고급회귀분석 실습 CH10

Advanced Regression Analysis
Author

SEOYEON CHOI

Published

November 21, 2022

CH10

회귀진단

library(lmtest)

데이터 입력

dt <- data.frame(x = c(15,26,10,9,15,20,18,11,
                       8,20,7,9,10,11,11,10,12,42,17,11,10),
                 y = c(95,71,83,91,102,87,93,100,
                       104,94,113,96,83,84,102,100,
                       105,57,121,86,100))

산점도

plot(y~x, dt,pch  = 20,cex  = 2,col  = "darkorange")

회귀적합

model_reg <- lm(y~x, dt)
summary(model_reg)

Call:
lm(formula = y ~ x, data = dt)

Residuals:
    Min      1Q  Median      3Q     Max 
-15.604  -8.731   1.396   4.523  30.285 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 109.8738     5.0678  21.681 7.31e-15 ***
x            -1.1270     0.3102  -3.633  0.00177 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 11.02 on 19 degrees of freedom
Multiple R-squared:   0.41, Adjusted R-squared:  0.3789 
F-statistic:  13.2 on 1 and 19 DF,  p-value: 0.001769
plot(y~x, dt,pch  = 20,cex  = 2,col  = "darkorange")
abline(model_reg, col='steelblue', lwd=2)

잔차

residual <- model_reg$residuals  ## e_i = y_i - hat(y_i)
## resid(model_reg)

내적으로 표준화된 잔차

s_residual<- rstandard(model_reg)
# # 또는
# s_xx <- sum((dt$x-mean(dt$x))^2)  #S_xx
# h_ii <- 1/21 + (dt$x- mean(dt$x))^2/s_xx
# ## h_ii <- influence(model_reg)$hat
# hat_sigma <-  summary(model_reg)$sigma   #hat sigma
# s_residual <- residual/(hat_sigma*sqrt(1-h_ii)) ## 내적

외적으로 스튜던트화된 잔차

s_residual_i <- rstudent(model_reg) ## 외적으로 스튜던트화 잔차
# # 또는
# hat_sigma_i <- sqrt(((21-1-1)*hat_sigma^2 - residual^2/(1-h_ii) )/(21-1-2))
# ## hat_sigma_i <- influence(model_reg)$sigma
# s_residual_i <-  residual/(hat_sigma_i*sqrt(1-h_ii)) ## 외적

잔차그림

par(mfrow = c(2, 2))

plot(fitted(model_reg), residual, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "Residuals", 
     main = "residual plot")
abline(h=0, lty=2)

plot(fitted(model_reg), s_residual, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "S_Residuals", 
     ylim=c(min(-3, min(s_residual)), 
            max(3,max(s_residual))),
     main = "standardized residual plot")
abline(h=c(-2,0,2), lty=2)

plot(fitted(model_reg), s_residual_i, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "S_Residuals_(i)", 
     ylim=c(min(-3, min(s_residual_i)), 
            max(3,max(s_residual_i))),
     main = "studentized residual plot")
abline(h=c(-3,-2,0,2,3), lty=2)

plot(fitted(model_reg), s_residual_i, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "S_Residuals_(i)", 
     ylim=c(min(-3, min(s_residual_i)), 
            max(3,max(s_residual_i))),
     main = "studentized residual plot")
abline(h=c(-qt(0.975,21-2),0,qt(0.975,21-2)), lty=2)
text (fitted(model_reg)[which(abs(s_residual_i)>qt(0.975,21-2))],
      s_residual_i[which(abs(s_residual_i)>qt(0.975,21-2))], 
      which(abs(s_residual_i)>qt(0.975,21-2)),adj = c(0,1))

## 이상치 검정
qt(0.975,21-2) #기각역
2.09302405440831 
s_residual_i
1
0.183968493379394
2
-0.941583351378201
3
-1.51081192291799
4
-0.814263363159438
5
0.832862917520795
6
-0.030631827537088
7
0.311246764732158
8
0.229715749649931
9
0.289910136925676
10
0.617660260595883
11
1.05084716358865
12
-0.342831483529281
13
-1.51081192291799
14
-1.27977575448039
15
0.413153195694502
16
0.127393415386012
17
0.798281144415116
18
-0.845110861537551
19
3.60697972130439
20
-1.07648107628971
21
0.127393415386012
s_residual_i[which(abs(s_residual_i)>qt(0.975,21-2))]
19: 3.60697972130439 
## 정규성 검정
par(mfrow=c(1,2))
hist(resid(model_reg),
     xlab   = "Residuals",
     main   = "Histogram of Residuals",
     col    = "darkorange",
     border = "dodgerblue",
     breaks = 20)

qqnorm(resid(model_reg), 
       main = "Normal Q-Q Plot", 
       col = "darkgrey",
       pch=16)
qqline(resid(model_reg), col = "dodgerblue", lwd = 2)

graphics.off()

독립성 검정

lmtest::dwtest(model_reg)

    Durbin-Watson test

data:  model_reg
DW = 2.0844, p-value = 0.5716
alternative hypothesis: true autocorrelation is greater than 0

영향점

par(mfrow=c(1,1))
plot(y~x, dt,pch  = 20,cex  = 2,col  = "darkorange")
abline(model_reg, col='steelblue', lwd=2)

# influence(model_reg)
influence.measures(model_reg)
Influence measures of
     lm(formula = y ~ x, data = dt) :

     dfb.1_    dfb.x    dffit cov.r   cook.d    hat inf
1   0.01664  0.00328  0.04127 1.166 8.97e-04 0.0479    
2   0.18862 -0.33480 -0.40252 1.197 8.15e-02 0.1545    
3  -0.33098  0.19239 -0.39114 0.936 7.17e-02 0.0628    
4  -0.20004  0.12788 -0.22433 1.115 2.56e-02 0.0705    
5   0.07532  0.01487  0.18686 1.085 1.77e-02 0.0479    
6   0.00113 -0.00503 -0.00857 1.201 3.88e-05 0.0726    
7   0.00447  0.03266  0.07722 1.170 3.13e-03 0.0580    
8   0.04430 -0.02250  0.05630 1.174 1.67e-03 0.0567    
9   0.07907 -0.05427  0.08541 1.200 3.83e-03 0.0799    
10 -0.02283  0.10141  0.17284 1.152 1.54e-02 0.0726    
11  0.31560 -0.22889  0.33200 1.088 5.48e-02 0.0908    
12 -0.08422  0.05384 -0.09445 1.183 4.68e-03 0.0705    
13 -0.33098  0.19239 -0.39114 0.936 7.17e-02 0.0628    
14 -0.24681  0.12536 -0.31367 0.992 4.76e-02 0.0567    
15  0.07968 -0.04047  0.10126 1.159 5.36e-03 0.0567    
16  0.02791 -0.01622  0.03298 1.187 5.74e-04 0.0628    
17  0.13328 -0.05493  0.18717 1.096 1.79e-02 0.0521    
18  0.83112 -1.11275 -1.15578 2.959 6.78e-01 0.6516   *
19  0.14348  0.27317  0.85374 0.396 2.23e-01 0.0531   *
20 -0.20761  0.10544 -0.26385 1.043 3.45e-02 0.0567    
21  0.02791 -0.01622  0.03298 1.187 5.74e-04 0.0628    
hatvalues(model_reg)
1
0.0479224794510218
2
0.154513234296056
3
0.0628157755825353
4
0.0705452077520549
5
0.0479224794510218
6
0.0726189578463163
7
0.0579895935449815
8
0.0566699343940879
9
0.0798582309026469
10
0.0726189578463163
11
0.0907548450343111
12
0.0705452077520549
13
0.0628157755825353
14
0.0566699343940879
15
0.0566699343940879
16
0.0628157755825353
17
0.0521076841867129
18
0.65160998416409
19
0.0530502978659226
20
0.0566699343940879
21
0.0628157755825353
dffits(model_reg)
1
0.0412740357514056
2
-0.402520687302525
3
-0.391140045474215
4
-0.224328533660804
5
0.186855983882421
6
-0.00857173640678122
7
0.0772239528389379
8
0.0563034865220476
9
0.085407472693718
10
0.172840518129759
11
0.331996853994253
12
-0.0944496430423618
13
-0.391140045474215
14
-0.313673908094842
15
0.101264129345836
16
0.0329813827461469
17
0.187166128054405
18
-1.15577873097521
19
0.853737107130766
20
-0.263846244162542
21
0.0329813827461469
cooks.distance(model_reg)
1
0.000897406392870691
2
0.0814979551507635
3
0.0716581442213833
4
0.0256159582452641
5
0.0177436626335013
6
3.87762740910137e-05
7
0.0031305748029949
8
0.00166820857813469
9
0.00383194880672965
10
0.0154395158127621
11
0.0548101351203612
12
0.00467762256482442
13
0.0716581442213833
14
0.0475978118328145
15
0.00536121617564154
16
0.000573584529113046
17
0.017856495213809
18
0.678112028575845
19
0.223288273631179
20
0.0345188940892692
21
0.000573584529113046
covratio(model_reg)
1
1.16589181683219
2
1.19699897676296
3
0.936347397341839
4
1.11510268993929
5
1.08504108257728
6
1.20131998275497
7
1.17015757898673
8
1.17423726760803
9
1.19966823450598
10
1.15209128858604
11
1.08783960928084
12
1.18326164825873
13
0.936347397341839
14
0.992331347870996
15
1.15904532932769
16
1.18673688685713
17
1.09643883044992
18
2.95868271380702
19
0.396431612340971
20
1.04257281407241
21
1.18673688685713
summary(influence.measures(model_reg))
Potentially influential observations of
     lm(formula = y ~ x, data = dt) :

   dfb.1_ dfb.x   dffit   cov.r   cook.d hat    
18  0.83  -1.11_* -1.16_*  2.96_*  0.68   0.65_*
19  0.14   0.27    0.85    0.40_*  0.22   0.05

기각역

p <- 1
n <- 21
2*(p+1)/n #hat (h_ii)
0.19047619047619 
2*sqrt((p+1)/(n-p-1)) #Dffits
0.64888568452305 
qf(0.5, p+1, n-p-1) #Cook d
0.719060569091733 
par(mfrow=c(2,2))
plot(y~x, dt,pch  = 20,
     cex  = 2,col  = "darkorange",
     main = "전체 데이터")
abline(model_reg, col='steelblue', lwd=2)
text (dt[18:19,],c('18', '19'),adj = c(0,0))

## 18제거 전후 
plot(y~x, dt,pch  = 20,
     cex  = 2,col  = "darkorange",
     main = "18번 제거")
abline(model_reg, col='steelblue', lwd=2)
abline(lm(y~x, dt[-18,]), col='red', lwd=2)
legend('topright', legend=c("full", "del(18)"),
       col=c('steelblue', 'red'), lty=1, lwd=2)
# high leverage and high influence, not outlier

## 19제거 전후 
plot(y~x, dt,pch  = 20,
     cex  = 2,col  = "darkorange",
     main = "19번 제거")
abline(model_reg, col='steelblue', lwd=2)
abline(lm(y~x, dt[-19,]), col='red', lwd=2)
legend('topright', legend=c("full", "del(19)"),
       col=c('steelblue', 'red'), lty=1, lwd=2)
# not leverage and high influence, outlier


## 18, 19제거 전후 
plot(y~x, dt,pch  = 20,
     cex  = 2,col  = "darkorange",
     main = "18,19번 제거")
abline(model_reg, col='steelblue', lwd=2)
abline(lm(y~x, dt[-c(18,19),]), col='red', lwd=2)
legend('topright', legend=c("full", "del(18,19)"),
       col=c('steelblue', 'red'), lty=1, lwd=2)

회귀진단 그림

par(mfrow = c(2, 2))
plot(model_reg, pch=16)

Hitters

library(ISLR)
hitters <- na.omit(Hitters)
dim(hitters)
  1. 263
  2. 20
head(hitters)
A data.frame: 6 × 20
AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks League Division PutOuts Assists Errors Salary NewLeague
<int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <fct> <fct> <int> <int> <int> <dbl> <fct>
-Alan Ashby 315 81 7 24 38 39 14 3449 835 69 321 414 375 N W 632 43 10 475.0 N
-Alvin Davis 479 130 18 66 72 76 3 1624 457 63 224 266 263 A W 880 82 14 480.0 A
-Andre Dawson 496 141 20 65 78 37 11 5628 1575 225 828 838 354 N E 200 11 3 500.0 N
-Andres Galarraga 321 87 10 39 42 30 2 396 101 12 48 46 33 N E 805 40 4 91.5 N
-Alfredo Griffin 594 169 4 74 51 35 11 4408 1133 19 501 336 194 A W 282 421 25 750.0 A
-Al Newman 185 37 1 23 8 21 2 214 42 1 30 9 24 N E 76 127 7 70.0 A 
reg_model <- lm(Salary ~ AtBat + Hits + HmRun, hitters)
summary(reg_model)

Call:
lm(formula = Salary ~ AtBat + Hits + HmRun, data = hitters)

Residuals:
    Min      1Q  Median      3Q     Max 
-884.75 -214.97  -58.05  175.88 1991.53 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  158.754     75.815   2.094  0.03724 *  
AtBat         -1.564      0.641  -2.440  0.01536 *  
Hits           8.329      2.053   4.056 6.61e-05 ***
HmRun          9.502      3.384   2.808  0.00536 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 398.9 on 259 degrees of freedom
Multiple R-squared:  0.2271,    Adjusted R-squared:  0.2182 
F-statistic: 25.37 on 3 and 259 DF,  p-value: 2.013e-14
vcov(reg_model)
A matrix: 4 × 4 of type dbl
(Intercept) AtBat Hits HmRun
(Intercept) 5747.87524 -26.2127535 48.158691 21.0663196
AtBat -26.21275 0.4108477 -1.249666 -0.4193544
Hits 48.15869 -1.2496656 4.216189 0.1404930
HmRun 21.06632 -0.4193544 0.140493 11.4506363 
pairs(hitters[,c(1,2,3,19)])

## 잔차그림 
residual <- resid(reg_model)
stad.res <- rstandard(reg_model)
stu.res <- rstudent(reg_model)
par(mfrow = c(2, 2))
plot(fitted(reg_model), residual, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "Residuals", 
     main = "residual plot")
abline(h=0, lty=2)

plot(fitted(reg_model), stad.res, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "S_Residuals", 
     ylim=c(min(-3, min(stad.res)), 
            max(3,max(stad.res))),
     main = "standardized residual plot")
abline(h=c(-2,0,2), lty=2)

plot(fitted(reg_model), stu.res, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "S_Residuals_(i)", 
     ylim=c(min(-3, min(stu.res)), 
            max(3,max(stu.res))),
     main = "studentized residual plot")
abline(h=c(-2,0,2), lty=2)

plot(fitted(reg_model), stu.res, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "S_Residuals_(i)", 
     ylim=c(min(-3, min(stu.res)), 
            max(3,max(stu.res))),
     main = "studentized residual plot")
abline(h=c(-qt(0.975,nrow(hitters)-4),0,qt(0.975,nrow(hitters)-4)), lty=2)
text (fitted(reg_model)[which(abs(stu.res)>qt(0.975,nrow(hitters)-4))],
      stu.res[which(abs(stu.res)>qt(0.975,nrow(hitters)-4))], 
      which(abs(stu.res)>qt(0.975,nrow(hitters)-4)),adj = c(0,1))

stu.res[abs(stu.res)>qt(0.975,nrow(hitters)-4)]
-Dale Murphy
2.74033829619024
-Dave Winfield
2.88089264730221
-Eddie Murray
4.31895378037471
-George Brett
2.05782174934042
-Gary Carter
3.24866258649007
-Joe Carter
-2.08071298999844
-Jack Clark
2.44291700843437
-Jim Rice
3.5583979165244
-Keith Hernandez
2.44056603081697
-Kirby Puckett
-2.29372779175543
-Mike Schmidt
5.33366401188885
-Ozzie Smith
3.5948319898282
-Rickey Henderson
2.20244386003162
-Steve Garvey
1.97931624811918
-Steve Sax
-2.30201279255003
which(abs(stu.res)>qt(0.975,nrow(hitters)-4))
-Dale Murphy
63
-Dave Winfield
74
-Eddie Murray
77
-George Brett
82
-Gary Carter
84
-Joe Carter
110
-Jack Clark
111
-Jim Rice
127
-Keith Hernandez
140
-Kirby Puckett
148
-Mike Schmidt
173
-Ozzie Smith
183
-Rickey Henderson
200
-Steve Garvey
226
-Steve Sax
230
influence(reg_model)
$hat
-Alan Ashby
0.00540428715355245
-Alvin Davis
0.00589170670784522
-Andre Dawson
0.00832644882765465
-Andres Galarraga
0.00543756565246947
-Alfredo Griffin
0.0246137118709988
-Al Newman
0.0141225554276349
-Argenis Salazar
0.010928273983481
-Andres Thomas
0.00583280157863637
-Andre Thornton
0.0118104032344835
-Alan Trammell
0.00994920971431027
-Alex Trevino
0.0116023974454147
-Andy VanSlyke
0.00392214855226506
-Alan Wiggins
0.01133266253963
-Bill Almon
0.0120577739078933
-Buddy Bell
0.00926235909199221
-Buddy Biancalana
0.012342136255686
-Bruce Bochy
0.0204159574317937
-Barry Bonds
0.0140367315219278
-Bobby Bonilla
0.0110632944090634
-Bob Brenly
0.00872907614618226
-Bill Buckner
0.0139048245540849
-Brett Butler
0.023168413560765
-Bob Dernier
0.0102008268559032
-Bo Diaz
0.00579243488480162
-Bill Doran
0.015434760936016
-Brian Downing
0.00777622895232283
-Billy Hatcher
0.00709689247443314
-Brook Jacoby
0.0108511422285614
-Bob Kearney
0.0108810262666556
-Bill Madlock
0.00473465384983353
-Bob Melvin
0.00900012174203842
-BillyJo Robidoux
0.0133294228418443
-Bill Schroeder
0.0112763637277587
-Chris Bando
0.00978612142405515
-Chris Brown
0.0166260339272529
-Carmen Castillo
0.0130280396536268
-Chili Davis
0.00704454319748951
-Carlton Fisk
0.017822764593868
-Curt Ford
0.0109708972674672
-Carney Lansford
0.0107121199405846
-Chet Lemon
0.004977264802092
-Candy Maldonado
0.00764992031384351
-Carmelo Martinez
0.0089685788087143
-Craig Reynolds
0.00600742640963073
-Cal Ripken
0.0154842953466146
-Cory Snyder
0.0142384557435194
-Chris Speier
0.0176408073638382
-Curt Wilkerson
0.011580828583756
-Dave Anderson
0.0114107120327874
-Don Baylor
0.0352479469918076
-Daryl Boston
0.0120025169206652
-Darnell Coles
0.00768936788078936
-Dave Concepcion
0.00754097071158992
-Doug DeCinces
0.016164784133267
-Darrell Evans
0.0264058825441862
-Dwight Evans
0.0156073759122261
-Damaso Garcia
0.00737202574736494
-Dan Gladden
0.00732057564815775
-Dave Henderson
0.00493766296992215
-Donnie Hill
0.00802999130926279
-Davey Lopes
0.00867219904074439
-Don Mattingly
0.0903700111079589
-Dale Murphy
0.0205781074488089
-Dwayne Murphy
0.00499065937964354
-Dave Parker
0.0233401084346804
-Dan Pasqua
0.0148260514260301
-Darrell Porter
0.0212335628824219
-Dick Schofield
0.00692844758375807
-Don Slaught
0.00665433551016605
-Darryl Strawberry
0.017694944503085
-Dale Sveum
0.00583616542870044
-Danny Tartabull
0.0128297967927647
-Denny Walling
0.0124382760330085
-Dave Winfield
0.0133528039520951
-Eric Davis
0.0205166608140052
-Eddie Milner
0.00477555388471096
-Eddie Murray
0.0126894264569264
-Ed Romero
0.0120154735656705
-Frank White
0.0103217756795036
-George Bell
0.0344024597514498
-Glenn Braggs
0.0102378206814018
-George Brett
0.0070249800741032
-Greg Brock
0.0102483444612376
-Gary Carter
0.0133493295035423
-Glenn Davis
0.0233784484234977
-Gary Gaetti
0.0300641988907722
-Greg Gagne
0.00756816838324455
-George Hendrick
0.00993821578501312
-Glenn Hubbard
0.0144050547662455
-Garth Iorg
0.00750828700013946
-Gary Matthews
0.0119812939218614
-Graig Nettles
0.0135988964718854
-Gary Pettis
0.0180946787493926
-Gary Redus
0.00533116613569048
-Garry Templeton
0.0231472795912073
-Greg Walker
0.00954059659043919
-Gary Ward
0.0158776584493562
-Glenn Wilson
0.0102664940810771
-Harold Baines
0.0136874329182192
-Hubie Brooks
0.0245534617574867
-Howard Johnson
0.0111605903106341
-Hal McRae
0.00660970775119084
-Harold Reynolds
0.0266174645810819
-Harry Spilman
0.0178175584405383
-Herm Winningham
0.0125072976893885
-Jesse Barfield
0.0472745129906935
-Juan Beniquez
0.0098405887950288
-John Cangelosi
0.0185585370145323
-Jose Canseco
0.0385966269231462
-Joe Carter
0.0279123839207128
-Jack Clark
0.00976153800810466
-Jose Cruz
0.00621927886532388
-Jody Davis
0.0125836354713245
-Jim Dwyer
0.0159318273881519
-Julio Franco
0.0230480594602062
-Jim Gantner
0.00960427626759017
-Johnny Grubb
0.0249337849541658
-Jack Howell
0.0166783571884679
-John Kruk
0.0135348618245948
-Jeffrey Leonard
0.00621692194497029
-Jim Morrison
0.0104347491092473
-John Moses
0.00955816927339891
-Jerry Mumphrey
0.0114527911454454
-Jim Presley
0.0181732014300399
-Johnny Ray
0.0222264061248388
-Jeff Reed
0.0141048942273143
-Jim Rice
0.0341630071931888
-Jerry Royster
0.00786584848798418
-John Russell
0.00732221183848203
-Juan Samuel
0.011233958379014
-John Shelby
0.0105769969697364
-Joel Skinner
0.00820725725265926
-Jim Sundberg
0.0196190015932163
-Jose Uribe
0.0243170465990865
-Joel Youngblood
0.0127513647950321
-Kevin Bass
0.0219191326187113
-Kal Daniels
0.0194979541215839
-Kirk Gibson
0.020556919885839
-Ken Griffey
0.0157391819211111
-Keith Hernandez
0.0186125240001884
-Kent Hrbek
0.0192503945544296
-Ken Landreaux
0.00738914265279174
-Kevin McReynolds
0.0156330543753078
-Kevin Mitchell
0.00623609661997075
-Keith Moreland
0.0121555120488774
-Ken Oberkfell
0.0126467584348519
-Ken Phelps
0.0198333298123843
-Kirby Puckett
0.0552718094796791
-Kurt Stillwell
0.011990041252144
-Leon Durham
0.00780417454171992
-Len Dykstra
0.00857784296541703
-Larry Herndon
0.0064990040160584
-Lee Lacy
0.00742301328937459
-Len Matuszek
0.0129926810188161
-Lloyd Moseby
0.0154094589566827
-Lance Parrish
0.0168397241242445
-Larry Parrish
0.0195480106203573
-Larry Sheets
0.0102053644915363
-Lou Whitaker
0.0103736298972029
-Mike Aldrete
0.0108976777772544
-Marty Barrett
0.0291908907582424
-Mike Davis
0.00667586668426171
-Mike Diaz
0.0147105547379761
-Mariano Duncan
0.0115422666932657
-Mike Easler
0.010820500442813
-Mel Hall
0.00976796679777078
-Mike Heath
0.0081507738805316
-Mike Kingery
0.0111519990806471
-Mike LaValliere
0.00901026773489625
-Mike Marshall
0.013711182342755
-Mike Pagliarulo
0.0255437587312095
-Mark Salas
0.00824038954487028
-Mike Schmidt
0.0308861245462707
-Mike Scioscia
0.00698057071979755
-Mickey Tettleton
0.0135500510047471
-Milt Thompson
0.00617205972690294
-Mitch Webster
0.0169403513647917
-Mookie Wilson
0.00619444773498657
-Marvell Wynne
0.0063403620095783
-Mike Young
0.00474275439485779
-Ozzie Guillen
0.0271620505926552
-Oddibe McDowell
0.00964328420757499
-Ozzie Smith
0.0229502793106078
-Ozzie Virgil
0.0114067190696189
-Phil Bradley
0.0168810816259417
-Phil Garner
0.00535812295602376
-Pete Incaviglia
0.025161431654974
-Paul Molitor
0.00570944294085908
-Pete Rose
0.0126156272171943
-Pat Sheridan
0.00888970164559414
-Pat Tabler
0.026279450164693
-Rafael Belliard
0.0123374671998298
-Rick Burleson
0.00906906701865493
-Randy Bush
0.00495753180334833
-Rick Cerone
0.0104730023394748
-Ron Cey
0.0113956391454122
-Rob Deer
0.0395521316143585
-Rick Dempsey
0.0136529420759308
-Ron Hassey
0.0158151139459369
-Rickey Henderson
0.0194628445140604
-Reggie Jackson
0.00963058080211747
-Ron Kittle
0.0195094238607815
-Ray Knight
0.0100975869646124
-Rick Leach
0.0140249162441515
-Rick Manning
0.0115898080723435
-Rance Mulliniks
0.00450212481049989
-Ron Oester
0.0122552708544235
-Rey Quinones
0.0128781945206417
-Rafael Ramirez
0.0155619012974591
-Ronn Reynolds
0.0174189559060563
-Ron Roenicke
0.007216482671799
-Ryne Sandberg
0.0148031952946029
-Rafael Santana
0.0213487186421553
-Rick Schu
0.0124262441988659
-Ruben Sierra
0.00575359430765965
-Roy Smalley
0.0106124476383773
-Robby Thompson
0.0140106441432452
-Rob Wilfong
0.0109282567228258
-Robin Yount
0.0199323190913311
-Steve Balboni
0.032832608857617
-Scott Bradley
0.013819143124654
-Sid Bream
0.0064848822413407
-Steve Buechele
0.010047792882046
-Shawon Dunston
0.0154878353515676
-Scott Fletcher
0.0231584911833167
-Steve Garvey
0.0124707214778381
-Steve Jeltz
0.0294334036298904
-Steve Lombardozzi
0.0163703558064671
-Spike Owen
0.0361863260829997
-Steve Sax
0.056205798190448
-Tony Bernazard
0.0137201779926164
-Tom Brookens
0.00842727602684437
-Tom Brunansky
0.0155535640161956
-Tony Fernandez
0.0384149427739519
-Tim Flannery
0.00879815995334561
-Tom Foley
0.010178072996595
-Tony Gwynn
0.0441255560927934
-Terry Harper
0.00728359774271928
-Tommy Herr
0.0283062395596944
-Tim Hulett
0.0193407789424842
-Terry Kennedy
0.0326924785968483
-Tito Landrum
0.0124610368212244
-Tim Laudner
0.0137152102414128
-Tom Paciorek
0.0126750030530696
-Tony Pena
0.00921261317536243
-Terry Pendleton
0.0411002808615697
-Tony Phillips
0.00947681648702826
-Terry Puhl
0.013480153488892
-Ted Simmons
0.0183540764261599
-Tim Teufel
0.00754075413540749
-Tim Wallach
0.014724129247963
-Vince Coleman
0.0540676127419561
-Von Hayes
0.0192039404330803
-Vance Law
0.0113459171671123
-Wally Backman
0.022556121420949
-Wade Boggs
0.0736687853777228
-Will Clark
0.00548420107775056
-Wally Joyner
0.01320331340394
-Willie McGee
0.0115854961579362
-Willie Randolph
0.011798792067581
-Wayne Tolleson
0.0136448610296419
-Willie Upshaw
0.0189725147824934
-Willie Wilson
0.0210111323582833
$coefficients
A matrix: 263 × 4 of type dbl
(Intercept) AtBat Hits HmRun
-Alan Ashby 0.65924938 -4.086660e-04 -1.281158e-03 -0.0083503671
-Alvin Davis 0.19498183 -6.704304e-04 -2.345890e-04 -0.0516648778
-Andre Dawson 0.06576750 1.100954e-02 -4.016280e-02 -0.0970298280
-Andres Galarraga -4.21682830 1.761848e-02 -3.703466e-02 -0.0320576617
-Alfredo Griffin -0.77018454 2.388378e-03 9.127765e-03 -0.0763167161
-Al Newman -2.01620004 -2.341329e-03 2.006901e-02 0.0297530788
-Argenis Salazar -1.85154500 -6.368273e-03 2.098820e-02 0.1194087080
-Andres Thomas -2.56590064 -5.396923e-03 2.574708e-02 0.0672680286
-Andre Thornton 0.10303912 6.698207e-02 -2.553939e-01 0.2464785215
-Alan Trammell 2.03660813 -3.586078e-03 -7.094059e-03 -0.0733319660
-Alex Trevino 3.73771207 -1.346635e-02 2.388866e-02 -0.0125752009
-Andy VanSlyke -0.06284050 1.416493e-04 -5.027719e-04 -0.0013033606
-Alan Wiggins 6.26418239 -7.921075e-03 6.495036e-03 -0.1867461933
-Bill Almon -0.66310602 5.527425e-04 3.398486e-03 -0.0058770693
-Buddy Bell 0.00952803 -1.127743e-05 -6.277069e-05 -0.0002924174
-Buddy Biancalana -1.70759169 3.655244e-03 -2.793180e-03 0.0165104010
-Bruce Bochy -4.44090060 1.869447e-02 -2.742246e-02 -0.0687457299
-Barry Bonds 0.65494620 -4.598393e-02 1.642284e-01 -0.0928787697
-Bobby Bonilla 0.21192170 -2.260935e-02 4.828845e-02 0.2152155106
-Bob Brenly -0.27252701 6.233813e-03 -1.957537e-02 0.0088001622
-Bill Buckner -0.45485652 2.949080e-03 -5.416430e-03 -0.0026034641
-Brett Butler -1.41235128 7.937832e-03 1.993044e-03 -0.1295576882
-Bob Dernier 2.22713238 3.647360e-02 -1.260762e-01 -0.1530605674
-Bo Diaz -0.26184766 3.227393e-03 1.145628e-03 -0.0465005599
-Bill Doran -0.02728711 1.626614e-04 5.683137e-05 -0.0026675099
-Brian Downing -0.91568606 6.678274e-03 -1.681666e-02 0.0729610721
-Billy Hatcher -0.20437836 -1.872251e-02 4.266133e-02 0.1567504397
-Brook Jacoby 1.34598144 4.664552e-03 -3.759005e-02 0.0063911208
-Bob Kearney -0.08820219 1.879015e-04 -2.026282e-05 -0.0003393462
-Bill Madlock 2.18222420 -1.384198e-02 4.418954e-02 -0.0163762368
⋮ ⋮ ⋮ ⋮ ⋮
-Tony Fernandez 7.06537284 0.0565156366 -0.351299510 0.483422041
-Tim Flannery -1.01933468 0.0045248195 -0.020810894 0.076494461
-Tom Foley -1.28244788 0.0034576426 -0.008433418 0.038790823
-Tony Gwynn 1.25204500 0.0641744467 -0.275670947 0.116733745
-Terry Harper 0.54502374 -0.0013766830 0.001170777 0.002694023
-Tommy Herr -5.99483011 0.0763894855 -0.160940404 -0.493581322
-Tim Hulett 3.59601814 -0.0625005547 0.192278681 -0.029916225
-Terry Kennedy 26.55838372 -0.1158123257 0.201345158 0.122066179
-Tito Landrum 1.13024912 0.0015617120 -0.012017503 -0.016340543
-Tim Laudner -1.98257829 0.0061722430 -0.004098792 -0.038386487
-Tom Paciorek -2.77226979 0.0144500766 -0.034564760 0.012078742
-Tony Pena -0.98487182 -0.0136270227 0.095360137 -0.171708913
-Terry Pendleton 4.54802865 -0.0638023359 0.153211680 0.316621222
-Tony Phillips 0.05485979 -0.0024171333 0.005349894 0.018807172
-Terry Puhl 13.38730788 -0.0374062086 0.043150123 -0.043522054
-Ted Simmons 6.09400873 -0.0236603094 0.037567620 0.027284006
-Tim Teufel -0.67151496 -0.0001857344 0.003288409 0.014743759
-Tim Wallach -1.61211169 0.0356716192 -0.116871942 0.063226245
-Vince Coleman 4.75964847 -0.0674930368 0.167442603 0.305677592
-Von Hayes -2.07154896 -0.0374915002 0.170440619 0.020979381
-Vance Law 0.41809764 0.0241963127 -0.078369026 -0.080688279
-Wally Backman -0.46933529 0.0066426159 -0.025722440 0.033033473
-Wade Boggs 2.53680391 -0.1858604097 0.733772104 -0.377519798
-Will Clark -2.78654493 0.0285231362 -0.100429173 0.023143027
-Wally Joyner 4.73172625 0.0304243580 -0.159518442 -0.218513250
-Willie McGee -1.25566058 0.0201839892 -0.045081166 -0.110406929
-Willie Randolph -0.95975323 0.0075263046 0.014433543 -0.211613919
-Wayne Tolleson 0.39638021 -0.0070850671 0.009543190 0.087366853
-Willie Upshaw -5.67666776 0.0673426811 -0.157285698 -0.253588560
-Willie Wilson -5.06778235 0.0352735234 -0.046913737 -0.244613940
$sigma
-Alan Ashby
399.634203569099
-Alvin Davis
399.492597339658
-Andre Dawson
399.357259506549
-Andres Galarraga
398.933958984569
-Alfredo Griffin
399.628837026824
-Al Newman
399.589183690645
-Argenis Salazar
399.45913958176
-Andres Thomas
399.186969057154
-Andre Thornton
397.63748684862
-Alan Trammell
399.305567442193
-Alex Trevino
399.47898208154
-Andy VanSlyke
399.654722352462
-Alan Wiggins
398.809647826131
-Bill Almon
399.649936999163
-Buddy Bell
399.656593829134
-Buddy Biancalana
399.617963490199
-Bruce Bochy
399.517436655539
-Barry Bonds
399.117135210789
-Bobby Bonilla
399.173453123254
-Bob Brenly
399.638214399165
-Bill Buckner
399.651742803744
-Brett Butler
399.574300125236
-Bob Dernier
398.830912043822
-Bo Diaz
399.52670812524
-Bill Doran
399.656542576923
-Brian Downing
399.435802080694
-Billy Hatcher
399.058122239888
-Brook Jacoby
399.469820860983
-Bob Kearney
399.656489418298
-Bill Madlock
399.199661955533
-Bob Melvin
399.466996751965
-BillyJo Robidoux
399.532114622873
-Bill Schroeder
399.617758642113
-Chris Bando
399.648029050811
-Chris Brown
398.616310438533
-Carmen Castillo
399.558389784502
-Chili Davis
399.561670241124
-Carlton Fisk
398.625143843004
-Curt Ford
399.431008718328
-Carney Lansford
398.926230716375
-Chet Lemon
399.478161122053
-Candy Maldonado
399.572887009363
-Carmelo Martinez
399.656443141091
-Craig Reynolds
399.648479206124
-Cal Ripken
398.612250898437
-Cory Snyder
397.956233002957
-Chris Speier
399.635873837542
-Curt Wilkerson
399.653274124473
-Dave Anderson
399.645838956195
-Don Baylor
399.332313144429
-Daryl Boston
399.320992119561
-Darnell Coles
397.824487497975
-Dave Concepcion
399.641570126188
-Doug DeCinces
399.539814233217
-Darrell Evans
399.581917564588
-Dwight Evans
399.431220069416
-Damaso Garcia
399.198095338432
-Dan Gladden
399.361682500835
-Dave Henderson
399.404765367991
-Donnie Hill
399.478033157219
-Davey Lopes
399.648557868608
-Don Mattingly
397.743646040557
-Dale Murphy
393.964283305825
-Dwayne Murphy
399.500396526051
-Dave Parker
399.565499922729
-Dan Pasqua
398.677165239333
-Darrell Porter
399.59464075442
-Dick Schofield
399.648624041364
-Don Slaught
399.643928622877
-Darryl Strawberry
398.303115961143
-Dale Sveum
399.190292541126
-Danny Tartabull
397.875762023231
-Denny Walling
399.624442702131
-Dave Winfield
393.379419635538
-Eric Davis
398.765458160105
-Eddie Milner
399.636464677271
-Eddie Murray
385.948066373798
-Ed Romero
399.540856668197
-Frank White
399.655475127278
-George Bell
399.628236270768
-Glenn Braggs
399.429525938891
-George Brett
396.416592064954
-Greg Brock
399.644129572991
-Gary Carter
391.724908196771
-Glenn Davis
397.825873937425
-Gary Gaetti
399.629327956353
-Greg Gagne
399.014594348095
-George Hendrick
399.441514335659
-Glenn Hubbard
399.472407530578
-Garth Iorg
399.654394940912
-Gary Matthews
399.539923897956
-Graig Nettles
399.462993329827
-Gary Pettis
399.584369549925
-Gary Redus
399.651883210097
-Garry Templeton
399.185460011545
-Greg Walker
399.656193673305
-Gary Ward
399.655966022193
-Glenn Wilson
399.648238491901
-Harold Baines
399.628458110819
-Hubie Brooks
399.631800047401
-Howard Johnson
399.637790944298
-Hal McRae
399.645132646166
-Harold Reynolds
399.438307895792
-Harry Spilman
399.5700147204
-Herm Winningham
399.545267959526
-Jesse Barfield
399.444717016645
-Juan Beniquez
399.600368849692
-John Cangelosi
399.346282156929
-Jose Canseco
398.02468475877
-Joe Carter
396.345005739808
-Jack Clark
395.113012819977
-Jose Cruz
399.530072034124
-Jody Davis
398.960009857206
-Jim Dwyer
399.650790727091
-Julio Franco
399.634941644984
-Jim Gantner
399.30120909998
-Johnny Grubb
399.509727897045
-Jack Howell
399.4451037316
-John Kruk
398.989538398825
-Jeffrey Leonard
398.974767418778
-Jim Morrison
398.505945585891
-John Moses
399.114195166899
-Jerry Mumphrey
399.613137347821
-Jim Presley
397.818000372507
-Johnny Ray
399.594524245333
-Jeff Reed
399.515249933965
-Jim Rice
390.196208465802
-Jerry Royster
399.603735704486
-John Russell
399.30666953672
-Juan Samuel
399.642278659429
-John Shelby
399.609869907446
-Joel Skinner
399.437654115013
-Jim Sundberg
398.584394963321
-Jose Uribe
399.579000294072
-Joel Youngblood
399.560223620739
-Kevin Bass
399.126373002493
-Kal Daniels
399.12015978781
-Kirk Gibson
397.975247493125
-Ken Griffey
399.53237331735
-Keith Hernandez
395.12160557951
-Kent Hrbek
398.360454780228
-Ken Landreaux
398.997937387274
-Kevin McReynolds
399.358715010895
-Kevin Mitchell
398.903463941795
-Keith Moreland
399.00989140517
-Ken Oberkfell
399.510017390875
-Ken Phelps
399.330435852697
-Kirby Puckett
395.642946606445
-Kurt Stillwell
399.496801962796
-Leon Durham
398.261636678748
-Len Dykstra
398.809639978878
-Larry Herndon
399.54653974752
-Lee Lacy
399.554332681094
-Len Matuszek
399.606362918436
-Lloyd Moseby
399.597604730663
-Lance Parrish
399.36277824941
-Larry Parrish
399.500451278616
-Larry Sheets
398.781597712039
-Lou Whitaker
399.145067821065
-Mike Aldrete
399.430603303995
-Marty Barrett
399.565465636137
-Mike Davis
399.592637413193
-Mike Diaz
399.145038102774
-Mariano Duncan
399.413058360128
-Mike Easler
399.640085387524
-Mel Hall
399.498717574299
-Mike Heath
399.142076130073
-Mike Kingery
399.369015887524
-Mike LaValliere
399.451525535306
-Mike Marshall
399.448864415595
-Mike Pagliarulo
398.597729793777
-Mark Salas
399.472597477717
-Mike Schmidt
379.292250579782
-Mike Scioscia
398.572806263645
-Mickey Tettleton
399.527735602914
-Milt Thompson
399.392147441609
-Mitch Webster
398.347346283402
-Mookie Wilson
399.385964043788
-Marvell Wynne
399.519163457209
-Mike Young
399.615621049389
-Ozzie Guillen
399.242206269624
-Oddibe McDowell
398.425124104216
-Ozzie Smith
390.008483574748
-Ozzie Virgil
399.232670321634
-Phil Bradley
399.640200646453
-Phil Garner
399.656525133287
-Pete Incaviglia
398.140184239167
-Paul Molitor
397.429741229718
-Pete Rose
398.280795633753
-Pat Sheridan
399.582502621366
-Pat Tabler
399.497740921433
-Rafael Belliard
399.553174081354
-Rick Burleson
399.65322242696
-Randy Bush
399.521546684067
-Rick Cerone
399.62878918092
-Ron Cey
397.973834039668
-Rob Deer
398.730746953908
-Rick Dempsey
399.637209844612
-Ron Hassey
399.634427225238
-Rickey Henderson
395.951714392753
-Reggie Jackson
399.652720587124
-Ron Kittle
399.652676908848
-Ray Knight
399.438845758554
-Rick Leach
399.450896732263
-Rick Manning
399.642943281909
-Rance Mulliniks
399.654922439105
-Ron Oester
399.44241283954
-Rey Quinones
399.486378350133
-Rafael Ramirez
398.766407058046
-Ronn Reynolds
399.653501886057
-Ron Roenicke
399.544472584493
-Ryne Sandberg
399.642443719266
-Rafael Santana
399.65494440862
-Rick Schu
399.363722079039
-Ruben Sierra
398.636609618147
-Roy Smalley
399.518322924908
-Robby Thompson
398.579898644176
-Rob Wilfong
399.625113730433
-Robin Yount
399.428710993818
-Steve Balboni
398.360706238665
-Scott Bradley
399.146876060407
-Sid Bream
398.620806071406
-Steve Buechele
398.846032824028
-Shawon Dunston
398.593654297952
-Scott Fletcher
399.442652563701
-Steve Garvey
396.65636455604
-Steve Jeltz
399.58260056726
-Steve Lombardozzi
399.272349470646
-Spike Owen
399.656235335859
-Steve Sax
395.614338602903
-Tony Bernazard
399.156464351707
-Tom Brookens
399.649134852872
-Tom Brunansky
399.408904165723
-Tony Fernandez
397.817017292335
-Tim Flannery
399.556718137648
-Tom Foley
399.616988419874
-Tony Gwynn
399.184364023896
-Terry Harper
399.64941906511
-Tommy Herr
398.657363966685
-Tim Hulett
399.145382261934
-Terry Kennedy
396.840786363831
-Tito Landrum
399.631568221619
-Tim Laudner
399.609029909848
-Tom Paciorek
399.564853400074
-Tony Pena
398.575984199143
-Terry Pendleton
399.33123547191
-Tony Phillips
399.651379214157
-Terry Puhl
397.688749711276
-Ted Simmons
399.38288948683
-Tim Teufel
399.640405908538
-Tim Wallach
399.377418080339
-Vince Coleman
399.412859480921
-Von Hayes
398.995072376167
-Vance Law
399.446049912437
-Wally Backman
399.646230007602
-Wade Boggs
398.079495263796
-Will Clark
398.533481524676
-Wally Joyner
397.186759775293
-Willie McGee
399.471318558753
-Willie Randolph
399.198237604745
-Wayne Tolleson
399.598450704678
-Willie Upshaw
398.81428332845
-Willie Wilson
399.12738883149
$wt.res
-Alan Ashby
67.7800562087087
-Alvin Davis
-183.345293019541
-Andre Dawson
-247.375182642532
-Andres Galarraga
-384.813327418291
-Alfredo Griffin
74.7315286332977
-Al Newman
-117.07197395248
-Argenis Salazar
-200.665020800462
-Andres Thomas
-310.205917546153
-Andre Thornton
640.648615530166
-Alan Trammell
-267.656083228693
-Alex Trevino
190.25352752117
-Andy VanSlyke
-19.6536365997382
-Alan Wiggins
415.330079297421
-Bill Almon
-36.8517287339844
-Buddy Bell
-1.35241541753995
-Buddy Biancalana
-88.7106348656366
-Bruce Bochy
-167.655635510768
-Barry Bonds
-331.081398558356
-Bobby Bonilla
-313.806646549598
-Bob Brenly
61.3099969638083
-Bill Buckner
31.4371793372293
-Brett Butler
128.754601606279
-Bob Dernier
410.323289380803
-Bo Diaz
163.180113095525
-Bill Doran
3.49626524769039
-Brian Downing
212.526647532097
-Billy Hatcher
-349.932396304933
-Brook Jacoby
-195.171249913134
-Bob Kearney
-4.80870487790564
-Bill Madlock
306.156580178178
-Bob Melvin
-196.82474768404
-BillyJo Robidoux
-159.141935211524
-Bill Schroeder
-88.993441680264
-Chris Bando
-41.8422889642001
-Chris Brown
-459.010482523421
-Carmen Castillo
-141.376931971695
-Chili Davis
139.416761251418
-Carlton Fisk
456.781868012672
-Curt Ford
-214.474379654876
-Carney Lansford
385.836455594581
-Chet Lemon
191.330626342117
-Candy Maldonado
-130.882535697752
-Carmelo Martinez
-5.71193253559322
-Craig Reynolds
40.8066844825446
-Cal Ripken
460.170947533131
-Cory Snyder
-587.304792470144
-Chris Speier
-64.8017087996083
-Curt Wilkerson
-26.0478888596196
-Dave Anderson
-46.8442929092329
-Don Baylor
253.953744692514
-Daryl Boston
-261.440549141057
-Darnell Coles
-611.603935126123
-Dave Concepcion
-55.4674758077263
-Doug DeCinces
153.921018529722
-Darrell Evans
-122.448748207027
-Dwight Evans
213.870844722575
-Damaso Garcia
306.274048898031
-Dan Gladden
-245.665992427704
-Dave Henderson
-227.29254394042
-Donnie Hill
-191.105371028528
-Davey Lopes
40.554165593647
-Don Mattingly
598.319277598617
-Dale Murphy
1068.42965654213
-Dwayne Murphy
179.014700419564
-Dave Parker
135.45070641864
-Dan Pasqua
-445.807053482183
-Darrell Porter
-111.828849079933
-Dick Schofield
-40.4225403345766
-Don Slaught
-50.9535759790935
-Darryl Strawberry
523.179287889077
-Dale Sveum
-309.106462763598
-Danny Tartabull
-601.440367261628
-Denny Walling
-80.9282759858087
-Dave Winfield
1125.69219116458
-Eric Davis
-424.032103920511
-Eddie Milner
-64.2884097306572
-Eddie Murray
1656.28214419654
-Ed Romero
153.55543035292
-Frank White
-15.1706074829492
-George Bell
75.1556565287132
-Glenn Braggs
-215.25760276689
-George Brett
812.88430477159
-Greg Brock
-50.4565048468612
-Gary Carter
1264.0594565789
-Glenn Davis
-606.520649566213
-Gary Gaetti
-73.8606997041783
-Greg Gagne
-362.338576182642
-George Hendrick
209.531632083408
-Glenn Hubbard
193.466934012087
-Garth Iorg
-21.2576387351008
-Gary Matthews
154.175498873463
-Graig Nettles
-198.429297664118
-Gary Pettis
-120.935011745943
-Gary Redus
-31.1141247211481
-Garry Templeton
307.986106586873
-Greg Walker
9.14124868112292
-Gary Ward
-11.3679009173431
-Glenn Wilson
-41.3180421898229
-Harold Baines
75.6599531231978
-Hubie Brooks
70.6338894140339
-Howard Johnson
-61.9357958533628
-Hal McRae
-48.474066324933
-Harold Reynolds
-209.301620327783
-Harry Spilman
-132.424978895246
-Herm Winningham
-150.563795884441
-Jesse Barfield
204.007229803057
-Juan Beniquez
-107.15312797439
-John Cangelosi
-250.565658249054
-Jose Canseco
-568.233122374574
-Joe Carter
-813.089352277853
-Jack Clark
960.505689659938
-Jose Cruz
161.019061085732
-Jody Davis
376.459891359261
-Jim Dwyer
-34.3434710507558
-Julio Franco
-66.0601688331282
-Jim Gantner
269.358699127131
-Johnny Grubb
-171.838022127467
-Jack Howell
-207.067953446457
-John Kruk
-368.223751958345
-Jeffrey Leonard
-373.653104622136
-Jim Morrison
-484.228919189103
-John Moses
-332.734871510109
-Jerry Mumphrey
94.1298253578462
-Jim Presley
-609.438149799754
-Johnny Ray
-111.877142843771
-Jeff Reed
-169.510879992981
-Jim Rice
1364.55006368818
-Jerry Royster
-103.999639155523
-John Russell
-267.590083275267
-Juan Samuel
-54.0437192880373
-John Shelby
-97.6467732452258
-Joel Skinner
-211.587726780924
-Jim Sundberg
465.279368155062
-Jose Uribe
-124.950915616423
-Joel Youngblood
140.070604499256
-Kevin Bass
-326.921657688736
-Kal Daniels
-329.236976542924
-Kirk Gibson
582.14402580365
-Ken Griffey
158.782267361893
-Keith Hernandez
955.303999211567
-Kent Hrbek
511.590308251624
-Ken Landreaux
367.038202402703
-Kevin McReynolds
-245.862477419598
-Kevin Mitchell
-392.683613419869
-Keith Moreland
362.820757982595
-Ken Oberkfell
172.746852451584
-Ken Phelps
-256.714055315183
-Kirby Puckett
-882.06124667897
-Kurt Stillwell
-180.42432563195
-Leon Durham
533.788943932952
-Len Dykstra
-415.910238696257
-Larry Herndon
-150.156223654492
-Lee Lacy
-144.676170013163
-Len Matuszek
-101.120476392784
-Lloyd Moseby
109.445769501835
-Lance Parrish
244.030830326028
-Larry Parrish
-177.669210096705
-Larry Sheets
-422.384856127069
-Lou Whitaker
-323.000076354027
-Mike Aldrete
-214.674900219887
-Marty Barrett
-135.06978793439
-Mike Davis
114.463998835635
-Mike Diaz
-322.300899557089
-Mariano Duncan
-222.776983156224
-Mike Easler
-58.0459834544182
-Mel Hall
-179.541420331312
-Mike Heath
324.306227919313
-Mike Kingery
-242.124936548447
-Mike LaValliere
-204.694391158619
-Mike Marshall
205.52862360045
-Mike Pagliarulo
-460.981610247946
-Mark Salas
-193.970967587303
-Mike Schmidt
1991.53081105811
-Mike Scioscia
470.789169935772
-Mickey Tettleton
-161.898200722661
-Milt Thompson
-232.770673155091
-Mitch Webster
-514.771716718755
-Mookie Wilson
235.472665331111
-Marvell Wynne
-167.805169548164
-Mike Young
-91.7107068988726
-Ozzie Guillen
-288.259770879492
-Oddibe McDowell
-501.121239537188
-Ozzie Smith
1385.83327291096
-Ozzie Virgil
293.907257636743
-Phil Bradley
-57.6656386051236
-Phil Garner
3.99086175422808
-Pete Incaviglia
-551.609693048556
-Paul Molitor
674.785595483477
-Pete Rose
528.830102649674
-Pat Sheridan
-123.060530334477
-Pat Tabler
-178.587959125593
-Rafael Belliard
-145.132631319866
-Rick Burleson
26.2827152966923
-Randy Bush
-166.459873267454
-Rick Cerone
-75.3361148411943
-Ron Cey
585.105514035373
-Rob Deer
-427.981756862369
-Rick Dempsey
62.805798909155
-Ron Hassey
-67.0869313322284
-Rickey Henderson
863.533325149634
-Reggie Jackson
-28.1581764674054
-Ron Kittle
-28.1745560525503
-Ray Knight
-210.810121188791
-Rick Leach
-204.488532219717
-Rick Manning
52.7655700191927
-Rance Mulliniks
-18.5732077775455
-Ron Oester
208.848830444002
-Rey Quinones
-186.130873802358
-Rafael Ramirez
424.877109067089
-Ronn Reynolds
-25.0665888740822
-Ron Roenicke
-151.504821453376
-Ryne Sandberg
-53.6343768278081
-Rafael Santana
-18.2946008972326
-Rick Schu
-244.184962221945
-Ruben Sierra
-457.021589556042
-Roy Smalley
167.955201592851
-Robby Thompson
-467.584330386837
-Rob Wilfong
80.1407632780496
-Robin Yount
214.584722465971
-Steve Balboni
-507.986296633222
-Scott Bradley
-321.867266069112
-Sid Bream
-460.374516763279
-Steve Buechele
-406.584104350852
-Shawon Dunston
-464.243720588218
-Scott Fletcher
-207.576715133793
-Steve Garvey
780.197594958407
-Steve Jeltz
-121.697951720275
-Steve Lombardozzi
-279.11845097516
-Spike Owen
-8.54596640943839
-Steve Sax
-884.745594770179
-Tony Bernazard
-318.843538559565
-Tom Brookens
-39.0776713143429
-Tom Brunansky
224.212014148684
-Tony Fernandez
-603.284068119108
-Tim Flannery
-142.880059322374
-Tom Foley
-89.9212735988276
-Tony Gwynn
-305.015041218915
-Terry Harper
38.3489586433606
-Tommy Herr
447.1941065268
-Tim Hulett
-321.434595545371
-Terry Kennedy
748.146213034522
-Tito Landrum
71.4017150776481
-Tim Laudner
-98.3640208138739
-Tom Paciorek
-136.670586581832
-Tony Pena
469.570742925334
-Terry Pendleton
-253.602476951105
-Tony Phillips
-32.6650132185081
-Terry Puhl
631.949441316095
-Ted Simmons
235.352792139137
-Tim Teufel
-57.5752552727432
-Tim Wallach
238.131704064234
-Vince Coleman
-218.02109227197
-Von Hayes
365.639256842471
-Vance Law
207.163816279912
-Wally Backman
-45.7255454440639
-Wade Boggs
548.344227020477
-Will Clark
-479.603323533331
-Wally Joyner
-707.855886902391
-Willie McGee
194.315202710728
-Willie Randolph
305.542963369166
-Wayne Tolleson
-108.755647406025
-Willie Upshaw
412.589715777102
-Willie Wilson
326.760120586328
influence.measures(reg_model)
Influence measures of
     lm(formula = Salary ~ AtBat + Hits + HmRun, data = hitters) :

                      dfb.1_  dfb.AtBt  dfb.Hits  dfb.HmRn     dffit cov.r
-Alan Ashby         8.68e-03 -6.36e-04 -6.23e-04 -2.46e-03  0.012536 1.021
-Alvin Davis        2.57e-03 -1.04e-03 -1.14e-04 -1.52e-02 -0.035436 1.018
-Andre Dawson       8.66e-04  1.72e-02 -1.95e-02 -2.86e-02 -0.056997 1.018
-Andres Galarraga  -5.56e-02  2.75e-02 -1.80e-02 -9.47e-03 -0.071519 1.006
-Alfredo Griffin   -1.01e-02  3.72e-03  4.44e-03 -2.25e-02  0.030079 1.041
-Al Newman         -2.65e-02 -3.65e-03  9.76e-03  8.78e-03 -0.035316 1.029
-Argenis Salazar   -2.44e-02 -9.92e-03  1.02e-02  3.52e-02 -0.053094 1.023
-Andres Thomas     -3.38e-02 -8.41e-03  1.25e-02  1.99e-02 -0.059697 1.012
-Andre Thornton     1.36e-03  1.05e-01 -1.25e-01  7.31e-02  0.177184 0.987
-Alan Trammell      2.68e-02 -5.59e-03 -3.45e-03 -2.16e-02 -0.067532 1.019
-Alex Trevino       4.92e-02 -2.10e-02  1.16e-02 -3.71e-03  0.051902 1.024
-Andy VanSlyke     -8.27e-04  2.21e-04 -2.44e-04 -3.84e-04 -0.003092 1.020
-Alan Wiggins       8.26e-02 -1.24e-02  3.16e-03 -5.52e-02  0.112136 1.010
-Bill Almon        -8.73e-03  8.61e-04  1.65e-03 -1.73e-03 -0.010249 1.028
-Buddy Bell         1.25e-04 -1.76e-05 -3.05e-05 -8.62e-05 -0.000329 1.025
-Buddy Biancalana  -2.25e-02  5.69e-03 -1.36e-03  4.87e-03 -0.024970 1.027
-Bruce Bochy       -5.85e-02  2.91e-02 -1.33e-02 -2.03e-02 -0.061210 1.034
-Barry Bonds        8.63e-03 -7.17e-02  7.99e-02 -2.74e-02 -0.099680 1.019
-Bobby Bonilla      2.79e-03 -3.52e-02  2.35e-02  6.36e-02 -0.083613 1.017
-Bob Brenly        -3.59e-03  9.71e-03 -9.52e-03  2.60e-03  0.014460 1.024
-Bill Buckner      -5.99e-03  4.59e-03 -2.63e-03 -7.68e-04  0.009406 1.030
-Brett Butler      -1.86e-02  1.24e-02  9.69e-04 -3.82e-02  0.050210 1.038
-Bob Dernier        2.94e-02  5.69e-02 -6.14e-02 -4.52e-02  0.104980 1.009
-Bo Diaz           -3.45e-03  5.03e-03  5.57e-04 -1.37e-02  0.031266 1.019
-Bill Doran        -3.59e-04  2.53e-04  2.76e-05 -7.87e-04  0.001104 1.032
-Brian Downing     -1.21e-02  1.04e-02 -8.18e-03  2.15e-02  0.047287 1.019
-Billy Hatcher     -2.69e-03 -2.92e-02  2.08e-02  4.63e-02 -0.074400 1.011
-Brook Jacoby       1.77e-02  7.27e-03 -1.83e-02  1.89e-03 -0.051453 1.023
-Bob Kearney       -1.16e-03  2.93e-04 -9.85e-06 -1.00e-04 -0.001269 1.027
-Bill Madlock       2.88e-02 -2.16e-02  2.15e-02 -4.84e-03  0.053022 1.011
-Bob Melvin        -2.82e-02 -1.33e-02  2.01e-02  9.44e-03 -0.047168 1.021
-BillyJo Robidoux  -4.00e-02  5.53e-03  2.48e-03  1.13e-02 -0.046609 1.027
-Bill Schroeder    -1.80e-02 -2.22e-03  7.72e-03 -2.78e-03 -0.023918 1.026
-Chris Bando       -8.41e-03  3.17e-03 -2.29e-03  4.15e-03 -0.010460 1.025
-Chris Brown       -5.22e-02  1.06e-01 -1.23e-01  4.74e-02 -0.150988 1.011
-Carmen Castillo   -3.90e-02  2.32e-02 -1.46e-02 -9.22e-03 -0.040920 1.027
-Chili Davis       -8.54e-03  2.74e-03  3.53e-03 -7.85e-03  0.029494 1.021
-Carlton Fisk      -4.14e-02  1.34e-01 -1.36e-01  3.39e-03  0.155755 1.013
-Curt Ford         -4.91e-02  1.14e-02 -2.96e-03  1.54e-02 -0.056865 1.022
-Carney Lansford   -4.05e-02 -5.02e-03  2.46e-02  1.04e-02  0.101187 1.012
-Chet Lemon         4.79e-03  1.53e-02 -1.64e-02  1.31e-03  0.033959 1.017
-Candy Maldonado   -4.62e-03 -6.67e-03  1.02e-02 -1.75e-02 -0.028870 1.022
-Carmelo Martinez  -1.11e-03  1.25e-04  1.93e-04 -3.20e-04 -0.001366 1.025
-Craig Reynolds     4.84e-03  9.61e-04 -1.67e-03 -2.32e-03  0.007962 1.022
-Cal Ripken        -6.35e-02 -1.31e-03  2.06e-02  6.02e-02  0.145912 1.010
-Cory Snyder       -3.92e-02  3.85e-02 -1.48e-02 -1.52e-01 -0.178644 0.996
-Chris Speier      -2.15e-02  1.29e-02 -8.23e-03 -3.79e-03 -0.021924 1.033
-Curt Wilkerson    -4.92e-03 -1.98e-04  8.58e-04  3.42e-03 -0.007096 1.027
-Dave Anderson     -1.04e-02  1.91e-03 -2.65e-04  4.45e-03 -0.012665 1.027
-Don Baylor        -4.88e-02  7.07e-02 -7.44e-02  7.34e-02  0.123757 1.046
-Daryl Boston      -6.99e-02  3.31e-02 -1.91e-02 -1.14e-03 -0.072599 1.021
-Darnell Coles      3.33e-02 -1.21e-02  2.66e-03 -5.92e-02 -0.135855 0.987
-Dave Concepcion   -7.21e-03  5.03e-04 -2.47e-04  6.59e-03 -0.012144 1.023
-Doug DeCinces     -1.06e-02  1.46e-02 -1.71e-02  3.55e-02  0.049785 1.030
-Darrell Evans      1.10e-02 -2.15e-02  2.57e-02 -3.68e-02 -0.051147 1.042
-Dwight Evans      -1.75e-02  1.92e-02 -2.10e-02  4.68e-02  0.067953 1.027
-Damaso Garcia      1.25e-02 -9.79e-03  1.97e-02 -4.08e-02  0.066363 1.014
-Dan Gladden       -2.67e-02  1.19e-02 -1.44e-02  3.06e-02 -0.053020 1.017
-Dave Henderson    -1.61e-02  4.05e-03  2.35e-04 -1.89e-02 -0.040187 1.016
-Donnie Hill       -2.50e-02  1.62e-02 -1.76e-02  2.21e-02 -0.043215 1.020
-Davey Lopes        8.74e-03 -4.75e-03  3.20e-03  3.12e-04  0.009532 1.024
-Don Mattingly      6.38e-03 -3.78e-01  4.24e-01  1.54e-01  0.497138 1.074
-Dale Murphy       -1.73e-01  1.10e-01 -9.41e-02  2.43e-01  0.397212 0.925
-Dwayne Murphy      1.95e-02  2.57e-03 -6.47e-03 -7.29e-04  0.031814 1.018
-Dave Parker       -2.20e-02  6.86e-03 -4.20e-03  3.43e-02  0.053028 1.038
-Dan Pasqua        -1.01e-01  9.04e-02 -6.41e-02 -8.27e-02 -0.138206 1.011
-Darrell Porter    -3.70e-02  2.10e-02 -1.01e-02 -2.10e-02 -0.041665 1.036
-Dick Schofield     1.66e-03 -5.59e-03  5.19e-03  4.62e-04 -0.008478 1.023
-Don Slaught       -7.59e-03  3.20e-03 -1.18e-03 -4.75e-03 -0.010470 1.022
-Darryl Strawberry -9.32e-03  2.04e-02 -3.76e-02  1.47e-01  0.177875 1.006
-Dale Sveum        -3.46e-02 -1.10e-02  1.72e-02  1.20e-02 -0.059502 1.012
-Danny Tartabull    2.40e-02 -4.75e-03  9.49e-03 -1.28e-01 -0.173445 0.993
-Denny Walling     -1.18e-02  1.88e-02 -1.86e-02 -4.02e-03 -0.022870 1.028
-Dave Winfield     -1.37e-01  1.24e-01 -1.08e-01  1.71e-01  0.335145 0.907
-Eric Davis        -3.51e-02  4.56e-02 -2.41e-02 -1.39e-01 -0.155503 1.019
-Eddie Milner      -1.32e-03 -2.68e-03  3.12e-03 -3.65e-03 -0.011170 1.020
-Eddie Murray       5.79e-02 -3.17e-01  3.64e-01  9.46e-02  0.489635 0.778
-Ed Romero          2.63e-02  1.13e-02 -1.72e-02 -1.35e-02  0.042641 1.026
-Frank White        1.53e-03 -6.98e-04  3.17e-04 -1.63e-03 -0.003897 1.026
-George Bell       -5.58e-03 -1.77e-02  2.05e-02  1.95e-02  0.036125 1.051
-Glenn Braggs      -4.78e-02  7.01e-03  3.28e-03  6.51e-03 -0.055092 1.021
-George Brett       4.71e-02 -9.45e-02  9.83e-02  5.71e-02  0.173086 0.958
-Greg Brock        -5.17e-03 -2.81e-03  5.50e-03 -7.43e-03 -0.012914 1.026
-Gary Carter       -6.17e-02  1.13e-01 -1.35e-01  2.62e-01  0.377879 0.877
-Glenn Davis        6.84e-02 -4.07e-02  4.56e-02 -1.81e-01 -0.238690 1.002
-Gary Gaetti        5.82e-03  6.93e-03 -6.77e-03 -2.60e-02 -0.033040 1.047
-Greg Gagne         2.08e-02 -5.44e-02  4.75e-02  1.55e-02 -0.079601 1.010
-George Hendrick    4.09e-02 -2.49e-02  1.37e-02  2.89e-02  0.052819 1.021
-Glenn Hubbard     -5.46e-03  4.28e-02 -3.89e-02 -3.31e-02  0.058976 1.027
-Garth Iorg        -2.36e-03 -1.37e-04  1.10e-04  2.77e-03 -0.004644 1.023
-Gary Matthews      1.44e-02 -4.54e-03 -3.11e-03  3.47e-02  0.042751 1.026
-Graig Nettles     -8.56e-03 -3.21e-02  4.14e-02 -2.49e-02 -0.058726 1.026
-Gary Pettis        1.61e-02 -2.34e-02  1.45e-02  2.93e-02 -0.041462 1.033
-Gary Redus        -2.88e-03 -1.19e-03  2.01e-03 -9.42e-04 -0.005715 1.021
-Garry Templeton   -3.95e-02  7.73e-02 -5.56e-02 -8.91e-02  0.120165 1.030
-Greg Walker        1.82e-03 -1.20e-03  7.46e-04  1.07e-03  0.002256 1.025
-Gary Ward         -1.60e-03  2.50e-03 -2.82e-03  1.37e-03 -0.003642 1.032
-Glenn Wilson       5.65e-03 -4.08e-03  1.71e-03  2.31e-03 -0.010584 1.026
-Harold Baines     -3.89e-03 -9.03e-03  1.20e-02  6.58e-03  0.022457 1.029
-Hubie Brooks       1.82e-02 -2.57e-02  2.35e-02  9.08e-03  0.028393 1.041
-Howard Johnson    -1.45e-02  4.60e-03 -4.42e-04 -5.91e-03 -0.016557 1.027
-Hal McRae         -7.99e-03  1.15e-03  4.67e-04  5.00e-04 -0.009927 1.022
-Harold Reynolds    2.01e-02 -6.84e-02  5.94e-02  5.59e-02 -0.087826 1.039
-Harry Spilman     -4.44e-02  2.41e-02 -1.43e-02 -5.96e-03 -0.045041 1.032
-Herm Winningham   -3.67e-02  2.79e-03  6.44e-03  1.44e-03 -0.042678 1.026
-Jesse Barfield    -1.17e-02 -2.82e-02  2.26e-02  1.02e-01  0.116556 1.061
-Juan Beniquez     -1.65e-02  1.75e-02 -1.81e-02  7.94e-03 -0.026865 1.025
-John Cangelosi     1.54e-02 -6.05e-02  5.05e-02  5.93e-02 -0.087092 1.028
-Jose Canseco       1.15e-01 -1.54e-01  1.63e-01 -1.84e-01 -0.291733 1.022
-Joe Carter         9.69e-02  1.31e-01 -1.72e-01 -1.61e-01 -0.352580 0.977
-Jack Clark         2.03e-01 -3.27e-02 -2.58e-02  6.29e-02  0.242548 0.936
-Jose Cruz         -2.58e-03  2.92e-04  5.81e-03 -1.40e-02  0.031982 1.019
-Jody Davis        -4.09e-02  6.34e-02 -6.09e-02  4.15e-02  0.107199 1.014
-Jim Dwyer         -1.04e-02  4.29e-03 -1.47e-03 -3.30e-03 -0.011022 1.032
-Julio Franco       5.20e-03  8.60e-03 -1.50e-02  1.13e-02 -0.025687 1.039
-Jim Gantner       -1.31e-02  1.36e-02  1.21e-03 -4.45e-02  0.066750 1.018
-Johnny Grubb      -5.67e-02  5.67e-02 -4.45e-02 -3.00e-02 -0.069655 1.039
-Jack Howell       -6.71e-02  3.52e-02 -2.12e-02 -3.63e-03 -0.068083 1.028
-John Kruk         -8.31e-02  7.74e-02 -7.30e-02  2.61e-02 -0.108842 1.016
-Jeffrey Leonard   -4.71e-02  2.71e-02 -2.69e-02  2.78e-02 -0.074305 1.008
-Jim Morrison       3.10e-02 -5.12e-03 -1.49e-04 -7.27e-02 -0.125433 1.003
-John Moses        -7.36e-03 -2.96e-02  2.05e-02  6.08e-02 -0.082292 1.014
-Jerry Mumphrey     1.80e-02 -1.75e-02  1.72e-02 -6.72e-03  0.025500 1.026
-Jim Presley        1.02e-01 -7.23e-02  5.83e-02 -1.10e-01 -0.210342 0.997
-Johnny Ray         8.54e-03  9.75e-03 -2.07e-02  2.48e-02 -0.042689 1.037
-Jeff Reed         -4.76e-02  1.35e-02 -3.51e-03  6.30e-03 -0.051111 1.027
-Jim Rice          -4.77e-02 -4.34e-01  5.39e-01  5.10e-02  0.669238 0.868
-Jerry Royster     -1.99e-02  5.33e-03 -1.91e-03  3.92e-03 -0.023265 1.023
-John Russell      -3.18e-02 -7.34e-03  1.91e-02 -2.43e-02 -0.057767 1.016
-Juan Samuel        8.35e-03 -7.32e-03  4.38e-03  2.18e-03 -0.014496 1.027
-John Shelby        1.47e-03 -1.95e-02  2.03e-02  1.73e-03 -0.025399 1.025
-Joel Skinner      -1.96e-02 -2.06e-02  2.41e-02  1.72e-02 -0.048386 1.020
-Jim Sundberg      -3.39e-02  1.46e-01 -1.49e-01 -7.63e-03  0.166777 1.014
-Jose Uribe         1.27e-02 -4.06e-02  3.59e-02  2.86e-02 -0.049979 1.039
-Joel Youngblood    3.87e-02 -1.59e-02  7.41e-03  2.04e-03  0.040097 1.027
-Kevin Bass         1.28e-02  7.12e-02 -9.02e-02 -1.74e-02 -0.123985 1.027
-Kal Daniels       -1.09e-01  8.83e-02 -6.92e-02 -1.37e-02 -0.117476 1.025
-Kirk Gibson        2.27e-02 -2.47e-02 -2.73e-03  1.92e-01  0.214128 1.003
-Ken Griffey        7.61e-03 -3.34e-02  3.51e-02  2.31e-02  0.050656 1.029
-Keith Hernandez   -1.52e-02 -1.83e-01  2.48e-01 -6.77e-02  0.336103 0.945
-Kent Hrbek        -4.24e-02  1.99e-02 -2.45e-02  1.39e-01  0.181680 1.009
-Ken Landreaux      6.06e-02 -1.48e-02  7.99e-03 -2.84e-02  0.079663 1.010
-Kevin McReynolds   1.30e-02  2.02e-02 -2.35e-02 -4.94e-02 -0.078198 1.026
-Kevin Mitchell    -5.85e-02  3.95e-02 -2.86e-02 -2.47e-02 -0.078225 1.007
-Keith Moreland    -5.18e-02  3.89e-02 -1.36e-02 -4.43e-02  0.101486 1.015
-Ken Oberkfell     -1.13e-02  1.44e-02 -3.38e-03 -3.68e-02  0.049249 1.026
-Ken Phelps        -2.88e-02  2.99e-03  1.60e-02 -7.95e-02 -0.092367 1.029
-Kirby Puckett      5.34e-02  3.55e-01 -4.12e-01 -2.14e-01 -0.554805 0.992
-Kurt Stillwell    -2.29e-02 -1.51e-02  1.71e-02  2.94e-02 -0.050053 1.025
-Leon Durham       -1.79e-02  2.93e-02 -3.04e-02  6.50e-02  0.119335 0.995
-Len Dykstra       -2.56e-02  4.61e-02 -5.92e-02  3.91e-02 -0.097424 1.007
-Larry Herndon     -2.34e-02  1.15e-03  4.27e-03 -1.07e-03 -0.030495 1.020
-Lee Lacy           1.21e-03  7.57e-03 -1.36e-02  1.06e-02 -0.031430 1.021
-Len Matuszek      -2.73e-02  1.32e-02 -6.25e-03 -9.11e-03 -0.029224 1.028
-Lloyd Moseby      -1.91e-02  2.26e-02 -1.93e-02  7.31e-03  0.034531 1.030
-Lance Parrish      3.46e-02 -1.47e-02 -2.45e-03  6.80e-02  0.080653 1.027
-Larry Parrish     -5.09e-03  1.29e-02 -6.60e-03 -5.55e-02 -0.063419 1.033
-Larry Sheets      -6.01e-02  4.13e-02 -2.12e-02 -7.80e-02 -0.108104 1.008
-Lou Whitaker       4.27e-02 -2.92e-02  1.69e-02 -1.65e-02 -0.083285 1.016
-Mike Aldrete      -4.90e-02  1.23e-02 -4.10e-03  1.57e-02 -0.056724 1.022
-Marty Barrett      2.22e-02 -7.08e-03 -9.51e-03  4.39e-02 -0.059492 1.044
-Mike Davis        -3.44e-03  3.40e-03 -2.79e-03  1.11e-02  0.023562 1.021
-Mike Diaz         -8.72e-02  4.92e-02 -2.48e-02 -4.78e-02 -0.099399 1.020
-Mariano Duncan     5.10e-03 -4.73e-02  4.63e-02  1.88e-02 -0.060623 1.022
-Mike Easler       -1.58e-03  9.03e-03 -1.11e-02  3.61e-04 -0.015274 1.026
-Mel Hall          -1.28e-02  2.82e-02 -2.81e-02 -2.03e-02 -0.044855 1.022
-Mike Heath         4.06e-02  2.41e-02 -3.66e-02  6.25e-04  0.073957 1.013
-Mike Kingery      -5.95e-02  2.18e-02 -1.13e-02  1.12e-02 -0.064746 1.021
-Mike LaValliere   -2.20e-02 -1.68e-02  1.94e-02  2.36e-02 -0.049084 1.021
-Mike Marshall      2.08e-02  1.06e-02 -2.35e-02  4.29e-02  0.061086 1.025
-Mike Pagliarulo    4.30e-02 -8.89e-02  1.04e-01 -1.29e-01 -0.189683 1.020
-Mark Salas        -3.31e-02 -2.78e-03  1.21e-02 -4.68e-03 -0.044444 1.020
-Mike Schmidt       9.44e-01 -4.08e-01  1.81e-01  5.15e-02  0.952182 0.690
-Mike Scioscia      2.27e-02  3.67e-02 -3.22e-02 -5.76e-02  0.099382 1.001
-Mickey Tettleton  -3.39e-02 -4.09e-03  1.65e-02 -1.62e-02 -0.047818 1.027
-Milt Thompson     -3.20e-02 -8.94e-04  6.04e-03  1.09e-02 -0.046072 1.017
-Mitch Webster      4.95e-02  8.30e-03 -5.39e-02  1.03e-01 -0.171094 1.006
-Mookie Wilson      2.45e-02 -2.53e-02  2.69e-02 -8.88e-03  0.046693 1.016
-Marvell Wynne     -2.80e-02  9.59e-03 -4.99e-03  2.78e-03 -0.033658 1.019
-Mike Young        -5.67e-03 -4.87e-03  5.52e-03  3.00e-03 -0.015880 1.020
-Ozzie Guillen      4.79e-02 -7.69e-02  5.21e-02  9.14e-02 -0.122317 1.035
-Oddibe McDowell    6.49e-02 -5.61e-02  3.61e-02 -8.15e-03 -0.124714 1.000
-Ozzie Smith       -9.51e-02  7.13e-02  5.76e-02 -4.69e-01  0.550953 0.855
-Ozzie Virgil       1.25e-02  4.37e-02 -5.55e-02  2.95e-02  0.079533 1.019
-Phil Bradley      -3.04e-04  1.08e-02 -1.43e-02  4.26e-03 -0.019070 1.033
-Phil Garner        5.74e-04 -2.01e-04  1.01e-04  3.37e-05  0.000735 1.021
-Pete Incaviglia    5.99e-02 -7.98e-02  9.24e-02 -1.65e-01 -0.225440 1.011
-Paul Molitor       2.29e-02 -2.78e-02  4.57e-02 -5.30e-02  0.129029 0.977
-Pete Rose          9.07e-02  3.25e-02 -4.72e-02 -7.08e-02  0.151041 1.001
-Pat Sheridan      -2.45e-02  2.13e-03  3.72e-03  3.06e-04 -0.029298 1.023
-Pat Tabler        -1.35e-02  4.82e-02 -6.01e-02  2.96e-02 -0.074424 1.040
-Rafael Belliard   -1.36e-02 -1.55e-02  1.55e-02  2.68e-02 -0.040850 1.026
-Rick Burleson      5.39e-03 -3.42e-03  2.82e-03 -1.20e-03  0.006320 1.025
-Randy Bush        -1.61e-02  4.00e-03 -3.97e-03  1.09e-02 -0.029482 1.018
-Rick Cerone       -1.81e-02  6.80e-03 -3.47e-03  2.24e-03 -0.019496 1.026
-Ron Cey            1.32e-01 -8.12e-02  4.58e-02  7.98e-02  0.158755 0.993
-Rob Deer           2.11e-02 -7.19e-02  1.01e-01 -1.81e-01 -0.222258 1.038
-Rick Dempsey       3.82e-03  1.10e-02 -1.40e-02  5.00e-03  0.018617 1.029
-Ron Hassey        -1.30e-02  1.82e-02 -1.81e-02  4.33e-04 -0.021450 1.031
-Rickey Henderson  -1.39e-01  1.03e-01 -8.99e-02  1.80e-01  0.310296 0.961
-Reggie Jackson    -1.87e-05 -3.39e-03  4.09e-03 -3.46e-03 -0.006982 1.025
-Ron Kittle        -6.74e-04 -4.78e-03  6.41e-03 -6.15e-03 -0.010043 1.036
-Ray Knight        -3.94e-03  2.58e-02 -3.50e-02  1.44e-02 -0.053574 1.021
-Rick Leach        -5.26e-02  4.51e-02 -3.92e-02  5.45e-03 -0.061488 1.026
-Rick Manning       1.35e-02 -5.40e-03  2.01e-03  3.37e-03  0.014381 1.027
-Rance Mulliniks   -1.84e-03  5.85e-05  3.26e-04 -4.75e-04 -0.003132 1.020
-Ron Oester        -2.26e-02  3.44e-02 -2.27e-02 -3.44e-02  0.058600 1.024
-Rey Quinones      -1.38e-02 -2.98e-02  3.16e-02  2.70e-02 -0.053564 1.025
-Rafael Ramirez    -4.85e-02  1.08e-01 -9.09e-02 -6.30e-02  0.135017 1.013
-Ronn Reynolds     -8.04e-03  2.36e-03 -3.87e-04 -3.01e-04 -0.008425 1.034
-Ron Roenicke      -2.42e-02  4.54e-04  3.78e-03  7.77e-03 -0.032447 1.021
-Ryne Sandberg      8.20e-03 -1.64e-03 -2.84e-03  5.71e-03 -0.016574 1.031
-Rafael Santana     6.45e-04 -5.08e-03  4.65e-03  4.18e-03 -0.006834 1.038
-Rick Schu         -6.57e-02  3.72e-02 -2.24e-02 -1.53e-02 -0.069016 1.022
-Ruben Sierra      -3.57e-02  9.90e-03  1.59e-03 -4.98e-02 -0.087465 1.001
-Roy Smalley       -5.91e-03  2.12e-02 -2.40e-02  2.31e-02  0.043772 1.024
-Robby Thompson     5.19e-02 -4.75e-02  1.27e-02  9.53e-02 -0.140832 1.008
-Rob Wilfong        8.69e-03  9.61e-03 -1.13e-02 -8.49e-03  0.021196 1.026
-Robin Yount        1.89e-03 -4.12e-02  5.64e-02 -2.92e-02  0.077390 1.032
-Steve Balboni      6.22e-02 -1.33e-01  1.52e-01 -1.51e-01 -0.238906 1.023
-Scott Bradley     -8.83e-02  6.52e-02 -5.21e-02  2.83e-03 -0.096123 1.019
-Sid Bream          3.29e-02 -2.99e-02  1.65e-02 -4.34e-03 -0.093611 1.001
-Steve Buechele     1.92e-02 -6.31e-02  6.69e-02 -3.78e-02 -0.103221 1.009
-Shawon Dunston     8.37e-02 -1.12e-01  9.27e-02  6.61e-03 -0.147228 1.010
-Scott Fletcher     7.47e-03  1.75e-02 -3.68e-02  5.70e-02 -0.080957 1.035
-Steve Garvey      -1.04e-01  1.28e-01 -1.12e-01  7.07e-02  0.222426 0.968
-Steve Jeltz        1.18e-02 -4.20e-02  3.67e-02  3.48e-02 -0.053836 1.045
-Steve Lombardozzi  2.34e-02 -7.74e-02  7.16e-02  3.31e-02 -0.090932 1.025
-Spike Owen         1.61e-03 -3.28e-03  2.63e-03  2.82e-03 -0.004220 1.054
-Steve Sax          4.74e-02  2.88e-01 -4.15e-01  2.57e-01 -0.561771 0.992
-Tony Bernazard     1.30e-02  4.32e-02 -6.01e-02 -2.28e-03 -0.094867 1.019
-Tom Brookens      -6.87e-03  2.70e-03 -2.15e-03  3.78e-03 -0.009053 1.024
-Tom Brunansky     -3.76e-02  3.98e-02 -3.40e-02  2.41e-02  0.071115 1.027
-Tony Fernandez     9.34e-02  8.84e-02 -1.72e-01  1.43e-01 -0.309101 1.018
-Tim Flannery      -1.34e-02  7.05e-03 -1.01e-02  2.26e-02 -0.033840 1.023
-Tom Foley         -1.69e-02  5.38e-03 -4.10e-03  1.14e-02 -0.022935 1.025
-Tony Gwynn         1.65e-02  1.00e-01 -1.34e-01  3.45e-02 -0.167916 1.052
-Terry Harper       7.18e-03 -2.14e-03  5.69e-04  7.95e-04  0.008249 1.023
-Tommy Herr        -7.91e-02  1.19e-01 -7.84e-02 -1.46e-01  0.194226 1.024
-Tim Hulett         4.74e-02 -9.74e-02  9.36e-02 -8.84e-03 -0.114204 1.025
-Terry Kennedy      3.52e-01 -1.82e-01  9.86e-02  3.63e-02  0.352395 0.992
-Tito Landrum       1.49e-02  2.43e-03 -5.84e-03 -4.82e-03  0.020196 1.028
-Tim Laudner       -2.61e-02  9.61e-03 -1.99e-03 -1.13e-02 -0.029228 1.029
-Tom Paciorek      -3.65e-02  2.25e-02 -1.68e-02  3.56e-03 -0.039003 1.027
-Tony Pena         -1.30e-02 -2.13e-02  4.65e-02 -5.08e-02  0.114130 1.003
-Terry Pendleton    5.99e-02 -9.94e-02  7.45e-02  9.35e-02 -0.134267 1.052
-Tony Phillips      7.22e-04 -3.76e-03  2.60e-03  5.55e-03 -0.008033 1.025
-Terry Puhl         1.77e-01 -5.85e-02  2.11e-02 -1.29e-02  0.187017 0.990
-Ted Simmons        8.03e-02 -3.69e-02  1.83e-02  8.05e-03  0.081328 1.029
-Tim Teufel        -8.84e-03 -2.89e-04  1.60e-03  4.35e-03 -0.012606 1.023
-Tim Wallach       -2.12e-02  5.56e-02 -5.68e-02  1.87e-02  0.073433 1.025
-Vince Coleman      6.27e-02 -1.05e-01  8.14e-02  9.02e-02 -0.134179 1.068
-Von Hayes         -2.73e-02 -5.85e-02  8.30e-02  6.20e-03  0.129480 1.022
-Vance Law          5.51e-03  3.77e-02 -3.81e-02 -2.38e-02  0.055877 1.023
-Wally Backman     -6.18e-03  1.03e-02 -1.25e-02  9.74e-03 -0.017580 1.039
-Wade Boggs         3.35e-02 -2.91e-01  3.58e-01 -1.12e-01  0.403607 1.062
-Will Clark        -3.68e-02  4.45e-02 -4.90e-02  6.85e-03 -0.089611 0.998
-Wally Joyner       6.27e-02  4.77e-02 -7.80e-02 -6.49e-02 -0.207522 0.979
-Willie McGee      -1.65e-02  3.14e-02 -2.19e-02 -3.26e-02  0.052971 1.024
-Willie Randolph   -1.26e-02  1.17e-02  7.02e-03 -6.25e-02  0.084131 1.018
-Wayne Tolleson     5.22e-03 -1.10e-02  4.64e-03  2.58e-02 -0.032231 1.028
-Willie Upshaw     -7.49e-02  1.05e-01 -7.66e-02 -7.50e-02  0.145254 1.018
-Willie Wilson     -6.68e-02  5.50e-02 -2.28e-02 -7.22e-02  0.121217 1.026
                     cook.d     hat inf
-Alan Ashby        3.94e-05 0.00540    
-Alvin Davis       3.15e-04 0.00589    
-Andre Dawson      8.14e-04 0.00833    
-Andres Galarraga  1.28e-03 0.00544    
-Alfredo Griffin   2.27e-04 0.02461    
-Al Newman         3.13e-04 0.01412    
-Argenis Salazar   7.07e-04 0.01093    
-Andres Thomas     8.92e-04 0.00583    
-Andre Thornton    7.80e-03 0.01181    
-Alan Trammell     1.14e-03 0.00995    
-Alex Trevino      6.75e-04 0.01160    
-Andy VanSlyke     2.40e-06 0.00392    
-Alan Wiggins      3.14e-03 0.01133    
-Bill Almon        2.64e-05 0.01206    
-Buddy Bell        2.71e-08 0.00926    
-Buddy Biancalana  1.56e-04 0.01234    
-Bruce Bochy       9.40e-04 0.02042    
-Barry Bonds       2.49e-03 0.01404    
-Bobby Bonilla     1.75e-03 0.01106    
-Bob Brenly        5.25e-05 0.00873    
-Bill Buckner      2.22e-05 0.01390    
-Brett Butler      6.32e-04 0.02317    
-Bob Dernier       2.75e-03 0.01020    
-Bo Diaz           2.45e-04 0.00579    
-Bill Doran        3.06e-07 0.01543    
-Brian Downing     5.61e-04 0.00778    
-Billy Hatcher     1.39e-03 0.00710    
-Brook Jacoby      6.64e-04 0.01085    
-Bob Kearney       4.04e-07 0.01088    
-Bill Madlock      7.04e-04 0.00473    
-Bob Melvin        5.58e-04 0.00900    
-BillyJo Robidoux  5.45e-04 0.01333    
-Bill Schroeder    1.44e-04 0.01128    
-Chris Bando       2.75e-05 0.00979    
-Chris Brown       5.69e-03 0.01663    
-Carmen Castillo   4.20e-04 0.01303    
-Chili Davis       2.18e-04 0.00704    
-Carlton Fisk      6.06e-03 0.01782    
-Curt Ford         8.11e-04 0.01097    
-Carney Lansford   2.56e-03 0.01071    
-Chet Lemon        2.89e-04 0.00498    
-Candy Maldonado   2.09e-04 0.00765    
-Carmelo Martinez  4.68e-07 0.00897    
-Craig Reynolds    1.59e-05 0.00601    
-Cal Ripken        5.32e-03 0.01548    
-Cory Snyder       7.94e-03 0.01424    
-Chris Speier      1.21e-04 0.01764    
-Curt Wilkerson    1.26e-05 0.01158    
-Dave Anderson     4.03e-05 0.01141    
-Don Baylor        3.84e-03 0.03525    
-Daryl Boston      1.32e-03 0.01200    
-Darnell Coles     4.59e-03 0.00769    
-Dave Concepcion   3.70e-05 0.00754    
-Doug DeCinces     6.22e-04 0.01616    
-Darrell Evans     6.56e-04 0.02641    
-Dwight Evans      1.16e-03 0.01561    
-Damaso Garcia     1.10e-03 0.00737    
-Dan Gladden       7.04e-04 0.00732    
-Dave Henderson    4.05e-04 0.00494    
-Donnie Hill       4.68e-04 0.00803    
-Davey Lopes       2.28e-05 0.00867    
-Don Mattingly     6.14e-02 0.09037   *
-Dale Murphy       3.85e-02 0.02058   *
-Dwayne Murphy     2.54e-04 0.00499    
-Dave Parker       7.05e-04 0.02334    
-Dan Pasqua        4.77e-03 0.01483    
-Darrell Porter    4.36e-04 0.02123    
-Dick Schofield    1.80e-05 0.00693    
-Don Slaught       2.75e-05 0.00665    
-Darryl Strawberry 7.89e-03 0.01769    
-Dale Sveum        8.86e-04 0.00584    
-Danny Tartabull   7.48e-03 0.01283    
-Denny Walling     1.31e-04 0.01244    
-Dave Winfield     2.73e-02 0.01335   *
-Eric Davis        6.04e-03 0.02052    
-Eddie Milner      3.13e-05 0.00478    
-Eddie Murray      5.61e-02 0.01269   *
-Ed Romero         4.56e-04 0.01202    
-Frank White       3.81e-06 0.01032    
-George Bell       3.27e-04 0.03440   *
-Glenn Braggs      7.61e-04 0.01024    
-George Brett      7.40e-03 0.00702    
-Greg Brock        4.18e-05 0.01025    
-Gary Carter       3.44e-02 0.01335   *
-Glenn Davis       1.42e-02 0.02338    
-Gary Gaetti       2.74e-04 0.03006   *
-Greg Gagne        1.59e-03 0.00757    
-George Hendrick   6.99e-04 0.00994    
-Glenn Hubbard     8.72e-04 0.01441    
-Garth Iorg        5.41e-06 0.00751    
-Gary Matthews     4.58e-04 0.01198    
-Graig Nettles     8.65e-04 0.01360    
-Gary Pettis       4.31e-04 0.01809    
-Gary Redus        8.20e-06 0.00533    
-Garry Templeton   3.62e-03 0.02315    
-Greg Walker       1.28e-06 0.00954    
-Gary Ward         3.33e-06 0.01588    
-Glenn Wilson      2.81e-05 0.01027    
-Harold Baines     1.27e-04 0.01369    
-Hubie Brooks      2.02e-04 0.02455    
-Howard Johnson    6.88e-05 0.01116    
-Hal McRae         2.47e-05 0.00661    
-Harold Reynolds   1.93e-03 0.02662    
-Harry Spilman     5.09e-04 0.01782    
-Herm Winningham   4.57e-04 0.01251    
-Jesse Barfield    3.41e-03 0.04727   *
-Juan Beniquez     1.81e-04 0.00984    
-John Cangelosi    1.90e-03 0.01856    
-Jose Canseco      2.12e-02 0.03860    
-Joe Carter        3.07e-02 0.02791    
-Jack Clark        1.44e-02 0.00976   *
-Jose Cruz         2.57e-04 0.00622    
-Jody Davis        2.87e-03 0.01258    
-Jim Dwyer         3.05e-05 0.01593    
-Julio Franco      1.66e-04 0.02305    
-Jim Gantner       1.12e-03 0.00960    
-Johnny Grubb      1.22e-03 0.02493    
-Jack Howell       1.16e-03 0.01668    
-John Kruk         2.96e-03 0.01353    
-Jeffrey Leonard   1.38e-03 0.00622    
-Jim Morrison      3.93e-03 0.01043    
-John Moses        1.69e-03 0.00956    
-Jerry Mumphrey    1.63e-04 0.01145    
-Jim Presley       1.10e-02 0.01817    
-Johnny Ray        4.57e-04 0.02223    
-Jeff Reed         6.55e-04 0.01410    
-Jim Rice          1.07e-01 0.03416   *
-Jerry Royster     1.36e-04 0.00787    
-John Russell      8.36e-04 0.00732    
-Juan Samuel       5.27e-05 0.01123    
-John Shelby       1.62e-04 0.01058    
-Joel Skinner      5.87e-04 0.00821    
-Jim Sundberg      6.94e-03 0.01962    
-Jose Uribe        6.27e-04 0.02432    
-Joel Youngblood   4.03e-04 0.01275    
-Kevin Bass        3.85e-03 0.02192    
-Kal Daniels       3.45e-03 0.01950    
-Kirk Gibson       1.14e-02 0.02056    
-Ken Griffey       6.44e-04 0.01574    
-Keith Hernandez   2.77e-02 0.01861   *
-Kent Hrbek        8.23e-03 0.01925    
-Ken Landreaux     1.59e-03 0.00739    
-Kevin McReynolds  1.53e-03 0.01563    
-Kevin Mitchell    1.53e-03 0.00624    
-Keith Moreland    2.58e-03 0.01216    
-Ken Oberkfell     6.08e-04 0.01265    
-Ken Phelps        2.14e-03 0.01983    
-Kirby Puckett     7.57e-02 0.05527   *
-Kurt Stillwell    6.28e-04 0.01199    
-Leon Durham       3.55e-03 0.00780    
-Len Dykstra       2.37e-03 0.00858    
-Larry Herndon     2.33e-04 0.00650    
-Lee Lacy          2.48e-04 0.00742    
-Len Matuszek      2.14e-04 0.01299    
-Lloyd Moseby      2.99e-04 0.01541    
-Lance Parrish     1.63e-03 0.01684    
-Larry Parrish     1.01e-03 0.01955    
-Larry Sheets      2.92e-03 0.01021    
-Lou Whitaker      1.74e-03 0.01037    
-Mike Aldrete      8.07e-04 0.01090    
-Marty Barrett     8.88e-04 0.02919    
-Mike Davis        1.39e-04 0.00668    
-Mike Diaz         2.47e-03 0.01471    
-Mariano Duncan    9.21e-04 0.01154    
-Mike Easler       5.85e-05 0.01082    
-Mel Hall          5.05e-04 0.00977    
-Mike Heath        1.37e-03 0.00815    
-Mike Kingery      1.05e-03 0.01115    
-Mike LaValliere   6.04e-04 0.00901    
-Mike Marshall     9.36e-04 0.01371    
-Mike Pagliarulo   8.98e-03 0.02554    
-Mark Salas        4.95e-04 0.00824    
-Mike Schmidt      2.05e-01 0.03089   *
-Mike Scioscia     2.47e-03 0.00698    
-Mickey Tettleton  5.73e-04 0.01355    
-Milt Thompson     5.32e-04 0.00617    
-Mitch Webster     7.30e-03 0.01694    
-Mookie Wilson     5.46e-04 0.00619    
-Marvell Wynne     2.84e-04 0.00634    
-Mike Young        6.33e-05 0.00474    
-Ozzie Guillen     3.75e-03 0.02716    
-Oddibe McDowell   3.88e-03 0.00964    
-Ozzie Smith       7.25e-02 0.02295   *
-Ozzie Virgil      1.58e-03 0.01141    
-Phil Bradley      9.13e-05 0.01688    
-Phil Garner       1.36e-07 0.00536    
-Pete Incaviglia   1.27e-02 0.02516    
-Paul Molitor      4.13e-03 0.00571    
-Pete Rose         5.69e-03 0.01262    
-Pat Sheridan      2.15e-04 0.00889    
-Pat Tabler        1.39e-03 0.02628    
-Rafael Belliard   4.19e-04 0.01234    
-Rick Burleson     1.00e-05 0.00907    
-Randy Bush        2.18e-04 0.00496    
-Rick Cerone       9.54e-05 0.01047    
-Ron Cey           6.27e-03 0.01140    
-Rob Deer          1.23e-02 0.03955    
-Rick Dempsey      8.70e-05 0.01365    
-Ron Hassey        1.15e-04 0.01582    
-Rickey Henderson  2.37e-02 0.01946    
-Reggie Jackson    1.22e-05 0.00963    
-Ron Kittle        2.53e-05 0.01951    
-Ray Knight        7.20e-04 0.01010    
-Rick Leach        9.48e-04 0.01402    
-Rick Manning      5.19e-05 0.01159    
-Rance Mulliniks   2.46e-06 0.00450    
-Ron Oester        8.61e-04 0.01226    
-Rey Quinones      7.19e-04 0.01288    
-Rafael Ramirez    4.55e-03 0.01556    
-Ronn Reynolds     1.78e-05 0.01742    
-Ron Roenicke      2.64e-04 0.00722    
-Ryne Sandberg     6.89e-05 0.01480    
-Rafael Santana    1.17e-05 0.02135    
-Rick Schu         1.19e-03 0.01243    
-Ruben Sierra      1.91e-03 0.00575    
-Roy Smalley       4.81e-04 0.01061    
-Robby Thompson    4.95e-03 0.01401    
-Rob Wilfong       1.13e-04 0.01093    
-Robin Yount       1.50e-03 0.01993    
-Steve Balboni     1.42e-02 0.03283    
-Scott Bradley     2.31e-03 0.01382    
-Sid Bream         2.19e-03 0.00648    
-Steve Buechele    2.66e-03 0.01005    
-Shawon Dunston    5.41e-03 0.01549    
-Scott Fletcher    1.64e-03 0.02316    
-Steve Garvey      1.22e-02 0.01247    
-Steve Jeltz       7.27e-04 0.02943    
-Steve Lombardozzi 2.07e-03 0.01637    
-Spike Owen        4.47e-06 0.03619   *
-Steve Sax         7.76e-02 0.05621   *
-Tony Bernazard    2.25e-03 0.01372    
-Tom Brookens      2.06e-05 0.00843    
-Tom Brunansky     1.27e-03 0.01555    
-Tony Fernandez    2.38e-02 0.03841    
-Tim Flannery      2.87e-04 0.00880    
-Tom Foley         1.32e-04 0.01018    
-Tony Gwynn        7.06e-03 0.04413   *
-Terry Harper      1.71e-05 0.00728    
-Tommy Herr        9.42e-03 0.02831    
-Tim Hulett        3.26e-03 0.01934    
-Terry Kennedy     3.07e-02 0.03269    
-Tito Landrum      1.02e-04 0.01246    
-Tim Laudner       2.14e-04 0.01372    
-Tom Paciorek      3.82e-04 0.01268    
-Tony Pena         3.25e-03 0.00921    
-Terry Pendleton   4.52e-03 0.04110   *
-Tony Phillips     1.62e-05 0.00948    
-Terry Puhl        8.69e-03 0.01348    
-Ted Simmons       1.66e-03 0.01835    
-Tim Teufel        3.99e-05 0.00754    
-Tim Wallach       1.35e-03 0.01472    
-Vince Coleman     4.51e-03 0.05407   *
-Von Hayes         4.19e-03 0.01920    
-Vance Law         7.83e-04 0.01135    
-Wally Backman     7.76e-05 0.02256    
-Wade Boggs        4.06e-02 0.07367   *
-Will Clark        2.00e-03 0.00548    
-Wally Joyner      1.07e-02 0.01320    
-Willie McGee      7.04e-04 0.01159    
-Willie Randolph   1.77e-03 0.01180    
-Wayne Tolleson    2.61e-04 0.01364    
-Willie Upshaw     5.27e-03 0.01897    
-Willie Wilson     3.68e-03 0.02101    
summary(influence.measures(reg_model))
Potentially influential observations of
     lm(formula = Salary ~ AtBat + Hits + HmRun, data = hitters) :

                 dfb.1_ dfb.AtBt dfb.Hits dfb.HmRn dffit   cov.r   cook.d
-Don Mattingly    0.01  -0.38     0.42     0.15     0.50_*  1.07_*  0.06 
-Dale Murphy     -0.17   0.11    -0.09     0.24     0.40_*  0.92_*  0.04 
-Dave Winfield   -0.14   0.12    -0.11     0.17     0.34    0.91_*  0.03 
-Eddie Murray     0.06  -0.32     0.36     0.09     0.49_*  0.78_*  0.06 
-George Bell     -0.01  -0.02     0.02     0.02     0.04    1.05_*  0.00 
-Gary Carter     -0.06   0.11    -0.13     0.26     0.38_*  0.88_*  0.03 
-Gary Gaetti      0.01   0.01    -0.01    -0.03    -0.03    1.05_*  0.00 
-Jesse Barfield  -0.01  -0.03     0.02     0.10     0.12    1.06_*  0.00 
-Jack Clark       0.20  -0.03    -0.03     0.06     0.24    0.94_*  0.01 
-Jim Rice        -0.05  -0.43     0.54     0.05     0.67_*  0.87_*  0.11 
-Keith Hernandez -0.02  -0.18     0.25    -0.07     0.34    0.94_*  0.03 
-Kirby Puckett    0.05   0.36    -0.41    -0.21    -0.55_*  0.99    0.08 
-Mike Schmidt     0.94  -0.41     0.18     0.05     0.95_*  0.69_*  0.20 
-Ozzie Smith     -0.10   0.07     0.06    -0.47     0.55_*  0.85_*  0.07 
-Spike Owen       0.00   0.00     0.00     0.00     0.00    1.05_*  0.00 
-Steve Sax        0.05   0.29    -0.41     0.26    -0.56_*  0.99    0.08 
-Tony Gwynn       0.02   0.10    -0.13     0.03    -0.17    1.05_*  0.01 
-Terry Pendleton  0.06  -0.10     0.07     0.09    -0.13    1.05_*  0.00 
-Vince Coleman    0.06  -0.11     0.08     0.09    -0.13    1.07_*  0.00 
-Wade Boggs       0.03  -0.29     0.36    -0.11     0.40_*  1.06_*  0.04 
                 hat    
-Don Mattingly    0.09_*
-Dale Murphy      0.02  
-Dave Winfield    0.01  
-Eddie Murray     0.01  
-George Bell      0.03  
-Gary Carter      0.01  
-Gary Gaetti      0.03  
-Jesse Barfield   0.05_*
-Jack Clark       0.01  
-Jim Rice         0.03  
-Keith Hernandez  0.02  
-Kirby Puckett    0.06_*
-Mike Schmidt     0.03  
-Ozzie Smith      0.02  
-Spike Owen       0.04  
-Steve Sax        0.06_*
-Tony Gwynn       0.04  
-Terry Pendleton  0.04  
-Vince Coleman    0.05_*
-Wade Boggs       0.07_*

기각역

p <- 3
n <- nrow(hitters)
2*(p+1)/n #hat (h_ii)
0.0304182509505703 
3*sqrt((p+1)/(n-p-1)) #Dffits
0.37282185960072 
2*sqrt((p+1)/(n)) #Dffits
0.246650566391283 
qf(0.5, p+1, n-p-1) #Cook d
0.841375151461702

변수 변환

hitters$log_Salary <- log(hitters$Salary)
reg_model_2 <- lm(log_Salary ~ AtBat + Hits + HmRun, hitters)
summary(reg_model_2)

Call:
lm(formula = log_Salary ~ AtBat + Hits + HmRun, data = hitters)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.2664 -0.6572  0.1122  0.5639  2.5886 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  5.103575   0.149615  34.111  < 2e-16 ***
AtBat       -0.002179   0.001265  -1.722 0.086196 .  
Hits         0.014012   0.004052   3.458 0.000636 ***
HmRun        0.016540   0.006678   2.477 0.013895 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7872 on 259 degrees of freedom
Multiple R-squared:  0.2253,    Adjusted R-squared:  0.2163 
F-statistic:  25.1 on 3 and 259 DF,  p-value: 2.729e-14

잔차그림

residual <- resid(reg_model_2)
stad.res <- rstandard(reg_model_2)
stu.res <- rstudent(reg_model_2)
par(mfrow = c(2, 2))
plot(fitted(reg_model_2), residual, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "Residuals", 
     main = "residual plot")
abline(h=0, lty=2)

plot(fitted(reg_model_2), stad.res, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "S_Residuals", 
     ylim=c(min(-3, min(stad.res)), 
            max(3,max(stad.res))),
     main = "standardized residual plot")
abline(h=c(-2,0,2), lty=2)

plot(fitted(reg_model_2), stu.res, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "S_Residuals_(i)", 
     ylim=c(min(-3, min(stu.res)), 
            max(3,max(stu.res))),
     main = "studentized residual plot")
abline(h=c(-2,0,2), lty=2)

plot(fitted(reg_model_2), stu.res, 
     pch=20,cex  = 2,col  = "darkorange",
     xlab = "Fitted", ylab = "S_Residuals_(i)", 
     ylim=c(min(-3, min(stu.res)), 
            max(3,max(stu.res))),
     main = "studentized residual plot")
abline(h=c(-qt(0.975,nrow(hitters)-4),0,qt(0.975,nrow(hitters)-4)), lty=2)
text (fitted(reg_model_2)[which(abs(stu.res)>qt(0.975,nrow(hitters)-4))],
      stu.res[which(abs(stu.res)>qt(0.975,nrow(hitters)-4))], 
      which(abs(stu.res)>qt(0.975,nrow(hitters)-4)),adj = c(0,1))

stu.res[abs(stu.res)>qt(0.975,nrow(hitters)-4)]
-Cory Snyder
-2.16182826573383
-Darnell Coles
-2.09872610566858
-Jack Clark
2.12385831075298
-Mike Schmidt
3.40826964934749
-Ozzie Smith
2.0286158569726
-Steve Sax
-3.00934037017267
-Terry Kennedy
2.19849337509094
which(abs(stu.res)>qt(0.975,nrow(hitters)-4))
-Cory Snyder
46
-Darnell Coles
52
-Jack Clark
111
-Mike Schmidt
173
-Ozzie Smith
183
-Steve Sax
230
-Terry Kennedy
241
influence(reg_model_2)
$hat
-Alan Ashby
0.00540428715355245
-Alvin Davis
0.00589170670784522
-Andre Dawson
0.00832644882765465
-Andres Galarraga
0.00543756565246947
-Alfredo Griffin
0.0246137118709988
-Al Newman
0.0141225554276349
-Argenis Salazar
0.010928273983481
-Andres Thomas
0.00583280157863637
-Andre Thornton
0.0118104032344835
-Alan Trammell
0.00994920971431027
-Alex Trevino
0.0116023974454147
-Andy VanSlyke
0.00392214855226506
-Alan Wiggins
0.01133266253963
-Bill Almon
0.0120577739078933
-Buddy Bell
0.00926235909199221
-Buddy Biancalana
0.012342136255686
-Bruce Bochy
0.0204159574317937
-Barry Bonds
0.0140367315219278
-Bobby Bonilla
0.0110632944090634
-Bob Brenly
0.00872907614618226
-Bill Buckner
0.0139048245540849
-Brett Butler
0.023168413560765
-Bob Dernier
0.0102008268559032
-Bo Diaz
0.00579243488480162
-Bill Doran
0.015434760936016
-Brian Downing
0.00777622895232283
-Billy Hatcher
0.00709689247443314
-Brook Jacoby
0.0108511422285614
-Bob Kearney
0.0108810262666556
-Bill Madlock
0.00473465384983353
-Bob Melvin
0.00900012174203842
-BillyJo Robidoux
0.0133294228418443
-Bill Schroeder
0.0112763637277587
-Chris Bando
0.00978612142405515
-Chris Brown
0.0166260339272529
-Carmen Castillo
0.0130280396536268
-Chili Davis
0.00704454319748951
-Carlton Fisk
0.017822764593868
-Curt Ford
0.0109708972674672
-Carney Lansford
0.0107121199405846
-Chet Lemon
0.004977264802092
-Candy Maldonado
0.00764992031384351
-Carmelo Martinez
0.0089685788087143
-Craig Reynolds
0.00600742640963073
-Cal Ripken
0.0154842953466146
-Cory Snyder
0.0142384557435194
-Chris Speier
0.0176408073638382
-Curt Wilkerson
0.011580828583756
-Dave Anderson
0.0114107120327874
-Don Baylor
0.0352479469918076
-Daryl Boston
0.0120025169206652
-Darnell Coles
0.00768936788078936
-Dave Concepcion
0.00754097071158992
-Doug DeCinces
0.016164784133267
-Darrell Evans
0.0264058825441862
-Dwight Evans
0.0156073759122261
-Damaso Garcia
0.00737202574736494
-Dan Gladden
0.00732057564815775
-Dave Henderson
0.00493766296992215
-Donnie Hill
0.00802999130926279
-Davey Lopes
0.00867219904074439
-Don Mattingly
0.0903700111079589
-Dale Murphy
0.0205781074488089
-Dwayne Murphy
0.00499065937964354
-Dave Parker
0.0233401084346804
-Dan Pasqua
0.0148260514260301
-Darrell Porter
0.0212335628824219
-Dick Schofield
0.00692844758375807
-Don Slaught
0.00665433551016605
-Darryl Strawberry
0.017694944503085
-Dale Sveum
0.00583616542870044
-Danny Tartabull
0.0128297967927647
-Denny Walling
0.0124382760330085
-Dave Winfield
0.0133528039520951
-Eric Davis
0.0205166608140052
-Eddie Milner
0.00477555388471096
-Eddie Murray
0.0126894264569264
-Ed Romero
0.0120154735656705
-Frank White
0.0103217756795036
-George Bell
0.0344024597514498
-Glenn Braggs
0.0102378206814018
-George Brett
0.0070249800741032
-Greg Brock
0.0102483444612376
-Gary Carter
0.0133493295035423
-Glenn Davis
0.0233784484234977
-Gary Gaetti
0.0300641988907722
-Greg Gagne
0.00756816838324455
-George Hendrick
0.00993821578501312
-Glenn Hubbard
0.0144050547662455
-Garth Iorg
0.00750828700013946
-Gary Matthews
0.0119812939218614
-Graig Nettles
0.0135988964718854
-Gary Pettis
0.0180946787493926
-Gary Redus
0.00533116613569048
-Garry Templeton
0.0231472795912073
-Greg Walker
0.00954059659043919
-Gary Ward
0.0158776584493562
-Glenn Wilson
0.0102664940810771
-Harold Baines
0.0136874329182192
-Hubie Brooks
0.0245534617574867
-Howard Johnson
0.0111605903106341
-Hal McRae
0.00660970775119084
-Harold Reynolds
0.0266174645810819
-Harry Spilman
0.0178175584405383
-Herm Winningham
0.0125072976893885
-Jesse Barfield
0.0472745129906935
-Juan Beniquez
0.0098405887950288
-John Cangelosi
0.0185585370145323
-Jose Canseco
0.0385966269231462
-Joe Carter
0.0279123839207128
-Jack Clark
0.00976153800810466
-Jose Cruz
0.00621927886532388
-Jody Davis
0.0125836354713245
-Jim Dwyer
0.0159318273881519
-Julio Franco
0.0230480594602062
-Jim Gantner
0.00960427626759017
-Johnny Grubb
0.0249337849541658
-Jack Howell
0.0166783571884679
-John Kruk
0.0135348618245948
-Jeffrey Leonard
0.00621692194497029
-Jim Morrison
0.0104347491092473
-John Moses
0.00955816927339891
-Jerry Mumphrey
0.0114527911454454
-Jim Presley
0.0181732014300399
-Johnny Ray
0.0222264061248388
-Jeff Reed
0.0141048942273143
-Jim Rice
0.0341630071931888
-Jerry Royster
0.00786584848798418
-John Russell
0.00732221183848203
-Juan Samuel
0.011233958379014
-John Shelby
0.0105769969697364
-Joel Skinner
0.00820725725265926
-Jim Sundberg
0.0196190015932163
-Jose Uribe
0.0243170465990865
-Joel Youngblood
0.0127513647950321
-Kevin Bass
0.0219191326187113
-Kal Daniels
0.0194979541215839
-Kirk Gibson
0.020556919885839
-Ken Griffey
0.0157391819211111
-Keith Hernandez
0.0186125240001884
-Kent Hrbek
0.0192503945544296
-Ken Landreaux
0.00738914265279174
-Kevin McReynolds
0.0156330543753078
-Kevin Mitchell
0.00623609661997075
-Keith Moreland
0.0121555120488774
-Ken Oberkfell
0.0126467584348519
-Ken Phelps
0.0198333298123843
-Kirby Puckett
0.0552718094796791
-Kurt Stillwell
0.011990041252144
-Leon Durham
0.00780417454171992
-Len Dykstra
0.00857784296541703
-Larry Herndon
0.0064990040160584
-Lee Lacy
0.00742301328937459
-Len Matuszek
0.0129926810188161
-Lloyd Moseby
0.0154094589566827
-Lance Parrish
0.0168397241242445
-Larry Parrish
0.0195480106203573
-Larry Sheets
0.0102053644915363
-Lou Whitaker
0.0103736298972029
-Mike Aldrete
0.0108976777772544
-Marty Barrett
0.0291908907582424
-Mike Davis
0.00667586668426171
-Mike Diaz
0.0147105547379761
-Mariano Duncan
0.0115422666932657
-Mike Easler
0.010820500442813
-Mel Hall
0.00976796679777078
-Mike Heath
0.0081507738805316
-Mike Kingery
0.0111519990806471
-Mike LaValliere
0.00901026773489625
-Mike Marshall
0.013711182342755
-Mike Pagliarulo
0.0255437587312095
-Mark Salas
0.00824038954487028
-Mike Schmidt
0.0308861245462707
-Mike Scioscia
0.00698057071979755
-Mickey Tettleton
0.0135500510047471
-Milt Thompson
0.00617205972690294
-Mitch Webster
0.0169403513647917
-Mookie Wilson
0.00619444773498657
-Marvell Wynne
0.0063403620095783
-Mike Young
0.00474275439485779
-Ozzie Guillen
0.0271620505926552
-Oddibe McDowell
0.00964328420757499
-Ozzie Smith
0.0229502793106078
-Ozzie Virgil
0.0114067190696189
-Phil Bradley
0.0168810816259417
-Phil Garner
0.00535812295602376
-Pete Incaviglia
0.025161431654974
-Paul Molitor
0.00570944294085908
-Pete Rose
0.0126156272171943
-Pat Sheridan
0.00888970164559414
-Pat Tabler
0.026279450164693
-Rafael Belliard
0.0123374671998298
-Rick Burleson
0.00906906701865493
-Randy Bush
0.00495753180334833
-Rick Cerone
0.0104730023394748
-Ron Cey
0.0113956391454122
-Rob Deer
0.0395521316143585
-Rick Dempsey
0.0136529420759308
-Ron Hassey
0.0158151139459369
-Rickey Henderson
0.0194628445140604
-Reggie Jackson
0.00963058080211747
-Ron Kittle
0.0195094238607815
-Ray Knight
0.0100975869646124
-Rick Leach
0.0140249162441515
-Rick Manning
0.0115898080723435
-Rance Mulliniks
0.00450212481049989
-Ron Oester
0.0122552708544235
-Rey Quinones
0.0128781945206417
-Rafael Ramirez
0.0155619012974591
-Ronn Reynolds
0.0174189559060563
-Ron Roenicke
0.007216482671799
-Ryne Sandberg
0.0148031952946029
-Rafael Santana
0.0213487186421553
-Rick Schu
0.0124262441988659
-Ruben Sierra
0.00575359430765965
-Roy Smalley
0.0106124476383773
-Robby Thompson
0.0140106441432452
-Rob Wilfong
0.0109282567228258
-Robin Yount
0.0199323190913311
-Steve Balboni
0.032832608857617
-Scott Bradley
0.013819143124654
-Sid Bream
0.0064848822413407
-Steve Buechele
0.010047792882046
-Shawon Dunston
0.0154878353515676
-Scott Fletcher
0.0231584911833167
-Steve Garvey
0.0124707214778381
-Steve Jeltz
0.0294334036298904
-Steve Lombardozzi
0.0163703558064671
-Spike Owen
0.0361863260829997
-Steve Sax
0.056205798190448
-Tony Bernazard
0.0137201779926164
-Tom Brookens
0.00842727602684437
-Tom Brunansky
0.0155535640161956
-Tony Fernandez
0.0384149427739519
-Tim Flannery
0.00879815995334561
-Tom Foley
0.010178072996595
-Tony Gwynn
0.0441255560927934
-Terry Harper
0.00728359774271928
-Tommy Herr
0.0283062395596944
-Tim Hulett
0.0193407789424842
-Terry Kennedy
0.0326924785968483
-Tito Landrum
0.0124610368212244
-Tim Laudner
0.0137152102414128
-Tom Paciorek
0.0126750030530696
-Tony Pena
0.00921261317536243
-Terry Pendleton
0.0411002808615697
-Tony Phillips
0.00947681648702826
-Terry Puhl
0.013480153488892
-Ted Simmons
0.0183540764261599
-Tim Teufel
0.00754075413540749
-Tim Wallach
0.014724129247963
-Vince Coleman
0.0540676127419561
-Von Hayes
0.0192039404330803
-Vance Law
0.0113459171671123
-Wally Backman
0.022556121420949
-Wade Boggs
0.0736687853777228
-Will Clark
0.00548420107775056
-Wally Joyner
0.01320331340394
-Willie McGee
0.0115854961579362
-Willie Randolph
0.011798792067581
-Wayne Tolleson
0.0136448610296419
-Willie Upshaw
0.0189725147824934
-Willie Wilson
0.0210111323582833
$coefficients
A matrix: 263 × 4 of type dbl
(Intercept) AtBat Hits HmRun
-Alan Ashby 4.817418e-03 -2.986297e-06 -9.361969e-06 -6.101971e-05
-Alvin Davis 5.783712e-06 -1.988686e-08 -6.958574e-09 -1.532526e-06
-Andre Dawson 3.051739e-05 5.108640e-06 -1.863631e-05 -4.502371e-05
-Andres Galarraga -1.394196e-02 5.825139e-05 -1.224464e-04 -1.059912e-04
-Alfredo Griffin -3.880218e-03 1.203274e-05 4.598602e-05 -3.844865e-04
-Al Newman -1.699795e-02 -1.973901e-05 1.691955e-04 2.508389e-04
-Argenis Salazar -8.046090e-03 -2.767402e-05 9.120649e-05 5.189035e-04
-Andres Thomas -1.089006e-02 -2.290534e-05 1.092744e-04 2.854954e-04
-Andre Thornton 1.934670e-04 1.257660e-04 -4.795294e-04 4.627899e-04
-Alan Trammell 1.368784e-03 -2.410167e-06 -4.767847e-06 -4.928569e-05
-Alex Trevino 1.506924e-02 -5.429191e-05 9.631131e-05 -5.069911e-05
-Andy VanSlyke 1.018986e-03 -2.296905e-06 8.152666e-06 2.113456e-05
-Alan Wiggins 1.700556e-02 -2.150357e-05 1.763226e-05 -5.069653e-04
-Bill Almon 1.543927e-03 -1.286964e-06 -7.912781e-06 1.368373e-05
-Buddy Bell -1.705882e-03 2.019092e-06 1.123836e-05 5.235392e-05
-Buddy Biancalana -3.897104e-03 8.342080e-06 -6.374658e-06 3.768041e-05
-Bruce Bochy -1.330506e-02 5.600915e-05 -8.215845e-05 -2.059641e-04
-Barry Bonds 2.279533e-03 -1.600465e-04 5.715951e-04 -3.232635e-04
-Bobby Bonilla 6.803360e-04 -7.258320e-05 1.550213e-04 6.909102e-04
-Bob Brenly -1.918921e-03 4.389361e-05 -1.378344e-04 6.196381e-05
-Bill Buckner -3.908655e-03 2.534192e-05 -4.654425e-05 -2.237198e-05
-Brett Butler -5.102074e-03 2.867516e-05 7.199807e-06 -4.680230e-04
-Bob Dernier 5.841442e-03 9.566493e-05 -3.306795e-04 -4.014555e-04
-Bo Diaz -9.247399e-04 1.139785e-05 4.045893e-06 -1.642212e-04
-Bill Doran -2.368204e-03 1.411712e-05 4.932303e-06 -2.315089e-04
-Brian Downing -2.439010e-03 1.778817e-05 -4.479265e-05 1.943382e-04
-Billy Hatcher -6.440503e-04 -5.899958e-05 1.344372e-04 4.939621e-04
-Brook Jacoby 3.516924e-04 1.218804e-06 -9.821930e-06 1.669940e-06
-Bob Kearney 4.747801e-03 -1.011448e-05 1.090719e-06 1.826653e-05
-Bill Madlock 5.821589e-03 -3.692670e-05 1.178859e-04 -4.368741e-05
⋮ ⋮ ⋮ ⋮ ⋮
-Tony Fernandez 1.052602e-02 8.419720e-05 -5.233673e-04 7.202039e-04
-Tim Flannery -4.068231e-05 1.805885e-07 -8.305763e-07 3.052943e-06
-Tom Foley -9.240389e-05 2.491327e-07 -6.076509e-07 2.794985e-06
-Tony Gwynn 1.174950e-03 6.022291e-05 -2.586965e-04 1.095459e-04
-Terry Harper 6.264040e-03 -1.582243e-05 1.345592e-05 3.096281e-05
-Tommy Herr -1.253907e-02 1.597799e-04 -3.366306e-04 -1.032398e-03
-Tim Hulett 7.975363e-03 -1.386157e-04 4.264418e-04 -6.634915e-05
-Terry Kennedy 5.997923e-02 -2.615496e-04 4.547162e-04 2.756732e-04
-Tito Landrum 5.790292e-03 8.000686e-06 -6.156594e-05 -8.371297e-05
-Tim Laudner -1.164993e-04 3.626904e-07 -2.408513e-07 -2.255649e-06
-Tom Paciorek -2.044713e-03 1.065779e-05 -2.549355e-05 8.908786e-06
-Tony Pena -1.740733e-03 -2.408537e-05 1.685463e-04 -3.034906e-04
-Terry Pendleton 1.289931e-02 -1.809589e-04 4.345455e-04 8.980146e-04
-Tony Phillips -4.086001e-04 1.800300e-05 -3.984644e-05 -1.400773e-04
-Terry Puhl 3.040861e-02 -8.496636e-05 9.801338e-05 -9.885820e-05
-Ted Simmons 2.260963e-02 -8.778308e-05 1.393812e-04 1.012275e-04
-Tim Teufel 1.132868e-03 3.133402e-07 -5.547655e-06 -2.487321e-05
-Tim Wallach -4.706632e-03 1.041449e-04 -3.412129e-04 1.845919e-04
-Vince Coleman 1.460109e-02 -2.070472e-04 5.136607e-04 9.377216e-04
-Von Hayes -2.691757e-03 -4.871620e-05 2.214694e-04 2.726047e-05
-Vance Law 1.466223e-03 8.485382e-05 -2.748316e-04 -2.829650e-04
-Wally Backman 3.033118e-03 -4.292845e-05 1.662334e-04 -2.134815e-04
-Wade Boggs 2.336669e-03 -1.711974e-04 6.758830e-04 -3.477363e-04
-Will Clark -7.253841e-03 7.425048e-05 -2.614339e-04 6.024516e-05
-Wally Joyner 9.890247e-03 6.359295e-05 -3.334252e-04 -4.567361e-04
-Willie McGee -4.103649e-03 6.596369e-05 -1.473306e-04 -3.608230e-04
-Willie Randolph -2.369271e-03 1.857962e-05 3.563100e-05 -5.223953e-04
-Wayne Tolleson -2.531200e-04 4.524374e-06 -6.094079e-06 -5.579062e-05
-Willie Upshaw -1.162878e-02 1.379530e-04 -3.222032e-04 -5.194818e-04
-Willie Wilson -1.005121e-02 6.995994e-05 -9.304662e-05 -4.851564e-04
$sigma
-Alan Ashby
0.788087989207047
-Alvin Davis
0.788694226481284
-Andre Dawson
0.788661650873323
-Andres Galarraga
0.784684794952982
-Alfredo Griffin
0.788337114130146
-Al Newman
0.786262541299155
-Argenis Salazar
0.786802916611473
-Andres Thomas
0.784398464793053
-Andre Thornton
0.7850881428335
-Alan Trammell
0.788613981103893
-Alex Trevino
0.787230271479112
-Andy VanSlyke
0.788443711432741
-Alan Wiggins
0.785528352743374
-Bill Almon
0.788675988334844
-Buddy Bell
0.788548875937367
-Buddy Biancalana
0.788592315971829
-Bruce Bochy
0.788061155890424
-Barry Bonds
0.785378068169425
-Bobby Bonilla
0.786168555191178
-Bob Brenly
0.788232201709835
-Bill Buckner
0.788512427646438
-Brett Butler
0.788149915578498
-Bob Dernier
0.785813660772349
-Bo Diaz
0.787873065428321
-Bill Doran
0.788464477186018
-Brian Downing
0.787900316001232
-Billy Hatcher
0.7856791859616
-Brook Jacoby
0.788687839162256
-Bob Kearney
0.788527835166416
-Bill Madlock
0.787045649653056
-Bob Melvin
0.786484980327064
-BillyJo Robidoux
0.785740087144776
-Bill Schroeder
0.788596702820322
-Chris Bando
0.788610055889589
-Chris Brown
0.787125654887832
-Carmen Castillo
0.788679721825813
-Chili Davis
0.78811228983753
-Carlton Fisk
0.786089349695099
-Curt Ford
0.785317749724202
-Carney Lansford
0.78778198480267
-Chet Lemon
0.787566707678007
-Candy Maldonado
0.788678389348269
-Carmelo Martinez
0.788477865126042
-Craig Reynolds
0.788261244175587
-Cal Ripken
0.787863635256176
-Cory Snyder
0.781646564196697
-Chris Speier
0.788648618053139
-Curt Wilkerson
0.788684111170213
-Dave Anderson
0.788692872574602
-Don Baylor
0.787874897329411
-Daryl Boston
0.785236358622793
-Darnell Coles
0.782046884888717
-Dave Concepcion
0.78863268553584
-Doug DeCinces
0.788090534667608
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influence.measures(reg_model_2)
Influence measures of
     lm(formula = log_Salary ~ AtBat + Hits + HmRun, data = hitters) :

                      dfb.1_  dfb.AtBt  dfb.Hits  dfb.HmRn     dffit cov.r
-Alan Ashby         3.22e-02 -2.36e-03 -2.31e-03 -9.13e-03  0.046453 1.015
-Alvin Davis        3.86e-05 -1.57e-05 -1.71e-06 -2.29e-04 -0.000532 1.022
-Andre Dawson       2.04e-04  4.03e-03 -4.59e-03 -6.73e-03 -0.013393 1.024
-Andres Galarraga  -9.35e-02  4.62e-02 -3.03e-02 -1.59e-02 -0.120216 0.980
-Alfredo Griffin   -2.59e-02  9.50e-03  1.13e-02 -5.75e-02  0.076818 1.037
-Al Newman         -1.14e-01 -1.56e-02  4.18e-02  3.76e-02 -0.151315 1.005
-Argenis Salazar   -5.38e-02 -2.19e-02  2.25e-02  7.77e-02 -0.117140 1.007
-Andres Thomas     -7.30e-02 -1.82e-02  2.71e-02  4.29e-02 -0.128939 0.978
-Andre Thornton     1.30e-03  9.97e-02 -1.19e-01  6.95e-02  0.168499 0.991
-Alan Trammell      9.13e-03 -1.90e-03 -1.17e-03 -7.37e-03 -0.022981 1.025
-Alex Trevino       1.01e-01 -4.29e-02  2.38e-02 -7.59e-03  0.106184 1.012
-Andy VanSlyke      6.80e-03 -1.81e-03  2.01e-03  3.16e-03  0.025414 1.017
-Alan Wiggins       1.14e-01 -1.70e-02  4.36e-03 -7.61e-02  0.154552 0.995
-Bill Almon         1.03e-02 -1.02e-03 -1.95e-03  2.05e-03  0.012092 1.028
-Buddy Bell        -1.14e-02  1.59e-03  2.77e-03  7.83e-03  0.029828 1.024
-Buddy Biancalana  -2.60e-02  6.58e-03 -1.57e-03  5.63e-03 -0.028878 1.027
-Bruce Bochy       -8.88e-02  4.42e-02 -2.03e-02 -3.08e-02 -0.092971 1.030
-Barry Bonds        1.53e-02 -1.27e-01  1.41e-01 -4.85e-02 -0.176307 0.996
-Bobby Bonilla      4.55e-03 -5.75e-02  3.83e-02  1.04e-01 -0.136291 1.001
-Bob Brenly        -1.28e-02  3.47e-02 -3.40e-02  9.27e-03  0.051620 1.020
-Bill Buckner      -2.61e-02  2.00e-02 -1.15e-02 -3.34e-03  0.040969 1.028
-Brett Butler      -3.41e-02  2.26e-02  1.77e-03 -7.00e-02  0.091957 1.034
-Bob Dernier        3.91e-02  7.58e-02 -8.17e-02 -6.02e-02  0.139750 0.996
-Bo Diaz           -6.18e-03  9.00e-03  9.98e-04 -2.46e-02  0.055993 1.013
-Bill Doran        -1.58e-02  1.11e-02  1.22e-03 -3.46e-02  0.048561 1.029
-Brian Downing     -1.63e-02  1.40e-02 -1.10e-02  2.91e-02  0.063853 1.015
-Billy Hatcher     -4.31e-03 -4.67e-02  3.32e-02  7.41e-02 -0.119083 0.992
-Brook Jacoby       2.35e-03  9.62e-04 -2.42e-03  2.50e-04 -0.006809 1.027
-Bob Kearney        3.17e-02 -7.98e-03  2.69e-04  2.73e-03  0.034619 1.025
-Bill Madlock       3.89e-02 -2.92e-02  2.91e-02 -6.54e-03  0.071745 1.003
-Bob Melvin        -6.87e-02 -3.23e-02  4.89e-02  2.30e-02 -0.114816 1.002
-BillyJo Robidoux  -1.39e-01  1.92e-02  8.61e-03  3.91e-02 -0.162044 0.999
-Bill Schroeder    -2.04e-02 -2.51e-03  8.72e-03 -3.14e-03 -0.026988 1.026
-Chris Bando        1.88e-02 -7.08e-03  5.11e-03 -9.26e-03  0.023341 1.025
-Chris Brown       -4.56e-02  9.28e-02 -1.07e-01  4.15e-02 -0.131922 1.016
-Carmen Castillo   -1.07e-02  6.37e-03 -4.01e-03 -2.53e-03 -0.011220 1.029
-Chili Davis       -1.51e-02  4.82e-03  6.22e-03 -1.38e-02  0.052004 1.017
-Carlton Fisk      -4.68e-02  1.52e-01 -1.53e-01  3.84e-03  0.176295 1.007
-Curt Ford         -1.35e-01  3.14e-02 -8.18e-03  4.26e-02 -0.157044 0.992
-Carney Lansford   -3.22e-02 -3.99e-03  1.95e-02  8.29e-03  0.080463 1.017
-Chet Lemon         8.58e-03  2.73e-02 -2.94e-02  2.34e-03  0.060812 1.009
-Candy Maldonado    1.43e-03  2.07e-03 -3.17e-03  5.44e-03  0.008958 1.023
-Carmelo Martinez   2.92e-02 -3.28e-03 -5.06e-03  8.39e-03  0.035805 1.023
-Craig Reynolds     2.52e-02  5.00e-03 -8.66e-03 -1.21e-02  0.041397 1.017
-Cal Ripken        -4.02e-02 -8.32e-04  1.31e-02  3.82e-02  0.092525 1.023
-Cory Snyder       -5.69e-02  5.60e-02 -2.15e-02 -2.21e-01 -0.259816 0.959
-Chris Speier       2.27e-02 -1.37e-02  8.69e-03  4.00e-03  0.023168 1.033
-Curt Wilkerson     6.13e-03  2.46e-04 -1.07e-03 -4.26e-03  0.008837 1.027
-Dave Anderson      2.70e-03 -4.95e-04  6.86e-05 -1.15e-03  0.003283 1.027
-Don Baylor        -5.52e-02  8.00e-02 -8.42e-02  8.30e-02  0.140061 1.044
-Daryl Boston      -1.60e-01  7.59e-02 -4.38e-02 -2.60e-03 -0.166329 0.992
-Darnell Coles      4.52e-02 -1.65e-02  3.62e-03 -8.05e-02 -0.184747 0.956
-Dave Concepcion    1.04e-02 -7.25e-04  3.56e-04 -9.50e-03  0.017502 1.023
-Doug DeCinces     -1.71e-02  2.36e-02 -2.76e-02  5.75e-02  0.080608 1.026
-Darrell Evans     -4.28e-03  8.38e-03 -1.00e-02  1.43e-02  0.019935 1.043
-Dwight Evans      -2.23e-02  2.45e-02 -2.68e-02  5.97e-02  0.086661 1.024
-Damaso Garcia      1.66e-02 -1.30e-02  2.61e-02 -5.40e-02  0.087782 1.007
-Dan Gladden       -2.30e-02  1.02e-02 -1.24e-02  2.63e-02 -0.045601 1.019
-Dave Henderson    -5.96e-03  1.49e-03  8.68e-05 -6.98e-03 -0.014840 1.020
-Donnie Hill       -1.06e-02  6.84e-03 -7.43e-03  9.34e-03 -0.018272 1.023
-Davey Lopes        5.08e-02 -2.76e-02  1.86e-02  1.82e-03  0.055380 1.019
-Don Mattingly      6.03e-04 -3.58e-02  4.01e-02  1.46e-02  0.047017 1.116
-Dale Murphy       -8.26e-02  5.28e-02 -4.50e-02  1.16e-01  0.190083 1.010
-Dwayne Murphy      3.86e-02  5.09e-03 -1.28e-02 -1.44e-03  0.062959 1.008
-Dave Parker       -2.32e-02  7.24e-03 -4.43e-03  3.62e-02  0.055955 1.038
-Dan Pasqua        -1.39e-01  1.24e-01 -8.81e-02 -1.14e-01 -0.189970 0.993
-Darrell Porter     3.66e-03 -2.08e-03  1.00e-03  2.08e-03  0.004123 1.038
-Dick Schofield    -5.11e-03  1.72e-02 -1.59e-02 -1.42e-03  0.026066 1.021
-Don Slaught        2.04e-02 -8.60e-03  3.17e-03  1.27e-02  0.028100 1.021
-Darryl Strawberry -7.83e-03  1.72e-02 -3.16e-02  1.23e-01  0.149374 1.014
-Dale Sveum        -7.82e-02 -2.49e-02  3.90e-02  2.71e-02 -0.134583 0.974
-Danny Tartabull    2.76e-02 -5.45e-03  1.09e-02 -1.46e-01 -0.199116 0.982
-Denny Walling      1.73e-02 -2.76e-02  2.74e-02  5.91e-03  0.033631 1.027
-Dave Winfield     -7.23e-02  6.53e-02 -5.71e-02  9.04e-02  0.176875 0.993
-Eric Davis        -2.32e-02  3.01e-02 -1.59e-02 -9.16e-02 -0.102739 1.029
-Eddie Milner       2.34e-03  4.75e-03 -5.54e-03  6.48e-03  0.019830 1.019
-Eddie Murray       2.38e-02 -1.31e-01  1.50e-01  3.90e-02  0.201707 0.980
-Ed Romero          5.30e-02  2.29e-02 -3.47e-02 -2.73e-02  0.086099 1.018
-Frank White       -1.17e-02  5.32e-03 -2.41e-03  1.24e-02  0.029675 1.025
-George Bell       -2.82e-03 -8.96e-03  1.04e-02  9.84e-03  0.018250 1.052
-Glenn Braggs      -1.32e-01  1.93e-02  9.04e-03  1.79e-02 -0.151972 0.991
-George Brett       3.25e-02 -6.52e-02  6.79e-02  3.94e-02  0.119507 0.991
-Greg Brock         1.19e-02  6.44e-03 -1.26e-02  1.70e-02  0.029601 1.025
-Gary Carter       -3.36e-02  6.16e-02 -7.35e-02  1.43e-01  0.205920 0.981
-Glenn Davis        6.42e-02 -3.82e-02  4.28e-02 -1.70e-01 -0.224204 1.007
-Gary Gaetti       -1.56e-03 -1.85e-03  1.81e-03  6.96e-03  0.008830 1.047
-Greg Gagne         2.58e-02 -6.73e-02  5.87e-02  1.92e-02 -0.098456 1.003
-George Hendrick    7.46e-02 -4.55e-02  2.49e-02  5.27e-02  0.096385 1.011
-Glenn Hubbard     -9.79e-03  7.68e-02 -6.98e-02 -5.95e-02  0.105819 1.018
-Garth Iorg         1.47e-02  8.55e-04 -6.87e-04 -1.73e-02  0.028927 1.022
-Gary Matthews      2.88e-02 -9.08e-03 -6.21e-03  6.93e-02  0.085459 1.018
-Graig Nettles     -8.25e-03 -3.09e-02  3.99e-02 -2.40e-02 -0.056618 1.026
-Gary Pettis       -2.15e-03  3.13e-03 -1.94e-03 -3.91e-03  0.005536 1.034
-Gary Redus         1.27e-02  5.23e-03 -8.83e-03  4.14e-03  0.025109 1.019
-Garry Templeton   -5.28e-02  1.03e-01 -7.44e-02 -1.19e-01  0.160741 1.022
-Greg Walker        4.22e-02 -2.78e-02  1.73e-02  2.48e-02  0.052231 1.021
-Gary Ward          2.54e-02 -3.99e-02  4.49e-02 -2.19e-02  0.058005 1.029
-Glenn Wilson      -1.41e-02  1.01e-02 -4.25e-03 -5.75e-03  0.026334 1.025
-Harold Baines     -7.27e-03 -1.69e-02  2.25e-02  1.23e-02  0.042035 1.028
-Hubie Brooks       6.44e-02 -9.14e-02  8.34e-02  3.22e-02  0.100778 1.035
-Howard Johnson     1.77e-02 -5.61e-03  5.40e-04  7.21e-03  0.020201 1.026
-Hal McRae          1.58e-02 -2.28e-03 -9.24e-04 -9.89e-04  0.019648 1.021
-Harold Reynolds    5.20e-02 -1.77e-01  1.54e-01  1.45e-01 -0.227396 1.013
-Harry Spilman     -4.36e-02  2.37e-02 -1.40e-02 -5.84e-03 -0.044190 1.032
-Herm Winningham   -1.02e-01  7.79e-03  1.80e-02  4.02e-03 -0.119059 1.011
-Jesse Barfield    -7.48e-03 -1.80e-02  1.44e-02  6.49e-02  0.074362 1.064
-Juan Beniquez      1.29e-02 -1.37e-02  1.41e-02 -6.20e-03  0.020968 1.025
-John Cangelosi     3.20e-02 -1.25e-01  1.04e-01  1.23e-01 -0.180186 1.008
-Jose Canseco       1.29e-01 -1.72e-01  1.82e-01 -2.06e-01 -0.326554 1.014
-Joe Carter         8.56e-02  1.16e-01 -1.52e-01 -1.42e-01 -0.311377 0.992
-Jack Clark         1.77e-01 -2.84e-02 -2.24e-02  5.46e-02  0.210870 0.957
-Jose Cruz         -4.56e-03  5.17e-04  1.03e-02 -2.48e-02  0.056579 1.014
-Jody Davis        -4.21e-02  6.53e-02 -6.28e-02  4.28e-02  0.110534 1.013
-Jim Dwyer          2.81e-02 -1.16e-02  3.96e-03  8.92e-03  0.029766 1.031
-Julio Franco      -4.98e-03 -8.23e-03  1.44e-02 -1.08e-02  0.024587 1.039
-Jim Gantner       -1.74e-02  1.79e-02  1.61e-03 -5.88e-02  0.088350 1.013
-Johnny Grubb       9.70e-03 -9.70e-03  7.62e-03  5.12e-03  0.011911 1.041
-Jack Howell       -1.42e-01  7.44e-02 -4.47e-02 -7.68e-03 -0.143773 1.014
-John Kruk         -1.22e-01  1.14e-01 -1.08e-01  3.84e-02 -0.160368 1.000
-Jeffrey Leonard   -7.59e-02  4.37e-02 -4.34e-02  4.49e-02 -0.119820 0.986
-Jim Morrison       2.43e-02 -4.00e-03 -1.17e-04 -5.68e-02 -0.098066 1.012
-John Moses        -1.50e-02 -6.03e-02  4.18e-02  1.24e-01 -0.167527 0.980
-Jerry Mumphrey     5.49e-02 -5.36e-02  5.25e-02 -2.05e-02  0.077875 1.019
-Jim Presley        1.01e-01 -7.18e-02  5.79e-02 -1.09e-01 -0.208752 0.997
-Johnny Ray        -3.55e-03 -4.05e-03  8.60e-03 -1.03e-02  0.017739 1.038
-Jeff Reed         -1.44e-01  4.06e-02 -1.06e-02  1.90e-02 -0.154169 1.004
-Jim Rice          -1.56e-02 -1.42e-01  1.76e-01  1.67e-02  0.218494 1.030
-Jerry Royster     -2.88e-03  7.71e-04 -2.76e-04  5.67e-04 -0.003362 1.024
-John Russell      -3.94e-02 -9.09e-03  2.37e-02 -3.00e-02 -0.071551 1.012
-Juan Samuel       -1.42e-02  1.24e-02 -7.43e-03 -3.70e-03  0.024606 1.026
-John Shelby       -7.14e-05  9.49e-04 -9.87e-04 -8.43e-05  0.001236 1.026
-Joel Skinner      -3.87e-02 -4.07e-02  4.76e-02  3.40e-02 -0.095446 1.007
-Jim Sundberg      -3.97e-02  1.70e-01 -1.74e-01 -8.92e-03  0.195072 1.006
-Jose Uribe         1.59e-02 -5.09e-02  4.49e-02  3.58e-02 -0.062522 1.038
-Joel Youngblood    9.32e-02 -3.83e-02  1.78e-02  4.92e-03  0.096620 1.017
-Kevin Bass         5.52e-03  3.08e-02 -3.90e-02 -7.53e-03 -0.053599 1.036
-Kal Daniels       -1.96e-01  1.58e-01 -1.24e-01 -2.46e-02 -0.210543 1.001
-Kirk Gibson        1.80e-02 -1.96e-02 -2.16e-03  1.52e-01  0.169506 1.015
-Ken Griffey        1.03e-02 -4.51e-02  4.74e-02  3.11e-02  0.068343 1.027
-Keith Hernandez   -7.84e-03 -9.44e-02  1.28e-01 -3.50e-02  0.173514 1.010
-Kent Hrbek        -3.07e-02  1.44e-02 -1.77e-02  1.01e-01  0.131723 1.021
-Ken Landreaux      8.49e-02 -2.08e-02  1.12e-02 -3.98e-02  0.111615 0.997
-Kevin McReynolds   3.53e-03  5.46e-03 -6.38e-03 -1.34e-02 -0.021208 1.031
-Kevin Mitchell    -7.82e-02  5.29e-02 -3.82e-02 -3.31e-02 -0.104551 0.995
-Keith Moreland    -5.04e-02  3.79e-02 -1.32e-02 -4.31e-02  0.098780 1.016
-Ken Oberkfell     -1.96e-02  2.49e-02 -5.85e-03 -6.38e-02  0.085324 1.020
-Ken Phelps        -1.36e-02  1.41e-03  7.52e-03 -3.74e-02 -0.043416 1.035
-Kirby Puckett      4.15e-02  2.77e-01 -3.20e-01 -1.66e-01 -0.431602 1.024
-Kurt Stillwell    -6.94e-02 -4.57e-02  5.18e-02  8.92e-02 -0.151611 0.998
-Leon Durham       -1.56e-02  2.55e-02 -2.64e-02  5.65e-02  0.103762 1.002
-Len Dykstra       -2.38e-02  4.30e-02 -5.53e-02  3.65e-02 -0.090853 1.009
-Larry Herndon     -1.45e-02  7.11e-04  2.65e-03 -6.66e-04 -0.018937 1.021
-Lee Lacy          -3.05e-04 -1.91e-03  3.43e-03 -2.66e-03  0.007921 1.023
-Len Matuszek       4.42e-03 -2.14e-03  1.01e-03  1.47e-03  0.004722 1.029
-Lloyd Moseby      -3.65e-02  4.33e-02 -3.69e-02  1.40e-02  0.066128 1.027
-Lance Parrish      5.42e-02 -2.31e-02 -3.84e-03  1.06e-01  0.126178 1.018
-Larry Parrish      3.86e-04 -9.79e-04  5.01e-04  4.21e-03  0.004809 1.036
-Larry Sheets      -7.05e-02  4.84e-02 -2.48e-02 -9.15e-02 -0.126844 1.002
-Lou Whitaker       2.15e-02 -1.47e-02  8.50e-03 -8.32e-03 -0.041981 1.024
-Mike Aldrete      -1.28e-01  3.22e-02 -1.07e-02  4.11e-02 -0.148469 0.996
-Marty Barrett     -3.19e-03  1.02e-03  1.36e-03 -6.29e-03  0.008528 1.046
-Mike Davis        -7.19e-03  7.11e-03 -5.83e-03  2.32e-02  0.049188 1.017
-Mike Diaz         -1.56e-01  8.78e-02 -4.42e-02 -8.52e-02 -0.177330 0.998
-Mariano Duncan     7.45e-03 -6.91e-02  6.76e-02  2.74e-02 -0.088537 1.017
-Mike Easler        2.90e-03 -1.65e-02  2.03e-02 -6.61e-04  0.027973 1.026
-Mel Hall           1.30e-03 -2.87e-03  2.86e-03  2.06e-03  0.004565 1.026
-Mike Heath         6.08e-02  3.62e-02 -5.48e-02  9.36e-04  0.110857 1.001
-Mike Kingery      -1.54e-01  5.65e-02 -2.93e-02  2.90e-02 -0.168032 0.988
-Mike LaValliere   -4.82e-02 -3.67e-02  4.25e-02  5.17e-02 -0.107468 1.005
-Mike Marshall      3.75e-02  1.90e-02 -4.23e-02  7.73e-02  0.109998 1.016
-Mike Pagliarulo    4.65e-02 -9.63e-02  1.13e-01 -1.40e-01 -0.205529 1.017
-Mark Salas        -5.14e-02 -4.32e-03  1.87e-02 -7.28e-03 -0.069072 1.015
-Mike Schmidt       6.04e-01 -2.61e-01  1.16e-01  3.29e-02  0.608455 0.879
-Mike Scioscia      2.65e-02  4.29e-02 -3.77e-02 -6.73e-02  0.116250 0.993
-Mickey Tettleton  -6.64e-02 -8.00e-03  3.22e-02 -3.16e-02 -0.093520 1.019
-Milt Thompson     -4.60e-02 -1.29e-03  8.69e-03  1.57e-02 -0.066305 1.011
-Mitch Webster      4.75e-02  7.95e-03 -5.16e-02  9.84e-02 -0.163968 1.008
-Mookie Wilson      3.80e-02 -3.93e-02  4.17e-02 -1.38e-02  0.072513 1.009
-Marvell Wynne     -1.49e-02  5.10e-03 -2.65e-03  1.48e-03 -0.017899 1.021
-Mike Young         3.33e-03  2.86e-03 -3.24e-03 -1.76e-03  0.009330 1.020
-Ozzie Guillen      5.89e-02 -9.46e-02  6.41e-02  1.12e-01 -0.150538 1.031
-Oddibe McDowell    6.48e-02 -5.60e-02  3.60e-02 -8.13e-03 -0.124412 1.001
-Ozzie Smith       -5.37e-02  4.02e-02  3.25e-02 -2.65e-01  0.310911 0.976
-Ozzie Virgil       1.85e-02  6.50e-02 -8.25e-02  4.39e-02  0.118163 1.008
-Phil Bradley       4.81e-04 -1.71e-02  2.26e-02 -6.75e-03  0.030182 1.032
-Phil Garner        2.74e-02 -9.59e-03  4.81e-03  1.61e-03  0.035079 1.017
-Pete Incaviglia    6.42e-02 -8.56e-02  9.92e-02 -1.77e-01 -0.241899 1.006
-Paul Molitor       1.92e-02 -2.32e-02  3.82e-02 -4.43e-02  0.107865 0.990
-Pete Rose          1.14e-01  4.07e-02 -5.91e-02 -8.86e-02  0.189130 0.985
-Pat Sheridan      -2.28e-02  1.98e-03  3.47e-03  2.85e-04 -0.027297 1.023
-Pat Tabler         1.26e-03 -4.50e-03  5.61e-03 -2.76e-03  0.006952 1.043
-Rafael Belliard   -2.71e-02 -3.09e-02  3.09e-02  5.36e-02 -0.081600 1.020
-Rick Burleson      4.52e-02 -2.87e-02  2.37e-02 -1.01e-02  0.052975 1.020
-Randy Bush        -4.05e-03  1.01e-03 -1.00e-03  2.74e-03 -0.007438 1.020
-Rick Cerone        4.58e-03 -1.72e-03  8.78e-04 -5.67e-04  0.004939 1.026
-Ron Cey            1.39e-01 -8.55e-02  4.82e-02  8.40e-02  0.167109 0.990
-Rob Deer           1.94e-02 -6.61e-02  9.31e-02 -1.66e-01 -0.204332 1.041
-Rick Dempsey       1.33e-02  3.85e-02 -4.89e-02  1.75e-02  0.065001 1.025
-Ron Hassey         2.71e-02 -3.82e-02  3.80e-02 -9.06e-04  0.044913 1.030
-Rickey Henderson  -7.61e-02  5.65e-02 -4.91e-02  9.83e-02  0.169443 1.013
-Reggie Jackson     9.62e-05  1.74e-02 -2.10e-02  1.78e-02  0.035902 1.023
-Ron Kittle         3.29e-03  2.33e-02 -3.13e-02  3.00e-02  0.049032 1.034
-Ray Knight        -4.14e-04  2.71e-03 -3.68e-03  1.51e-03 -0.005632 1.026
-Rick Leach        -2.53e-02  2.17e-02 -1.88e-02  2.61e-03 -0.029509 1.029
-Rick Manning       6.13e-02 -2.46e-02  9.16e-03  1.53e-02  0.065449 1.022
-Rance Mulliniks    1.61e-02 -5.13e-04 -2.86e-03  4.16e-03  0.027430 1.018
-Ron Oester        -3.47e-02  5.27e-02 -3.48e-02 -5.28e-02  0.089931 1.018
-Rey Quinones      -4.39e-02 -9.47e-02  1.00e-01  8.58e-02 -0.169986 0.994
-Rafael Ramirez    -5.50e-02  1.23e-01 -1.03e-01 -7.16e-02  0.153327 1.008
-Ronn Reynolds     -1.62e-03  4.75e-04 -7.79e-05 -6.08e-05 -0.001698 1.034
-Ron Roenicke      -2.33e-02  4.36e-04  3.63e-03  7.47e-03 -0.031217 1.021
-Ryne Sandberg     -1.11e-02  2.22e-03  3.85e-03 -7.74e-03  0.022466 1.030
-Rafael Santana    -9.78e-04  7.70e-03 -7.05e-03 -6.34e-03  0.010362 1.038
-Rick Schu         -8.73e-02  4.94e-02 -2.98e-02 -2.04e-02 -0.091678 1.018
-Ruben Sierra      -5.44e-02  1.51e-02  2.43e-03 -7.59e-02 -0.133435 0.974
-Roy Smalley       -1.05e-02  3.77e-02 -4.26e-02  4.11e-02  0.077840 1.018
-Robby Thompson     6.59e-02 -6.03e-02  1.61e-02  1.21e-01 -0.178764 0.995
-Rob Wilfong        2.34e-02  2.59e-02 -3.04e-02 -2.28e-02  0.057036 1.022
-Robin Yount        2.27e-03 -4.95e-02  6.78e-02 -3.51e-02  0.092987 1.029
-Steve Balboni      9.36e-02 -2.00e-01  2.28e-01 -2.28e-01 -0.359398 0.990
-Scott Bradley     -1.58e-01  1.17e-01 -9.31e-02  5.05e-03 -0.171774 0.997
-Sid Bream          3.24e-02 -2.95e-02  1.63e-02 -4.27e-03 -0.092135 1.002
-Steve Buechele     2.54e-02 -8.36e-02  8.86e-02 -5.01e-02 -0.136695 0.997
-Shawon Dunston     1.01e-01 -1.35e-01  1.12e-01  8.00e-03 -0.178151 1.000
-Scott Fletcher     1.15e-03  2.69e-03 -5.66e-03  8.76e-03 -0.012451 1.040
-Steve Garvey      -7.05e-02  8.68e-02 -7.66e-02  4.81e-02  0.151404 1.000
-Steve Jeltz        2.37e-02 -8.42e-02  7.36e-02  6.98e-02 -0.108023 1.040
-Steve Lombardozzi  4.43e-02 -1.46e-01  1.35e-01  6.25e-02 -0.171813 1.005
-Spike Owen        -1.71e-02  3.48e-02 -2.79e-02 -2.99e-02  0.044732 1.053
-Steve Sax          6.20e-02  3.77e-01 -5.42e-01  3.35e-01 -0.734384 0.937
-Tony Bernazard     5.29e-03  1.75e-02 -2.44e-02 -9.23e-04 -0.038471 1.028
-Tom Brookens       2.03e-02 -7.98e-03  6.36e-03 -1.12e-02  0.026764 1.023
-Tom Brunansky     -4.45e-02  4.71e-02 -4.03e-02  2.86e-02  0.084252 1.024
-Tony Fernandez     7.04e-02  6.66e-02 -1.29e-01  1.08e-01 -0.232886 1.034
-Tim Flannery      -2.71e-04  1.42e-04 -2.05e-04  4.56e-04 -0.000684 1.025
-Tom Foley         -6.16e-04  1.97e-04 -1.50e-04  4.18e-04 -0.000837 1.026
-Tony Gwynn         7.84e-03  4.75e-02 -6.37e-02  1.64e-02 -0.079776 1.060
-Terry Harper       4.18e-02 -1.25e-02  3.32e-03  4.63e-03  0.048072 1.018
-Tommy Herr        -8.39e-02  1.26e-01 -8.31e-02 -1.55e-01  0.205925 1.022
-Tim Hulett         5.33e-02 -1.10e-01  1.05e-01 -9.93e-03 -0.128391 1.022
-Terry Kennedy      4.04e-01 -2.08e-01  1.13e-01  4.16e-02  0.404173 0.975
-Tito Landrum       3.86e-02  6.32e-03 -1.52e-02 -1.25e-02  0.052448 1.025
-Tim Laudner       -7.77e-04  2.86e-04 -5.93e-05 -3.37e-04 -0.000870 1.030
-Tom Paciorek      -1.36e-02  8.41e-03 -6.28e-03  1.33e-03 -0.014574 1.028
-Tony Pena         -1.16e-02 -1.90e-02  4.16e-02 -4.55e-02  0.102164 1.007
-Terry Pendleton    8.62e-02 -1.43e-01  1.07e-01  1.34e-01 -0.193138 1.045
-Tony Phillips     -2.73e-03  1.42e-02 -9.82e-03 -2.09e-02  0.030323 1.024
-Terry Puhl         2.04e-01 -6.75e-02  2.43e-02 -1.49e-02  0.215607 0.977
-Ted Simmons        1.51e-01 -6.94e-02  3.44e-02  1.52e-02  0.153167 1.015
-Tim Teufel         7.56e-03  2.47e-04 -1.37e-03 -3.72e-03  0.010776 1.023
-Tim Wallach       -3.14e-02  8.23e-02 -8.42e-02  2.76e-02  0.108729 1.018
-Vince Coleman      9.75e-02 -1.64e-01  1.27e-01  1.40e-01 -0.208761 1.061
-Von Hayes         -1.80e-02 -3.85e-02  5.46e-02  4.08e-03  0.085175 1.030
-Vance Law          9.80e-03  6.71e-02 -6.78e-02 -4.24e-02  0.099409 1.014
-Wally Backman      2.02e-02 -3.39e-02  4.10e-02 -3.19e-02  0.057586 1.037
-Wade Boggs         1.56e-02 -1.35e-01  1.67e-01 -5.20e-02  0.187803 1.089
-Will Clark        -4.86e-02  5.89e-02 -6.47e-02  9.05e-03 -0.118454 0.982
-Wally Joyner       6.64e-02  5.05e-02 -8.27e-02 -6.87e-02 -0.219968 0.973
-Willie McGee      -2.74e-02  5.21e-02 -3.63e-02 -5.40e-02  0.087794 1.017
-Willie Randolph   -1.58e-02  1.47e-02  8.79e-03 -7.82e-02  0.105311 1.013
-Wayne Tolleson    -1.69e-03  3.57e-03 -1.50e-03 -8.34e-03  0.010428 1.030
-Willie Upshaw     -7.78e-02  1.09e-01 -7.95e-02 -7.78e-02  0.150806 1.017
-Willie Wilson     -6.71e-02  5.53e-02 -2.29e-02 -7.26e-02  0.121829 1.026
                     cook.d     hat inf
-Alan Ashby        5.41e-04 0.00540    
-Alvin Davis       7.11e-08 0.00589    
-Andre Dawson      4.50e-05 0.00833    
-Andres Galarraga  3.59e-03 0.00544    
-Alfredo Griffin   1.48e-03 0.02461    
-Al Newman         5.71e-03 0.01412    
-Argenis Salazar   3.43e-03 0.01093    
-Andres Thomas     4.13e-03 0.00583    
-Andre Thornton    7.06e-03 0.01181    
-Alan Trammell     1.33e-04 0.00995    
-Alex Trevino      2.82e-03 0.01160    
-Andy VanSlyke     1.62e-04 0.00392    
-Alan Wiggins      5.95e-03 0.01133    
-Bill Almon        3.67e-05 0.01206    
-Buddy Bell        2.23e-04 0.00926    
-Buddy Biancalana  2.09e-04 0.01234    
-Bruce Bochy       2.17e-03 0.02042    
-Barry Bonds       7.74e-03 0.01404    
-Bobby Bonilla     4.63e-03 0.01106    
-Bob Brenly        6.68e-04 0.00873    
-Bill Buckner      4.21e-04 0.01390    
-Brett Butler      2.12e-03 0.02317    
-Bob Dernier       4.87e-03 0.01020    
-Bo Diaz           7.85e-04 0.00579    
-Bill Doran        5.91e-04 0.01543    
-Brian Downing     1.02e-03 0.00778    
-Billy Hatcher     3.53e-03 0.00710    
-Brook Jacoby      1.16e-05 0.01085    
-Bob Kearney       3.01e-04 0.01088    
-Bill Madlock      1.29e-03 0.00473    
-Bob Melvin        3.29e-03 0.00900    
-BillyJo Robidoux  6.54e-03 0.01333    
-Bill Schroeder    1.83e-04 0.01128    
-Chris Bando       1.37e-04 0.00979    
-Chris Brown       4.35e-03 0.01663    
-Carmen Castillo   3.16e-05 0.01303    
-Chili Davis       6.78e-04 0.00704    
-Carlton Fisk      7.75e-03 0.01782    
-Curt Ford         6.14e-03 0.01097    
-Carney Lansford   1.62e-03 0.01071    
-Chet Lemon        9.25e-04 0.00498    
-Candy Maldonado   2.01e-05 0.00765    
-Carmelo Martinez  3.22e-04 0.00897    
-Craig Reynolds    4.30e-04 0.00601    
-Cal Ripken        2.14e-03 0.01548    
-Cory Snyder       1.66e-02 0.01424    
-Chris Speier      1.35e-04 0.01764    
-Curt Wilkerson    1.96e-05 0.01158    
-Dave Anderson     2.70e-06 0.01141    
-Don Baylor        4.91e-03 0.03525    
-Daryl Boston      6.88e-03 0.01200    
-Darnell Coles     8.42e-03 0.00769    
-Dave Concepcion   7.69e-05 0.00754    
-Doug DeCinces     1.63e-03 0.01616    
-Darrell Evans     9.97e-05 0.02641    
-Dwight Evans      1.88e-03 0.01561    
-Damaso Garcia     1.93e-03 0.00737    
-Dan Gladden       5.21e-04 0.00732    
-Dave Henderson    5.53e-05 0.00494    
-Donnie Hill       8.38e-05 0.00803    
-Davey Lopes       7.69e-04 0.00867    
-Don Mattingly     5.55e-04 0.09037   *
-Dale Murphy       9.01e-03 0.02058    
-Dwayne Murphy     9.92e-04 0.00499    
-Dave Parker       7.85e-04 0.02334    
-Dan Pasqua        8.97e-03 0.01483    
-Darrell Porter    4.27e-06 0.02123    
-Dick Schofield    1.70e-04 0.00693    
-Don Slaught       1.98e-04 0.00665    
-Darryl Strawberry 5.57e-03 0.01769    
-Dale Sveum        4.49e-03 0.00584    
-Danny Tartabull   9.83e-03 0.01283    
-Denny Walling     2.84e-04 0.01244    
-Dave Winfield     7.78e-03 0.01335    
-Eric Davis        2.64e-03 0.02052    
-Eddie Milner      9.87e-05 0.00478    
-Eddie Murray      1.01e-02 0.01269    
-Ed Romero         1.86e-03 0.01202    
-Frank White       2.21e-04 0.01032    
-George Bell       8.36e-05 0.03440   *
-Glenn Braggs      5.75e-03 0.01024    
-George Brett      3.56e-03 0.00702    
-Greg Brock        2.20e-04 0.01025    
-Gary Carter       1.05e-02 0.01335    
-Glenn Davis       1.25e-02 0.02338    
-Gary Gaetti       1.96e-05 0.03006   *
-Greg Gagne        2.42e-03 0.00757    
-George Hendrick   2.32e-03 0.00994    
-Glenn Hubbard     2.80e-03 0.01441    
-Garth Iorg        2.10e-04 0.00751    
-Gary Matthews     1.83e-03 0.01198    
-Graig Nettles     8.04e-04 0.01360    
-Gary Pettis       7.69e-06 0.01809    
-Gary Redus        1.58e-04 0.00533    
-Garry Templeton   6.46e-03 0.02315    
-Greg Walker       6.84e-04 0.00954    
-Gary Ward         8.44e-04 0.01588    
-Glenn Wilson      1.74e-04 0.01027    
-Harold Baines     4.43e-04 0.01369    
-Hubie Brooks      2.54e-03 0.02455    
-Howard Johnson    1.02e-04 0.01116    
-Hal McRae         9.69e-05 0.00661    
-Harold Reynolds   1.29e-02 0.02662    
-Harry Spilman     4.90e-04 0.01782    
-Herm Winningham   3.54e-03 0.01251    
-Jesse Barfield    1.39e-03 0.04727   *
-Juan Beniquez     1.10e-04 0.00984    
-John Cangelosi    8.09e-03 0.01856    
-Jose Canseco      2.65e-02 0.03860    
-Joe Carter        2.40e-02 0.02791    
-Jack Clark        1.10e-02 0.00976    
-Jose Cruz         8.02e-04 0.00622    
-Jody Davis        3.05e-03 0.01258    
-Jim Dwyer         2.22e-04 0.01593    
-Julio Franco      1.52e-04 0.02305    
-Jim Gantner       1.95e-03 0.00960    
-Johnny Grubb      3.56e-05 0.02493    
-Jack Howell       5.16e-03 0.01668    
-John Kruk         6.41e-03 0.01353    
-Jeffrey Leonard   3.57e-03 0.00622    
-Jim Morrison      2.41e-03 0.01043    
-John Moses        6.96e-03 0.00956    
-Jerry Mumphrey    1.52e-03 0.01145    
-Jim Presley       1.08e-02 0.01817    
-Johnny Ray        7.90e-05 0.02223    
-Jeff Reed         5.93e-03 0.01410    
-Jim Rice          1.19e-02 0.03416    
-Jerry Royster     2.84e-06 0.00787    
-John Russell      1.28e-03 0.00732    
-Juan Samuel       1.52e-04 0.01123    
-John Shelby       3.83e-07 0.01058    
-Joel Skinner      2.28e-03 0.00821    
-Jim Sundberg      9.48e-03 0.01962    
-Jose Uribe        9.80e-04 0.02432    
-Joel Youngblood   2.34e-03 0.01275    
-Kevin Bass        7.21e-04 0.02192    
-Kal Daniels       1.10e-02 0.01950    
-Kirk Gibson       7.17e-03 0.02056    
-Ken Griffey       1.17e-03 0.01574    
-Keith Hernandez   7.51e-03 0.01861    
-Kent Hrbek        4.34e-03 0.01925    
-Ken Landreaux     3.11e-03 0.00739    
-Kevin McReynolds  1.13e-04 0.01563    
-Kevin Mitchell    2.72e-03 0.00624    
-Keith Moreland    2.44e-03 0.01216    
-Ken Oberkfell     1.82e-03 0.01265    
-Ken Phelps        4.73e-04 0.01983    
-Kirby Puckett     4.62e-02 0.05527   *
-Kurt Stillwell    5.73e-03 0.01199    
-Leon Durham       2.69e-03 0.00780    
-Len Dykstra       2.06e-03 0.00858    
-Larry Herndon     9.00e-05 0.00650    
-Lee Lacy          1.57e-05 0.00742    
-Len Matuszek      5.59e-06 0.01299    
-Lloyd Moseby      1.10e-03 0.01541    
-Lance Parrish     3.98e-03 0.01684    
-Larry Parrish     5.80e-06 0.01955    
-Larry Sheets      4.01e-03 0.01021    
-Lou Whitaker      4.42e-04 0.01037    
-Mike Aldrete      5.49e-03 0.01090    
-Marty Barrett     1.83e-05 0.02919    
-Mike Davis        6.06e-04 0.00668    
-Mike Diaz         7.83e-03 0.01471    
-Mariano Duncan    1.96e-03 0.01154    
-Mike Easler       1.96e-04 0.01082    
-Mel Hall          5.23e-06 0.00977    
-Mike Heath        3.07e-03 0.00815    
-Mike Kingery      7.02e-03 0.01115    
-Mike LaValliere   2.88e-03 0.00901    
-Mike Marshall     3.03e-03 0.01371    
-Mike Pagliarulo   1.05e-02 0.02554    
-Mark Salas        1.19e-03 0.00824    
-Mike Schmidt      8.89e-02 0.03089   *
-Mike Scioscia     3.37e-03 0.00698    
-Mickey Tettleton  2.19e-03 0.01355    
-Milt Thompson     1.10e-03 0.00617    
-Mitch Webster     6.71e-03 0.01694    
-Mookie Wilson     1.32e-03 0.00619    
-Marvell Wynne     8.04e-05 0.00634    
-Mike Young        2.18e-05 0.00474    
-Ozzie Guillen     5.67e-03 0.02716    
-Oddibe McDowell   3.86e-03 0.00964    
-Ozzie Smith       2.39e-02 0.02295    
-Ozzie Virgil      3.49e-03 0.01141    
-Phil Bradley      2.29e-04 0.01688    
-Phil Garner       3.09e-04 0.00536    
-Pete Incaviglia   1.46e-02 0.02516    
-Paul Molitor      2.90e-03 0.00571    
-Pete Rose         8.88e-03 0.01262    
-Pat Sheridan      1.87e-04 0.00889    
-Pat Tabler        1.21e-05 0.02628    
-Rafael Belliard   1.67e-03 0.01234    
-Rick Burleson     7.03e-04 0.00907    
-Randy Bush        1.39e-05 0.00496    
-Rick Cerone       6.12e-06 0.01047    
-Ron Cey           6.94e-03 0.01140    
-Rob Deer          1.04e-02 0.03955    
-Rick Dempsey      1.06e-03 0.01365    
-Ron Hassey        5.06e-04 0.01582    
-Rickey Henderson  7.17e-03 0.01946    
-Reggie Jackson    3.23e-04 0.00963    
-Ron Kittle        6.03e-04 0.01951    
-Ray Knight        7.96e-06 0.01010    
-Rick Leach        2.18e-04 0.01402    
-Rick Manning      1.07e-03 0.01159    
-Rance Mulliniks   1.89e-04 0.00450    
-Ron Oester        2.02e-03 0.01226    
-Rey Quinones      7.19e-03 0.01288    
-Rafael Ramirez    5.87e-03 0.01556    
-Ronn Reynolds     7.24e-07 0.01742    
-Ron Roenicke      2.44e-04 0.00722    
-Ryne Sandberg     1.27e-04 0.01480    
-Rafael Santana    2.69e-05 0.02135    
-Rick Schu         2.10e-03 0.01243    
-Ruben Sierra      4.42e-03 0.00575    
-Roy Smalley       1.52e-03 0.01061    
-Robby Thompson    7.95e-03 0.01401    
-Rob Wilfong       8.15e-04 0.01093    
-Robin Yount       2.17e-03 0.01993    
-Steve Balboni     3.19e-02 0.03283    
-Scott Bradley     7.35e-03 0.01382    
-Sid Bream         2.12e-03 0.00648    
-Steve Buechele    4.66e-03 0.01005    
-Shawon Dunston    7.90e-03 0.01549    
-Scott Fletcher    3.89e-05 0.02316    
-Steve Garvey      5.71e-03 0.01247    
-Steve Jeltz       2.92e-03 0.02943    
-Steve Lombardozzi 7.36e-03 0.01637    
-Spike Owen        5.02e-04 0.03619   *
-Steve Sax         1.31e-01 0.05621   *
-Tony Bernazard    3.71e-04 0.01372    
-Tom Brookens      1.80e-04 0.00843    
-Tom Brunansky     1.78e-03 0.01555    
-Tony Fernandez    1.35e-02 0.03841    
-Tim Flannery      1.17e-07 0.00880    
-Tom Foley         1.76e-07 0.01018    
-Tony Gwynn        1.60e-03 0.04413   *
-Terry Harper      5.79e-04 0.00728    
-Tommy Herr        1.06e-02 0.02831    
-Tim Hulett        4.12e-03 0.01934    
-Terry Kennedy     4.02e-02 0.03269   *
-Tito Landrum      6.90e-04 0.01246    
-Tim Laudner       1.90e-07 0.01372    
-Tom Paciorek      5.33e-05 0.01268    
-Tony Pena         2.61e-03 0.00921    
-Terry Pendleton   9.33e-03 0.04110    
-Tony Phillips     2.31e-04 0.00948    
-Terry Puhl        1.15e-02 0.01348    
-Ted Simmons       5.86e-03 0.01835    
-Tim Teufel        2.91e-05 0.00754    
-Tim Wallach       2.96e-03 0.01472    
-Vince Coleman     1.09e-02 0.05407   *
-Von Hayes         1.82e-03 0.01920    
-Vance Law         2.47e-03 0.01135    
-Wally Backman     8.32e-04 0.02256    
-Wade Boggs        8.84e-03 0.07367   *
-Will Clark        3.49e-03 0.00548    
-Wally Joyner      1.20e-02 0.01320    
-Willie McGee      1.93e-03 0.01159    
-Willie Randolph   2.77e-03 0.01180    
-Wayne Tolleson    2.73e-05 0.01364    
-Willie Upshaw     5.68e-03 0.01897    
-Willie Wilson     3.71e-03 0.02101    
summary(influence.measures(reg_model_2))
Potentially influential observations of
     lm(formula = log_Salary ~ AtBat + Hits + HmRun, data = hitters) :

                dfb.1_ dfb.AtBt dfb.Hits dfb.HmRn dffit   cov.r   cook.d
-Don Mattingly   0.00  -0.04     0.04     0.01     0.05    1.12_*  0.00 
-George Bell     0.00  -0.01     0.01     0.01     0.02    1.05_*  0.00 
-Gary Gaetti     0.00   0.00     0.00     0.01     0.01    1.05_*  0.00 
-Jesse Barfield -0.01  -0.02     0.01     0.06     0.07    1.06_*  0.00 
-Kirby Puckett   0.04   0.28    -0.32    -0.17    -0.43_*  1.02    0.05 
-Mike Schmidt    0.60  -0.26     0.12     0.03     0.61_*  0.88_*  0.09 
-Spike Owen     -0.02   0.03    -0.03    -0.03     0.04    1.05_*  0.00 
-Steve Sax       0.06   0.38    -0.54     0.34    -0.73_*  0.94_*  0.13 
-Tony Gwynn      0.01   0.05    -0.06     0.02    -0.08    1.06_*  0.00 
-Terry Kennedy   0.40  -0.21     0.11     0.04     0.40_*  0.97    0.04 
-Vince Coleman   0.10  -0.16     0.13     0.14    -0.21    1.06_*  0.01 
-Wade Boggs      0.02  -0.14     0.17    -0.05     0.19    1.09_*  0.01 
                hat    
-Don Mattingly   0.09_*
-George Bell     0.03  
-Gary Gaetti     0.03  
-Jesse Barfield  0.05_*
-Kirby Puckett   0.06_*
-Mike Schmidt    0.03  
-Spike Owen      0.04  
-Steve Sax       0.06_*
-Tony Gwynn      0.04  
-Terry Kennedy   0.03  
-Vince Coleman   0.05_*
-Wade Boggs      0.07_*
summary(influence.measures(reg_model))
Potentially influential observations of
     lm(formula = Salary ~ AtBat + Hits + HmRun, data = hitters) :

                 dfb.1_ dfb.AtBt dfb.Hits dfb.HmRn dffit   cov.r   cook.d
-Don Mattingly    0.01  -0.38     0.42     0.15     0.50_*  1.07_*  0.06 
-Dale Murphy     -0.17   0.11    -0.09     0.24     0.40_*  0.92_*  0.04 
-Dave Winfield   -0.14   0.12    -0.11     0.17     0.34    0.91_*  0.03 
-Eddie Murray     0.06  -0.32     0.36     0.09     0.49_*  0.78_*  0.06 
-George Bell     -0.01  -0.02     0.02     0.02     0.04    1.05_*  0.00 
-Gary Carter     -0.06   0.11    -0.13     0.26     0.38_*  0.88_*  0.03 
-Gary Gaetti      0.01   0.01    -0.01    -0.03    -0.03    1.05_*  0.00 
-Jesse Barfield  -0.01  -0.03     0.02     0.10     0.12    1.06_*  0.00 
-Jack Clark       0.20  -0.03    -0.03     0.06     0.24    0.94_*  0.01 
-Jim Rice        -0.05  -0.43     0.54     0.05     0.67_*  0.87_*  0.11 
-Keith Hernandez -0.02  -0.18     0.25    -0.07     0.34    0.94_*  0.03 
-Kirby Puckett    0.05   0.36    -0.41    -0.21    -0.55_*  0.99    0.08 
-Mike Schmidt     0.94  -0.41     0.18     0.05     0.95_*  0.69_*  0.20 
-Ozzie Smith     -0.10   0.07     0.06    -0.47     0.55_*  0.85_*  0.07 
-Spike Owen       0.00   0.00     0.00     0.00     0.00    1.05_*  0.00 
-Steve Sax        0.05   0.29    -0.41     0.26    -0.56_*  0.99    0.08 
-Tony Gwynn       0.02   0.10    -0.13     0.03    -0.17    1.05_*  0.01 
-Terry Pendleton  0.06  -0.10     0.07     0.09    -0.13    1.05_*  0.00 
-Vince Coleman    0.06  -0.11     0.08     0.09    -0.13    1.07_*  0.00 
-Wade Boggs       0.03  -0.29     0.36    -0.11     0.40_*  1.06_*  0.04 
                 hat    
-Don Mattingly    0.09_*
-Dale Murphy      0.02  
-Dave Winfield    0.01  
-Eddie Murray     0.01  
-George Bell      0.03  
-Gary Carter      0.01  
-Gary Gaetti      0.03  
-Jesse Barfield   0.05_*
-Jack Clark       0.01  
-Jim Rice         0.03  
-Keith Hernandez  0.02  
-Kirby Puckett    0.06_*
-Mike Schmidt     0.03  
-Ozzie Smith      0.02  
-Spike Owen       0.04  
-Steve Sax        0.06_*
-Tony Gwynn       0.04  
-Terry Pendleton  0.04  
-Vince Coleman    0.05_*
-Wade Boggs       0.07_*
plot(reg_model, pch=16)

plot(reg_model_2, pch=16)