290647 -0.3281932 -0.3281909
## AverageNumofPutts -0.3317156 -0.3347518 -0.3292445 -0.3282139 -0.3283316
## SavePercent -0.3308431 -0.3332799 -0.3291362 -0.3281996 -0.3282359
## MoneyRank -0.3275494 -0.3271761 -0.3290685 -0.3282141 -0.3282399
## NumEvents -0.3312299 -0.3340438 -0.3291764 -0.3282060 -0.3282738
## TotalWinnings 2.8438426 2.8432295 2.8441143 2.8443679 2.8443719
## AverageWinnings -0.2047306 -0.1903470 -0.2117164 -0.2188151 -0.2189308
## V196
## Age -0.3278463
## AverageDrive -0.3275083
## DrivingAccuracy -0.3277887
## GreensonRegulation -0.3277940
## AverageNumofPutts -0.3278808
## SavePercent -0.3278236
## MoneyRank -0.3278581
## NumEvents -0.3278437
## TotalWinnings 2.8444805
## AverageWinnings -0.2221370#redo regression
model1_Pga_Normalized <- lm(PGA$AverageWinnings ~ PGA$Age+PGA$AverageDrive+PGA$DrivingAccuracy+PGA$GreensonRegulation+PGA$AverageNumofPutts+PGA$SavePercent+PGA$NumEvents, data=Pga_Normalized)
model1_Pga_Normalized##
## Call:
## lm(formula = PGA$AverageWinnings ~ PGA$Age + PGA$AverageDrive +
## PGA$DrivingAccuracy + PGA$GreensonRegulation + PGA$AverageNumofPutts +
## PGA$SavePercent + PGA$NumEvents, data = Pga_Normalized)
##
## Coefficients:
## (Intercept) PGA$Age PGA$AverageDrive
## 945579.88 -587.13 -94.76
## PGA$DrivingAccuracy PGA$GreensonRegulation PGA$AverageNumofPutts
## -2360.57 8466.04 -694226.49
## PGA$SavePercent PGA$NumEvents
## 1395.67 -3159.22summary(model1_Pga_Normalized)##
## Call:
## lm(formula = PGA$AverageWinnings ~ PGA$Age + PGA$AverageDrive +
## PGA$DrivingAccuracy + PGA$GreensonRegulation + PGA$AverageNumofPutts +
## PGA$SavePercent + PGA$NumEvents, data = Pga_Normalized)
##
## Residuals:
## Min 1Q Median 3Q Max
## -71690 -22176 -6735 17147 247928
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 945579.88 305886.59 3.091 0.00230 **
## PGA$Age -587.13 519.32 -1.131 0.25968
## PGA$AverageDrive -94.76 567.42 -0.167 0.86755
## PGA$DrivingAccuracy -2360.57 854.02 -2.764 0.00628 **
## PGA$GreensonRegulation 8466.04 1303.87 6.493 7.30e-10 ***
## PGA$AverageNumofPutts -694226.49 138155.99 -5.025 1.17e-06 ***
## PGA$SavePercent 1395.67 587.54 2.375 0.01853 *
## PGA$NumEvents -3159.22 644.24 -4.904 2.03e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 41430 on 188 degrees of freedom
## Multiple R-squared: 0.4527, Adjusted R-squared: 0.4323
## F-statistic: 22.21 on 7 and 188 DF, p-value: < 2.2e-16summary(model_pga)##
## Call:
## lm(formula = AverageWinnings ~ Age + AverageDrive + DrivingAccuracy +
## NumEvents + AverageNumofPutts + SavePercent + GreensonRegulation,
## data = PGA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -71690 -22176 -6735 17147 247928
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 945579.88 305886.59 3.091 0.00230 **
## Age -587.13 519.32 -1.131 0.25968
## AverageDrive -94.76 567.42 -0.167 0.86755
## DrivingAccuracy -2360.57 854.02 -2.764 0.00628 **
## NumEvents -3159.22 644.24 -4.904 2.03e-06 ***
## AverageNumofPutts -694226.49 138155.99 -5.025 1.17e-06 ***
## SavePercent 1395.67 587.54 2.375 0.01853 *
## GreensonRegulation 8466.04 1303.87 6.493 7.30e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 41430 on 188 degrees of freedom
## Multiple R-squared: 0.4527, Adjusted R-squared: 0.4323
## F-statistic: 22.21 on 7 and 188 DF, p-value: < 2.2e-16Average No if Putts and greens on regulation affect the averagewinning the most after the variables in the model are standardized.
- Obtain the residuals of the fitted regression. Perform the residual analysis. What does the residual analysis tell you? For example, are all four assumptions satisfied? If not, which ones are not satisfied. Suppose you take a logarithm of the response variable and fit the regression, does that help with the residuals?
model_pga$residuals## 1 2 3 4 5 6
## -7763.9747 97689.0095 18807.2522 -13861.9772 -9996.6673 -10123.5373
## 7 8 9 10 11 12
## -10593.3840 -37173.6736 -2773.3291 -18942.3176 -20839.4118 27672.1374
## 13 14 15 16 17 18
## 6716.3936 -6323.1582 2725.7362 -14906.6410 4107.5204 -3653.2150
## 19 20 21 22 23 24
## -45992.2552 8699.3642 -32095.3714 -35056.5710 -13121.5366 15249.8967
## 25 26 27 28 29 30
## -33339.7647 -24059.8661 -37421.4212 11044.5512 30938.3846 22924.2846
## 31 32 33 34 35 36
## -1724.2369 36729.1197 -1490.0068 -15622.6725 37749.1317 4362.8128
## 37 38 39 40 41 42
## -42754.7836 28856.1308 41657.2840 -10844.6481 -21974.1088 -4259.7446
## 43 44 45 46 47 48
## -9257.9100 -34539.0808 -31703.1139 -45557.6648 31286.8330 -10083.6707
## 49 50 51 52 53 54
## -11745.0047 56807.9479 18445.9081 -18721.6214 -10321.2893 59960.8572
## 55 56 57 58 59 60
## -8555.3835 -34093.4117 -38398.3564 36324.2744 -7269.3055 -5590.4775
## 61 62 63 64 65 66
## 232199.2639 47168.6227 6947.4691 -5262.6742 52121.0984 -32741.4274
## 67 68 69 70 71 72
## 23037.6870 -57314.2402 3999.9073 7676.3741 -62050.8333 29050.8108
## 73 74 75 76 77 78
## -48928.0964 -19887.4571 -3343.6799 3901.8448 51215.7962 -7146.9241
## 79 80 81 82 83 84
## -5434.5448 -8989.9523 -11286.3346 -22873.0401 -38276.7524 -26465.1308
## 85 86 87 88 89 90
## 3265.3484 -8021.1939 26322.9736 8910.1620 -19645.6910 21502.2450
## 91 92 93 94 95 96
## -24251.3500 -29365.3351 12970.9630 47369.3486 -38816.9649 -25859.1838
## 97 98 99 100 101 102
## -38830.2985 -62455.8766 9942.7136 -53967.5365 -4558.1357 31272.7256
## 103 104 105 106 107 108
## -21836.0891 -68733.7925 -7544.2305 -51916.3028 15199.1644 -5701.3114
## 109 110 111 112 113 114
## 1616.8938 -12325.7656 -2154.7779 10860.3905 23713.4904 -8858.4922
## 115 116 117 118 119 120
## 2057.3635 -45133.3295 8338.2777 -51681.1838 -28254.4647 -11216.9956
## 121 122 123 124 125 126
## 49603.4630 -24508.8090 41242.9350 -24949.7821 -64606.1785 19828.5734
## 127 128 129 130 131 132
## -21016.6829 -16156.4183 -26059.0851 -16828.4227 35569.8657 -20516.1260
## 133 134 135 136 137 138
## -595.7606 3890.8253 -30281.2924 -22037.1769 24101.4668 4118.3974
## 139 140 141 142 143 144
## -20425.7380 4537.9770 -52040.9725 15498.7974 137343.9149 95996.1593
## 145 146 147 148 149 150
## -17720.0318 -13839.7705 -19699.4015 -16311.3946 21483.9410 -18829.6178
## 151 152 153 154 155 156
## -23783.0006 -25101.2803 -20795.4087 -43026.8762 42963.4547 -10106.8893
## 157 158 159 160 161 162
## 1835.8322 -5548.3888 -11886.5715 -19900.7317 -2777.1531 25013.4668
## 163 164 165 166 167 168
## 47529.0397 -16705.4165 18814.8420 27237.8741 19402.2220 29490.7733
## 169 170 171 172 173 174
## 6413.2172 -22592.4810 -38539.1967 33810.3306 2220.9333 -27671.1562
## 175 176 177 178 179 180
## -29840.6902 41821.4188 47803.7822 -71689.6767 15280.5052 130114.7662
## 181 182 183 184 185 186
## -14835.7644 10452.0349 19998.4811 -959.9942 80010.9178 16713.9600
## 187 188 189 190 191 192
## 6158.3642 -28237.4473 5941.8382 23542.8129 -35284.3437 -18784.1037
## 193 194 195 196
## -33901.0125 247928.2363 -11605.1512 20538.1655MSRes=summary(model_pga)$sigma^2
MSRes## [1] 1716669098obtain standardized residuals
standardized_res=model_pga$residuals/summary(model_pga)$sigma
standardized_res## 1 2 3 4 5 6
## -0.18738759 2.35777529 0.45392286 -0.33456606 -0.24127479 -0.24433686
## 7 8 9 10 11 12
## -0.25567686 -0.89720604 -0.06693575 -0.45718273 -0.50297009 0.66788150
## 13 14 15 16 17 18
## 0.16210367 -0.15261273 0.06578707 -0.35977957 0.09913715 -0.08817225
## 19 20 21 22 23 24
## -1.11004711 0.20996370 -0.77463856 -0.84610866 -0.31669514 0.36806422
## 25 26 27 28 29 30
## -0.80467264 -0.58069744 -0.90318555 0.26656602 0.74671408 0.55328959
## 31 32 33 34 35 36
## -0.04161536 0.88647650 -0.03596209 -0.37706136 0.91109502 0.10529877
## 37 38 39 40 41 42
## -1.03190904 0.69645779 1.00542031 -0.26174125 -0.53035660 -0.10281116
## 43 44 45 46 47 48
## -0.22344449 -0.83361876 -0.76517122 -1.09955804 0.75512406 -0.24337466
## 49 50 51 52 53 54
## -0.28347182 1.37108950 0.44520163 -0.45185612 -0.24910971 1.44718662
## 55 56 57 58 59 60
## -0.20648865 -0.82286230 -0.92676440 0.87670534 -0.17544849 -0.13492910
## 61 62 63 64 65 66
## 5.60425056 1.13843936 0.16768080 -0.12701739 1.25796994 -0.79023146
## 67 68 69 70 71 72
## 0.55602661 -1.38330913 0.09653985 0.18527330 -1.49762928 0.70115650
## 73 74 75 76 77 78
## -1.18090517 -0.47999417 -0.08070146 0.09417306 1.23612000 -0.17249475
## 79 80 81 82 83 84
## -0.13116558 -0.21697720 -0.27240158 -0.55205277 -0.92382942 -0.63874976
## 85 86 87 88 89 90
## 0.07881089 -0.19359571 0.63531872 0.21505142 -0.47415902 0.51896792
## 91 92 93 94 95 96
## -0.58531900 -0.70874771 0.31306097 1.14328398 -0.93686773 -0.62412491
## 97 98 99 100 101 102
## -0.93718954 -1.50740521 0.23997259 -1.30253469 -0.11001299 0.75478357
## 103 104 105 106 107 108
## -0.52702542 -1.65892600 -0.18208395 -1.25302709 0.36683977 -0.13760413
## 109 110 111 112 113 114
## 0.03902458 -0.29748879 -0.05200669 0.26212120 0.57233748 -0.21380434
## 115 116 117 118 119 120
## 0.04965554 -1.08931649 0.20124869 -1.24735238 -0.68193627 -0.27072805
## 121 122 123 124 125 126
## 1.19720550 -0.59153291 0.99541979 -0.60217603 -1.55930388 0.47857298
## 127 128 129 130 131 132
## -0.50724862 -0.38994360 -0.62894964 -0.40616278 0.85849729 -0.49516742
## 133 134 135 136 137 138
## -0.01437899 0.09390710 -0.73085481 -0.53187878 0.58170149 0.09939967
## 139 140 141 142 143 144
## -0.49298586 0.10952645 -1.25603606 0.37407157 3.31486715 2.31691746
## 145 146 147 148 149 150
## -0.42768223 -0.33403009 -0.47545535 -0.39368403 0.51852614 -0.45446267
## 151 152 153 154 155 156
## -0.57401515 -0.60583252 -0.50190806 -1.03847614 1.03694543 -0.24393506
## 157 158 159 160 161 162
## 0.04430877 -0.13391326 -0.28688861 -0.48031456 -0.06702804 0.60371309
## 163 164 165 166 167 168
## 1.14713821 -0.40319396 0.45410604 0.65740032 0.46828277 0.71177522
## 169 170 171 172 173 174
## 0.15478635 -0.54528133 -0.93016365 0.81602999 0.05360339 -0.66785781
## 175 176 177 178 179 180
## -0.72022065 1.00938180 1.15376926 -1.73026781 0.36880298 3.14038787
## 181 182 183 184 185 186
## -0.35806893 0.25226532 0.48267379 -0.02316996 1.93110531 0.40340016
## 187 188 189 190 191 192
## 0.14863534 -0.68152554 0.14340937 0.56821809 -0.85160607 -0.45336416
## 193 194 195 196
## -0.81821865 5.98387753 -0.28009639 0.49569936par(mfrow=c(1,2))
# generate QQ plot
qqnorm(model_pga$residuals,main="Model_PGA")
qqline(model_pga$residuals)
The qqplot shows that the residuals are normally distributed and hence it is a 45 degree line.
# residual plot for delivery time data set
par(mfrow=c(1,3))
# generate residual plot, NumberofCases vs residuals
plot(PGA$Age,model_pga$residuals,pch=20)
abline(h=0,col="grey")
plot(PGA$AverageDrive,model_pga$residuals,pch=20)
abline(h=0,col="grey")
plot(PGA$DrivingAccuracy,model_pga$residuals,pch=20)
abline(h=0,col="grey")
plot(PGA$GreensonRegulation,model_pga$residuals,pch=20)
abline(h=0,col="grey")
plot(PGA$AverageNumofPutts,model_pga$residuals,pch=20)
abline(h=0,col="grey")
plot(PGA$SavePercent,model_pga$residuals,pch=20)
abline(h=0,col="grey")
plot(PGA$NumEvents,model_pga$residuals,pch=20)
abline(h=0,col="grey")
# generate residual plot, fitted values vs residual