> data <- read.csv("pgatour2006.csv",header=T) > par(mfrow=c(4,3)) > for (i in names(data)[-1]) { hist(data[,i],main=i)} > dev.new() > par(mfrow=c(4,3)) > for (i in names(data)[-1]) { qqnorm(data[,i],main=i); qqline(data[,i]) } > library(car) Loading required package: carData Warning messages: 1: package ¡®car¡¯ was built under R version 3.4.4 2: package ¡®carData¡¯ was built under R version 3.4.4 > help(boxCox) starting httpd help server ... done > dev.new() > fit <- lm(PrizeMoney ~ ., data=data) > par(mfrow=c(2,2)) > plot(fit) Error in qqnorm.default(rs, main = main, ylab = ylab23, ylim = ylim, ...) : y is empty or has only NAs In addition: Warning messages: 1: not plotting observations with leverage one: 1, 2, 3, 4, 5, 8, 9, 12, 13, 14, 15, 16, 18, 21, 22, 23, 24, 28, 29, 32, 35, 36, 37, 40, 42, 43, 44, 53, 54, 55, 57, 59, 60, 62, 63, 65, 67, 68, 69, 73, 74, 75, 78, 79, 80, 82, 83, 84, 85, 86, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 106, 108, 109, 111, 112, 114, 115, 116, 118, 121, 123, 124, 126, 128, 130, 131, 132, 133, 134, 137, 138, 140, 141, 143, 144, 145, 147, 148, 149, 150, 152, 154, 155, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196 2: In min(x) : no non-missing arguments to min; returning Inf 3: In max(x) : no non-missing arguments to max; returning -Inf > summary(fit) Call: lm(formula = PrizeMoney ~ ., data = data) Residuals: ALL 196 residuals are 0: no residual degrees of freedom! Coefficients: (10 not defined because of singularities) Estimate Std. Error t value Pr(>|t|) (Intercept) 60661 NA NA NA NameAdam Scott 201384 NA NA NA NameAlex Aragon -57026 NA NA NA NameAlex Cejka -43145 NA NA NA NameArjun Atwal -43978 NA NA NA NameArron Oberholser 46633 NA NA NA NameBart Bryant -10041 NA NA NA NameBen Crane -3388 NA NA NA NameBen Curtis 26121 NA NA NA NameBernhard Langer -37265 NA NA NA NameBill Haas -31094 NA NA NA NameBilly Andrade -16581 NA NA NA NameBilly Mayfair -13489 NA NA NA NameBo Van Pelt -11021 NA NA NA NameBob Estes -7051 NA NA NA NameBob May -34532 NA NA NA NameBob Tway -48672 NA NA NA NameBrad Faxon -39750 NA NA NA NameBrandt Jobe -32003 NA NA NA NameBrent Geiberger -40978 NA NA NA NameBrett Quigley 18655 NA NA NA NameBrett Wetterich 60266 NA NA NA NameBrian Bateman -35847 NA NA NA NameBrian Davis -33437 NA NA NA NameBrian Gay -27190 NA NA NA NameBriny Baird -26879 NA NA NA NameBubba Dickerson -40339 NA NA NA NameBubba Watson -22910 NA NA NA NameCamilo Villegas -588 NA NA NA NameCarl Pettersson 33910 NA NA NA NameCarlos Franco -44993 NA NA NA NameChad Campbell 51782 NA NA NA NameCharles Howell III -8891 NA NA NA NameCharles Warren -22926 NA NA NA NameCharley Hoffman -22206 NA NA NA NameChris Couch -10412 NA NA NA NameChris DiMarco -1510 NA NA NA NameChris Riley -42316 NA NA NA NameChris Smith -51927 NA NA NA NameCorey Pavin -3788 NA NA NA NameCraig Barlow -14909 NA NA NA NameD.A. Points -46162 NA NA NA NameD.J. Trahan -29290 NA NA NA NameDaisuke Maruyama -22386 NA NA NA NameDaniel Chopra -14284 NA NA NA NameDanny Ellis -44031 NA NA NA NameDarron Stiles -50157 NA NA NA NameDavid Duval -47399 NA NA NA NameDavid Howell 4513 NA NA NA NameDavid McKenzie -45474 NA NA NA NameDavid Toms 71666 NA NA NA NameDavis Love III 58783 NA NA NA NameDean Wilson 13158 NA NA NA NameDoug Barron -46796 NA NA NA NameDudley Hart -34360 NA NA NA NameDuffy Waldorf -38321 NA NA NA NameEric Axley -16710 NA NA NA NameErnie Els 68573 NA NA NA NameFrank Lickliter II -3569 NA NA NA NameFred Couples -14757 NA NA NA NameFred Funk -6184 NA NA NA NameFredrik Jacobson -16841 NA NA NA NameGeoff Ogilvy 157087 NA NA NA NameGreg Chalmers -55259 NA NA NA NameGreg Kraft -50133 NA NA NA NameGreg Owen -5799 NA NA NA NameHarrison Frazar -30005 NA NA NA NameHeath Slocum -21305 NA NA NA NameHenrik Bjornstad -44821 NA NA NA NameHidemichi Tanaka -58421 NA NA NA NameHunter Mahan -22473 NA NA NA NameIan Leggatt -47630 NA NA NA NameIan Poulter 42933 NA NA NA NameJ.B. Holmes -3445 NA NA NA NameJ.J. Henry 21535 NA NA NA NameJ.L. Lewis -34857 NA NA NA NameJ.P. Hayes -23743 NA NA NA NameJames Driscoll -53078 NA NA NA NameJason Bohn -2837 NA NA NA NameJason Gore -35937 NA NA NA NameJason Schultz -55396 NA NA NA NameJeff Brehaut -43734 NA NA NA NameJeff Gove -33300 NA NA NA NameJeff Maggert -5647 NA NA NA NameJeff Overton -40049 NA NA NA NameJeff Sluman -17488 NA NA NA NameJerry Kelly -4603 NA NA NA NameJerry Smith -41067 NA NA NA NameJesper Parnevik -6148 NA NA NA NameJim Furyk 239894 NA NA NA NameJimmy Walker -53330 NA NA NA NameJoe Durant 39737 NA NA NA NameJoe Ogilvie -23657 NA NA NA NameJoey Sindelar -32988 NA NA NA NameJohn Cook -31365 NA NA NA NameJohn Daly -51512 NA NA NA NameJohn Engler, Jr. -57969 NA NA NA NameJohn Huston -44697 NA NA NA NameJohn Rollins -7131 NA NA NA NameJohn Senden -1708 NA NA NA NameJon Mills -58235 NA NA NA NameJonathan Byrd 9760 NA NA NA NameJonathan Kaye -42576 NA NA NA NameJose Maria Olazabal 57140 NA NA NA NameJustin Leonard -30593 NA NA NA NameJustin Rose -2472 NA NA NA NameK.J. Choi 30745 NA NA NA NameKenny Perry -23447 NA NA NA NameKent Jones -33762 NA NA NA NameKevin Sutherland -34743 NA NA NA NameKirk Triplett -18072 NA NA NA NameKris Cox -42167 NA NA NA NameLarry Mize -48551 NA NA NA NameLee Janzen -41940 NA NA NA NameLen Mattiace -57636 NA NA NA NameLucas Glover 22822 NA NA NA NameLuke Donald 115862 NA NA NA NameMarco Dawson -40473 NA NA NA NameMark Brooks -54884 NA NA NA NameMark Calcavecchia -34538 NA NA NA NameMark O'Meara -49346 NA NA NA NameMark Wilson -42148 NA NA NA NameMathew Goggin -19271 NA NA NA NameMathias Gronberg -38194 NA NA NA NameMatt Hansen -53171 NA NA NA NameMichael Allen -41823 NA NA NA NameMichael Connell -56217 NA NA NA NameMike Sposa -55376 NA NA NA NameMike Weir 17828 NA NA NA NameNathan Green -3968 NA NA NA NameNicholas Thompson -52389 NA NA NA NameNick Watney -17771 NA NA NA NameOlin Browne -35526 NA NA NA NameOmar Uresti -34129 NA NA NA NamePadraig Harrington 28651 NA NA NA NamePat Perez -22792 NA NA NA NamePatrick Sheehan -49285 NA NA NA NamePaul Azinger -37258 NA NA NA NamePaul Goydos -23561 NA NA NA NamePaul Stankowski -46134 NA NA NA NamePeter Lonard -22615 NA NA NA NamePhil Mickelson 163366 NA NA NA NameRetief Goosen 84753 NA NA NA NameRich Beem -36282 NA NA NA NameRichard S. Johnson -7027 NA NA NA NameRobert Allenby 7684 NA NA NA NameRobert Damron -46103 NA NA NA NameRobert Gamez -44206 NA NA NA NameRobert Garrigus -41461 NA NA NA NameRod Pampling 50367 NA NA NA NameRoger Tambellini -55994 NA NA NA NameRon Whittaker -49946 NA NA NA NameRory Sabbatini 58579 NA NA NA NameRyan Hietala -56845 NA NA NA NameRyan Moore -9656 NA NA NA NameRyan Palmer -24233 NA NA NA NameRyuji Imada -27818 NA NA NA NameScott Gutschewski -40688 NA NA NA NameScott Verplank 8512 NA NA NA NameSean O'Hair -13615 NA NA NA NameSergio Garcia 31147 NA NA NA NameShane Bertsch -40159 NA NA NA NameShaun Micheel -4356 NA NA NA NameShigeki Maruyama -22190 NA NA NA NameSkip Kendall -40664 NA NA NA NameStephen Ames 53394 NA NA NA NameStephen Leaney -33004 NA NA NA NameSteve Elkington -45649 NA NA NA NameSteve Flesch -17703 NA NA NA NameSteve Jones -49240 NA NA NA NameSteve Lowery -24372 NA NA NA NameSteve Stricker 45916 NA NA NA NameStewart Cink 45336 NA NA NA NameStuart Appleby 90228 NA NA NA NameTag Ridings -45563 NA NA NA NameTed Purdy -23800 NA NA NA NameThomas Levet -51599 NA NA NA NameTiger Woods 602110 NA NA NA NameTim Clark 29109 NA NA NA NameTim Herron 5122 NA NA NA NameTim Petrovic -40597 NA NA NA NameTjaart van der Walt -49474 NA NA NA NameTodd Fischer -49352 NA NA NA NameTodd Hamilton -54544 NA NA NA NameTom Lehman 23943 NA NA NA NameTom Pernice, Jr. 11962 NA NA NA NameTommy Armour III -46563 NA NA NA NameTrevor Immelman 99514 NA NA NA NameTroy Matteson -5080 NA NA NA NameVance Veazey -50307 NA NA NA NameVaughn Taylor 7952 NA NA NA NameVijay Singh 109799 NA NA NA NameWes Short, Jr. -47858 NA NA NA NameWill MacKenzie -30317 NA NA NA NameWoody Austin -22618 NA NA NA NameZach Johnson 30163 NA NA NA TigerWoods NA NA NA NA AveDrivingDistance NA NA NA NA DrivingAccuracy NA NA NA NA GIR NA NA NA NA PuttingAverage NA NA NA NA BirdieConversion NA NA NA NA SandSaves NA NA NA NA Scrambling NA NA NA NA BounceBack NA NA NA NA PuttsPerRound NA NA NA NA Residual standard error: NaN on 0 degrees of freedom Multiple R-squared: 1, Adjusted R-squared: NaN F-statistic: NaN on 195 and 0 DF, p-value: NA > fit <- lm(PrizeMoney ~ ., data=data[,-1]) > summary(fit) Call: lm(formula = PrizeMoney ~ ., data = data[, -1]) Residuals: Min 1Q Median 3Q Max -65534 -23613 -7381 13142 182971 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -188632.2 453436.7 -0.416 0.6779 TigerWoods 488647.8 40987.0 11.922 <2e-16 *** AveDrivingDistance -206.0 579.2 -0.356 0.7225 DrivingAccuracy -1357.4 837.6 -1.621 0.1068 GIR 6511.2 2858.3 2.278 0.0239 * PuttingAverage -336448.0 438789.9 -0.767 0.4442 BirdieConversion 4641.7 2928.3 1.585 0.1146 SandSaves 961.9 572.7 1.680 0.0947 . Scrambling 2970.5 1871.8 1.587 0.1142 BounceBack 1394.7 1197.3 1.165 0.2456 PuttsPerRound 6072.5 28134.2 0.216 0.8294 --- Signif. codes: 0 ¡®***¡¯ 0.001 ¡®**¡¯ 0.01 ¡®*¡¯ 0.05 ¡®.¡¯ 0.1 ¡® ¡¯ 1 Residual standard error: 37910 on 185 degrees of freedom Multiple R-squared: 0.6662, Adjusted R-squared: 0.6481 F-statistic: 36.92 on 10 and 185 DF, p-value: < 2.2e-16 > par(mfrow=c(2,2)) > summary(fit) Call: lm(formula = PrizeMoney ~ ., data = data[, -1]) Residuals: Min 1Q Median 3Q Max -65534 -23613 -7381 13142 182971 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -188632.2 453436.7 -0.416 0.6779 TigerWoods 488647.8 40987.0 11.922 <2e-16 *** AveDrivingDistance -206.0 579.2 -0.356 0.7225 DrivingAccuracy -1357.4 837.6 -1.621 0.1068 GIR 6511.2 2858.3 2.278 0.0239 * PuttingAverage -336448.0 438789.9 -0.767 0.4442 BirdieConversion 4641.7 2928.3 1.585 0.1146 SandSaves 961.9 572.7 1.680 0.0947 . Scrambling 2970.5 1871.8 1.587 0.1142 BounceBack 1394.7 1197.3 1.165 0.2456 PuttsPerRound 6072.5 28134.2 0.216 0.8294 --- Signif. codes: 0 ¡®***¡¯ 0.001 ¡®**¡¯ 0.01 ¡®*¡¯ 0.05 ¡®.¡¯ 0.1 ¡® ¡¯ 1 Residual standard error: 37910 on 185 degrees of freedom Multiple R-squared: 0.6662, Adjusted R-squared: 0.6481 F-statistic: 36.92 on 10 and 185 DF, p-value: < 2.2e-16 > plot(fit) Warning messages: 1: not plotting observations with leverage one: 178 2: not plotting observations with leverage one: 178 > > dev.new() > par(mfrow=c(2,2)) > plot(fit) Warning messages: 1: not plotting observations with leverage one: 178 2: not plotting observations with leverage one: 178 > dev.new() > boxCox(fit) > summary(fit) Call: lm(formula = PrizeMoney ~ ., data = data[, -1]) Residuals: Min 1Q Median 3Q Max -65534 -23613 -7381 13142 182971 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -188632.2 453436.7 -0.416 0.6779 TigerWoods 488647.8 40987.0 11.922 <2e-16 *** AveDrivingDistance -206.0 579.2 -0.356 0.7225 DrivingAccuracy -1357.4 837.6 -1.621 0.1068 GIR 6511.2 2858.3 2.278 0.0239 * PuttingAverage -336448.0 438789.9 -0.767 0.4442 BirdieConversion 4641.7 2928.3 1.585 0.1146 SandSaves 961.9 572.7 1.680 0.0947 . Scrambling 2970.5 1871.8 1.587 0.1142 BounceBack 1394.7 1197.3 1.165 0.2456 PuttsPerRound 6072.5 28134.2 0.216 0.8294 --- Signif. codes: 0 ¡®***¡¯ 0.001 ¡®**¡¯ 0.01 ¡®*¡¯ 0.05 ¡®.¡¯ 0.1 ¡® ¡¯ 1 Residual standard error: 37910 on 185 degrees of freedom Multiple R-squared: 0.6662, Adjusted R-squared: 0.6481 F-statistic: 36.92 on 10 and 185 DF, p-value: < 2.2e-16