ref

import

library(MASS) #lm.ridge 
library(car) #vif
library(caret) #예측
library(ggplot2)
library(glmnet) #Ridge, Lasso
library(tidyverse)

get_high_vif_variables <- function(data, threshold) {
  vif_values <- vif(data)
  high_vif_variables <- names(vif_values[vif_values > threshold])
  return(high_vif_variables)
}

데이터셋

picher <- read.csv("~/Dropbox/coco/posts/Applied statistics/picher_stats_2017.csv")
head(picher)

A data.frame: 6 × 22
	선수명	팀명	승	패	세	홀드	블론	경기	선발	이닝	⋯	홈런.9	BABIP	LOB.	ERA	RA9.WAR	FIP	kFIP	WAR	연봉.2018.	연봉.2017.
	<chr>	<chr>	<int>	<int>	<int>	<int>	<int>	<int>	<int>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<int>
1	켈리	SK	16	7	0	0	0	30	30	190.0	⋯	0.76	0.342	73.7	3.60	6.91	3.69	3.44	6.62	140000	85000
2	소사	LG	11	11	1	0	0	30	29	185.1	⋯	0.53	0.319	67.1	3.88	6.80	3.52	3.41	6.08	120000	50000
3	양현종	KIA	20	6	0	0	0	31	31	193.1	⋯	0.79	0.332	72.1	3.44	6.54	3.94	3.82	5.64	230000	150000
4	차우찬	LG	10	7	0	0	0	28	28	175.2	⋯	1.02	0.298	75.0	3.43	6.11	4.20	4.03	4.63	100000	100000
5	레일리	롯데	13	7	0	0	0	30	30	187.1	⋯	0.91	0.323	74.1	3.80	6.13	4.36	4.31	4.38	111000	85000
6	피어밴드	KT	8	10	0	0	0	26	26	160.0	⋯	1.12	0.289	76.1	3.04	6.52	4.42	4.32	3.94	85000	35000

dt2018 <- data.frame(new_col = picher$연봉.2018.)

dt2017 <- data.frame(new_col = picher$연봉.2017.)

dt <- subset(picher, select = -c(연봉.2017.,연봉.2018.))

head(dt)

A data.frame: 6 × 20
	선수명	팀명	승	패	세	홀드	블론	경기	선발	이닝	삼진.9	볼넷.9	홈런.9	BABIP	LOB.	ERA	RA9.WAR	FIP	kFIP	WAR
	<chr>	<chr>	<int>	<int>	<int>	<int>	<int>	<int>	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
1	켈리	SK	16	7	0	0	0	30	30	190.0	8.95	2.13	0.76	0.342	73.7	3.60	6.91	3.69	3.44	6.62
2	소사	LG	11	11	1	0	0	30	29	185.1	7.43	1.85	0.53	0.319	67.1	3.88	6.80	3.52	3.41	6.08
3	양현종	KIA	20	6	0	0	0	31	31	193.1	7.36	2.09	0.79	0.332	72.1	3.44	6.54	3.94	3.82	5.64
4	차우찬	LG	10	7	0	0	0	28	28	175.2	8.04	1.95	1.02	0.298	75.0	3.43	6.11	4.20	4.03	4.63
5	레일리	롯데	13	7	0	0	0	30	30	187.1	7.49	2.11	0.91	0.323	74.1	3.80	6.13	4.36	4.31	4.38
6	피어밴드	KT	8	10	0	0	0	26	26	160.0	7.42	1.74	1.12	0.289	76.1	3.04	6.52	4.42	4.32	3.94

dt <- cbind(dt, new_col = dt2017)
names(dt)[length(names(dt))] <- "연봉.2017."

dt <- cbind(dt, new_col = dt2018)
names(dt)[length(names(dt))] <- "연봉.2018."

head(dt)

A data.frame: 6 × 22
	선수명	팀명	승	패	세	홀드	블론	경기	선발	이닝	⋯	홈런.9	BABIP	LOB.	ERA	RA9.WAR	FIP	kFIP	WAR	연봉.2017.	연봉.2018.
	<chr>	<chr>	<int>	<int>	<int>	<int>	<int>	<int>	<int>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<int>
1	켈리	SK	16	7	0	0	0	30	30	190.0	⋯	0.76	0.342	73.7	3.60	6.91	3.69	3.44	6.62	85000	140000
2	소사	LG	11	11	1	0	0	30	29	185.1	⋯	0.53	0.319	67.1	3.88	6.80	3.52	3.41	6.08	50000	120000
3	양현종	KIA	20	6	0	0	0	31	31	193.1	⋯	0.79	0.332	72.1	3.44	6.54	3.94	3.82	5.64	150000	230000
4	차우찬	LG	10	7	0	0	0	28	28	175.2	⋯	1.02	0.298	75.0	3.43	6.11	4.20	4.03	4.63	100000	100000
5	레일리	롯데	13	7	0	0	0	30	30	187.1	⋯	0.91	0.323	74.1	3.80	6.13	4.36	4.31	4.38	85000	111000
6	피어밴드	KT	8	10	0	0	0	26	26	160.0	⋯	1.12	0.289	76.1	3.04	6.52	4.42	4.32	3.94	35000	85000

dt <- subset(dt, select = -c(팀명,선수명))

head(dt)

A data.frame: 6 × 20
	승	패	세	홀드	블론	경기	선발	이닝	삼진.9	볼넷.9	홈런.9	BABIP	LOB.	ERA	RA9.WAR	FIP	kFIP	WAR	연봉.2017.	연봉.2018.
	<int>	<int>	<int>	<int>	<int>	<int>	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<int>
1	16	7	0	0	0	30	30	190.0	8.95	2.13	0.76	0.342	73.7	3.60	6.91	3.69	3.44	6.62	85000	140000
2	11	11	1	0	0	30	29	185.1	7.43	1.85	0.53	0.319	67.1	3.88	6.80	3.52	3.41	6.08	50000	120000
3	20	6	0	0	0	31	31	193.1	7.36	2.09	0.79	0.332	72.1	3.44	6.54	3.94	3.82	5.64	150000	230000
4	10	7	0	0	0	28	28	175.2	8.04	1.95	1.02	0.298	75.0	3.43	6.11	4.20	4.03	4.63	100000	100000
5	13	7	0	0	0	30	30	187.1	7.49	2.11	0.91	0.323	74.1	3.80	6.13	4.36	4.31	4.38	85000	111000
6	8	10	0	0	0	26	26	160.0	7.42	1.74	1.12	0.289	76.1	3.04	6.52	4.42	4.32	3.94	35000	85000

회귀직선적합

model1(원본)

model1 <- lm(연봉.2018. ~ ., dt)
summary(model1)


Call:
lm(formula = 연봉.2018. ~ ., data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-46529  -2418    424   2649  47773 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.513e+04  1.826e+04   0.829   0.4087    
승           1.004e+03  5.375e+02   1.869   0.0639 .  
패          -1.836e+02  5.504e+02  -0.334   0.7392    
세          -2.112e+01  2.713e+02  -0.078   0.9381    
홀드        -1.817e+01  3.161e+02  -0.057   0.9542    
블론         4.535e+02  7.610e+02   0.596   0.5522    
경기        -1.760e+02  1.456e+02  -1.209   0.2289    
선발        -6.719e+02  4.616e+02  -1.456   0.1479    
이닝         7.425e+01  1.156e+02   0.642   0.5217    
삼진.9      -4.603e+02  2.349e+03  -0.196   0.8449    
볼넷.9       1.194e+03  2.256e+03   0.529   0.5976    
홈런.9       4.874e+03  1.413e+04   0.345   0.7306    
BABIP       -9.997e+03  1.486e+04  -0.673   0.5022    
LOB.        -4.350e+01  1.299e+02  -0.335   0.7382    
ERA         -7.413e+01  5.693e+02  -0.130   0.8966    
RA9.WAR     -7.584e+02  1.487e+03  -0.510   0.6109    
FIP         -6.436e+03  4.477e+04  -0.144   0.8859    
kFIP         3.805e+03  3.593e+04   0.106   0.9158    
WAR          8.559e+03  1.789e+03   4.783 4.55e-06 ***
연봉.2017.   8.755e-01  4.444e-02  19.698  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9198 on 132 degrees of freedom
Multiple R-squared:  0.9228,    Adjusted R-squared:  0.9116 
F-statistic: 82.99 on 19 and 132 DF,  p-value: < 2.2e-16

model1 <- lm(연봉.2018. ~ +WAR+연봉.2017., dt)
summary(model1)


Call:
lm(formula = 연봉.2018. ~ +WAR + 연봉.2017., data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-50442  -1849    758   2050  56166 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -576.58811  889.09610  -0.649    0.518    
WAR         7007.17364  761.83979   9.198 3.03e-16 ***
연봉.2017.     0.89926    0.04022  22.360  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9124 on 149 degrees of freedom
Multiple R-squared:  0.9142,    Adjusted R-squared:  0.913 
F-statistic: 793.8 on 2 and 149 DF,  p-value: < 2.2e-16

vif(model1)

승: 7.69934669638176
패: 5.30032799820878
세: 3.03718565968123
홀드: 3.63605161357374
블론: 2.75956034802692
경기: 14.2011271199637
선발: 36.1601878733279
이닝: 60.3244538179009
삼진.9: 78.7161704892493
볼넷.9: 50.7257985016107
홈런.9: 368.399308168573
BABIP: 3.11936893312554
LOB.: 4.04602533224649
ERA: 10.0441738232824
RA9.WAR: 13.4198973515016
FIP: 12525.2424059086
kFIP: 9046.04880487446
WAR: 9.99177856816849
연봉.2017.: 2.21186942564398

threshold <- 10

high_vif_vars <- get_high_vif_variables(model1, threshold)
print(high_vif_vars)

 [1] "경기"    "선발"    "이닝"    "삼진.9"  "볼넷.9"  "홈런.9"  "ERA"    
 [8] "RA9.WAR" "FIP"     "kFIP"

threshold <- 15

high_vif_vars <- get_high_vif_variables(model1, threshold)
print(high_vif_vars)

[1] "선발"   "이닝"   "삼진.9" "볼넷.9" "홈런.9" "FIP"    "kFIP"

pairs(dt,panel=panel.smooth)

수치형 데이터들끼리의 상관계수 확인..

dt_numeric <- dt[, sapply(dt, is.numeric)]
cor_matrix <- cor(dt_numeric)
print(round(cor_matrix,2))

              승    패    세  홀드  블론  경기  선발  이닝 삼진.9 볼넷.9 홈런.9
승          1.00  0.71  0.05  0.09  0.11  0.40  0.77  0.91   0.08  -0.40  -0.12
패          0.71  1.00  0.07  0.10  0.12  0.34  0.77  0.83   0.03  -0.39  -0.06
세          0.05  0.07  1.00  0.11  0.61  0.43 -0.18  0.02   0.17  -0.13  -0.07
홀드        0.09  0.10  0.11  1.00  0.49  0.72 -0.29  0.02   0.19  -0.15  -0.08
블론        0.11  0.12  0.61  0.49  1.00  0.63 -0.26  0.01   0.19  -0.14  -0.06
경기        0.40  0.34  0.43  0.72  0.63  1.00 -0.04  0.38   0.19  -0.36  -0.11
선발        0.77  0.77 -0.18 -0.29 -0.26 -0.04  1.00  0.89  -0.06  -0.31  -0.06
이닝        0.91  0.83  0.02  0.02  0.01  0.38  0.89  1.00   0.04  -0.45  -0.11
삼진.9      0.08  0.03  0.17  0.19  0.19  0.19 -0.06  0.04   1.00   0.11   0.22
볼넷.9     -0.40 -0.39 -0.13 -0.15 -0.14 -0.36 -0.31 -0.45   0.11   1.00   0.30
홈런.9     -0.12 -0.06 -0.07 -0.08 -0.06 -0.11 -0.06 -0.11   0.22   0.30   1.00
BABIP      -0.17 -0.13 -0.09 -0.10 -0.11 -0.24 -0.10 -0.19   0.46   0.28   0.36
LOB.        0.13 -0.02  0.17  0.05  0.10  0.11  0.04  0.10  -0.07  -0.15  -0.27
ERA        -0.27 -0.19 -0.15 -0.16 -0.16 -0.32 -0.16 -0.29   0.26   0.52   0.63
RA9.WAR     0.85  0.60  0.17  0.00  0.01  0.28  0.74  0.85   0.10  -0.40  -0.19
FIP        -0.30 -0.23 -0.20 -0.21 -0.21 -0.35 -0.15 -0.30  -0.15   0.63   0.83
kFIP       -0.31 -0.24 -0.23 -0.24 -0.24 -0.37 -0.14 -0.30  -0.32   0.61   0.74
WAR         0.82  0.63  0.08 -0.04 -0.06  0.20  0.76  0.83   0.15  -0.39  -0.21
연봉.2017.  0.63  0.43  0.26  0.00  0.15  0.23  0.49  0.59   0.10  -0.33  -0.10
연봉.2018.  0.71  0.47  0.21 -0.02  0.10  0.21  0.56  0.66   0.10  -0.33  -0.12
           BABIP  LOB.   ERA RA9.WAR   FIP  kFIP   WAR 연봉.2017. 연봉.2018.
승         -0.17  0.13 -0.27    0.85 -0.30 -0.31  0.82       0.63       0.71
패         -0.13 -0.02 -0.19    0.60 -0.23 -0.24  0.63       0.43       0.47
세         -0.09  0.17 -0.15    0.17 -0.20 -0.23  0.08       0.26       0.21
홀드       -0.10  0.05 -0.16    0.00 -0.21 -0.24 -0.04       0.00      -0.02
블론       -0.11  0.10 -0.16    0.01 -0.21 -0.24 -0.06       0.15       0.10
경기       -0.24  0.11 -0.32    0.28 -0.35 -0.37  0.20       0.23       0.21
선발       -0.10  0.04 -0.16    0.74 -0.15 -0.14  0.76       0.49       0.56
이닝       -0.19  0.10 -0.29    0.85 -0.30 -0.30  0.83       0.59       0.66
삼진.9      0.46 -0.07  0.26    0.10 -0.15 -0.32  0.15       0.10       0.10
볼넷.9      0.28 -0.15  0.52   -0.40  0.63  0.61 -0.39      -0.33      -0.33
홈런.9      0.36 -0.27  0.63   -0.19  0.83  0.74 -0.21      -0.10      -0.12
BABIP       1.00 -0.51  0.73   -0.19  0.25  0.17 -0.08      -0.09      -0.10
LOB.       -0.51  1.00 -0.72    0.29 -0.29 -0.27  0.14       0.11       0.13
ERA         0.73 -0.72  1.00   -0.34  0.65  0.58 -0.26      -0.20      -0.22
RA9.WAR    -0.19  0.29 -0.34    1.00 -0.37 -0.38  0.92       0.64       0.74
FIP         0.25 -0.29  0.65   -0.37  1.00  0.98 -0.39      -0.27      -0.28
kFIP        0.17 -0.27  0.58   -0.38  0.98  1.00 -0.41      -0.28      -0.30
WAR        -0.08  0.14 -0.26    0.92 -0.39 -0.41  1.00       0.68       0.79
연봉.2017. -0.09  0.11 -0.20    0.64 -0.27 -0.28  0.68       1.00       0.93
연봉.2018. -0.10  0.13 -0.22    0.74 -0.28 -0.30  0.79       0.93       1.00

다중공산성 해결 방법

VIF계수가 높은 변수 제거

model2(Vif 10 이상인 변수 제거)

model2 <- lm(연봉.2018. ~ .-경기-선발-이닝-삼진.9-볼넷.9-홈런.9-ERA-RA9.WAR-FIP-kFIP, dt)
summary(model2)


Call:
lm(formula = 연봉.2018. ~ . - 경기 - 선발 - 이닝 - 삼진.9 - 
    볼넷.9 - 홈런.9 - ERA - RA9.WAR - FIP - kFIP, data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-48657  -1981    511   2303  51073 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  6.432e+03  7.893e+03   0.815   0.4165    
승           4.770e+02  4.061e+02   1.175   0.2421    
패          -7.851e+02  3.525e+02  -2.227   0.0275 *  
세          -1.172e+02  2.150e+02  -0.545   0.5865    
홀드        -1.229e+02  1.973e+02  -0.623   0.5344    
블론         6.340e+02  7.188e+02   0.882   0.3792    
BABIP       -7.810e+03  9.994e+03  -0.781   0.4358    
LOB.        -4.979e+01  7.793e+01  -0.639   0.5239    
WAR          7.298e+03  1.169e+03   6.243 4.67e-09 ***
연봉.2017.   8.846e-01  4.322e-02  20.469  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9149 on 142 degrees of freedom
Multiple R-squared:  0.9178,    Adjusted R-squared:  0.9126 
F-statistic: 176.1 on 9 and 142 DF,  p-value: < 2.2e-16

vif(model2)

승: 4.44133840452701
패: 2.19787784118271
세: 1.9291576101908
홀드: 1.43155944990414
블론: 2.48814143828698
BABIP: 1.42670331782564
LOB.: 1.47225296358887
WAR: 4.30937396392511
연봉.2017.: 2.11357639082776

model1에서 다중공산성이 높았던 변수들을 제외하고 lm을 돌렸더니, 회귀모형은 유의하게 나왔고 R^2값도 91%로 높게 나왔지만 model1보다는 R^2값이 조금 적게 나왔다.
다중공산성이 높은 변수를 제외하는 것은 다른 것들도 확인을 해보아야 한다.

VIF제거시 고려사항

1. VIF계수가 높은 피처 우선 제거하되, FIP, kFIP와 같이 유사한 변수들은 두개 중에서 하나만 제거해보자.

model3 <- lm(연봉.2018. ~ .-FIP, dt)
summary(model3)


Call:
lm(formula = 연봉.2018. ~ . - FIP, data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-46688  -2466    423   2597  47710 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.406e+04  1.660e+04   0.847    0.399    
승           1.007e+03  5.352e+02   1.882    0.062 .  
패          -1.723e+02  5.427e+02  -0.317    0.751    
세          -2.263e+01  2.701e+02  -0.084    0.933    
홀드        -1.779e+01  3.149e+02  -0.056    0.955    
블론         4.563e+02  7.579e+02   0.602    0.548    
경기        -1.738e+02  1.443e+02  -1.205    0.230    
선발        -6.701e+02  4.598e+02  -1.458    0.147    
이닝         7.216e+01  1.142e+02   0.632    0.529    
삼진.9      -7.714e+02  9.085e+02  -0.849    0.397    
볼넷.9       8.998e+02  9.504e+02   0.947    0.346    
홈런.9       2.904e+03  3.404e+03   0.853    0.395    
BABIP       -9.797e+03  1.474e+04  -0.665    0.507    
LOB.        -4.465e+01  1.292e+02  -0.346    0.730    
ERA         -8.076e+01  5.654e+02  -0.143    0.887    
RA9.WAR     -7.473e+02  1.480e+03  -0.505    0.614    
kFIP        -1.347e+03  2.371e+03  -0.568    0.571    
WAR          8.560e+03  1.783e+03   4.802 4.17e-06 ***
연봉.2017.   8.757e-01  4.426e-02  19.787  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9164 on 133 degrees of freedom
Multiple R-squared:  0.9227,    Adjusted R-squared:  0.9123 
F-statistic: 88.25 on 18 and 133 DF,  p-value: < 2.2e-16

vif(model3)

승: 7.68840921316788
패: 5.19140274673014
세: 3.03263975401923
홀드: 3.63578951116975
블론: 2.75775305712261
경기: 14.0426530671348
선발: 36.1331990754777
이닝: 59.3709458069269
삼진.9: 11.8666574529657
볼넷.9: 9.0682604275144
홈런.9: 21.5595297493918
BABIP: 3.09205217740503
LOB.: 4.03056643053091
ERA: 9.9781711774582
RA9.WAR: 13.3837520395074
kFIP: 39.6977412189025
WAR: 9.99134587181084
연봉.2017.: 2.20945320867407

VIF계수가 가장 높았떤 FIP를 제거하니 전체적으로 VIF값들이 많이 감소했다. 볼넷의 경우 50에서 9로 감소함

model3 <- lm(연봉.2018. ~ .-FIP-이닝, dt)
summary(model3)
vif(model3)


Call:
lm(formula = 연봉.2018. ~ . - FIP - 이닝, data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-47170  -2539    292   2603  47529 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.425e+04  1.656e+04   0.860   0.3912    
승           1.053e+03  5.292e+02   1.989   0.0487 *  
패          -1.258e+02  5.365e+02  -0.234   0.8150    
세          -7.264e+01  2.576e+02  -0.282   0.7784    
홀드        -7.025e+01  3.031e+02  -0.232   0.8171    
블론         4.745e+02  7.557e+02   0.628   0.5312    
경기        -1.021e+02  8.877e+01  -1.150   0.2523    
선발        -4.306e+02  2.595e+02  -1.659   0.0994 .  
삼진.9      -7.892e+02  9.060e+02  -0.871   0.3853    
볼넷.9       8.829e+02  9.479e+02   0.931   0.3533    
홈런.9       2.956e+03  3.396e+03   0.871   0.3855    
BABIP       -1.004e+04  1.470e+04  -0.683   0.4957    
LOB.        -4.506e+01  1.289e+02  -0.350   0.7272    
ERA         -6.838e+01  5.637e+02  -0.121   0.9036    
RA9.WAR     -4.551e+02  1.402e+03  -0.325   0.7460    
kFIP        -1.349e+03  2.366e+03  -0.570   0.5696    
WAR          8.733e+03  1.758e+03   4.968 2.03e-06 ***
연봉.2017.   8.784e-01  4.395e-02  19.984  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9143 on 134 degrees of freedom
Multiple R-squared:  0.9225,    Adjusted R-squared:  0.9127 
F-statistic: 93.84 on 17 and 134 DF,  p-value: < 2.2e-16

승: 7.54995904402493
패: 5.09588128549648
세: 2.77188079102657
홀드: 3.38288542173628
블론: 2.75379743632109
경기: 5.34096225137479
선발: 11.5652288817222
삼진.9: 11.8553164987874
볼넷.9: 9.06115155090058
홈런.9: 21.5464901061541
BABIP: 3.0899457520436
LOB.: 4.03046844648891
ERA: 9.96618149145026
RA9.WAR: 12.0759322801392
kFIP: 39.6977185280435
WAR: 9.75717291579296
연봉.2017.: 2.18906326524158

그 다음 vif계수값이 높은 ’이닝’을 제거했다.

model3 <- lm(연봉.2018. ~ .-FIP-이닝-kFIP, dt)
summary(model3)
vif(model3)


Call:
lm(formula = 연봉.2018. ~ . - FIP - 이닝 - kFIP, data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-47261  -2379    309   2742  47813 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  6.978e+03  1.054e+04   0.662   0.5090    
승           1.055e+03  5.278e+02   1.999   0.0476 *  
패          -1.135e+02  5.347e+02  -0.212   0.8323    
세          -7.382e+01  2.569e+02  -0.287   0.7743    
홀드        -7.661e+01  3.021e+02  -0.254   0.8002    
블론         5.038e+02  7.521e+02   0.670   0.5040    
경기        -9.923e+01  8.841e+01  -1.122   0.2637    
선발        -4.402e+02  2.583e+02  -1.704   0.0906 .  
삼진.9      -3.109e+02  3.413e+02  -0.911   0.3639    
볼넷.9       4.082e+02  4.514e+02   0.904   0.3675    
홈런.9       1.129e+03  1.118e+03   1.010   0.3143    
BABIP       -9.576e+03  1.464e+04  -0.654   0.5141    
LOB.        -3.779e+01  1.279e+02  -0.295   0.7681    
ERA         -8.963e+01  5.611e+02  -0.160   0.8733    
RA9.WAR     -4.669e+02  1.399e+03  -0.334   0.7390    
WAR          8.800e+03  1.749e+03   5.030 1.53e-06 ***
연봉.2017.   8.779e-01  4.384e-02  20.027  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9120 on 135 degrees of freedom
Multiple R-squared:  0.9223,    Adjusted R-squared:  0.9131 
F-statistic: 100.2 on 16 and 135 DF,  p-value: < 2.2e-16

승: 7.54945354936935
패: 5.08758327243023
세: 2.77170233465349
홀드: 3.37829494203411
블론: 2.74099514800148
경기: 5.32417495720081
선발: 11.5165551404735
삼진.9: 1.691074402967
볼넷.9: 2.06526070907551
홈런.9: 2.34713984614222
BABIP: 3.08046557773165
LOB.: 3.99101474806593
ERA: 9.92261602645989
RA9.WAR: 12.0732896169765
WAR: 9.71340804685137
연봉.2017.: 2.18834997395971

KFIP제거

model3 <- lm(연봉.2018. ~ .-FIP-이닝-kFIP-RA9.WAR, dt)
summary(model3)
vif(model3)


Call:
lm(formula = 연봉.2018. ~ . - FIP - 이닝 - kFIP - RA9.WAR, 
    data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-47256  -2340    228   2820  48394 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  8.002e+03  1.005e+04   0.796   0.4273    
승           1.005e+03  5.044e+02   1.993   0.0483 *  
패          -6.188e+01  5.102e+02  -0.121   0.9036    
세          -1.005e+02  2.434e+02  -0.413   0.6805    
홀드        -8.969e+01  2.986e+02  -0.300   0.7643    
블론         5.293e+02  7.457e+02   0.710   0.4790    
경기        -1.027e+02  8.749e+01  -1.174   0.2424    
선발        -4.671e+02  2.447e+02  -1.909   0.0584 .  
삼진.9      -3.052e+02  3.398e+02  -0.898   0.3707    
볼넷.9       4.218e+02  4.481e+02   0.941   0.3482    
홈런.9       1.154e+03  1.112e+03   1.037   0.3013    
BABIP       -9.059e+03  1.451e+04  -0.624   0.5334    
LOB.        -5.310e+01  1.190e+02  -0.446   0.6562    
ERA         -1.249e+02  5.493e+02  -0.227   0.8205    
WAR          8.406e+03  1.289e+03   6.523 1.25e-09 ***
연봉.2017.   8.790e-01  4.358e-02  20.168  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9090 on 136 degrees of freedom
Multiple R-squared:  0.9223,    Adjusted R-squared:  0.9137 
F-statistic: 107.6 on 15 and 136 DF,  p-value: < 2.2e-16

승: 6.94042688100102
패: 4.66294914095306
세: 2.50425253772256
홀드: 3.32146243586634
블론: 2.71278267026247
경기: 5.24904766467952
선발: 10.3991198289636
삼진.9: 1.68672132907842
볼넷.9: 2.04837389574494
홈런.9: 2.33709850623971
BABIP: 3.046073880605
LOB.: 3.47761526760098
ERA: 9.57142193166993
WAR: 5.30623103354661
연봉.2017.: 2.17720905024618

model3 <- lm(연봉.2018. ~ .-FIP-이닝-kFIP-RA9.WAR-선발, dt)
summary(model3)
vif(model3)


Call:
lm(formula = 연봉.2018. ~ . - FIP - 이닝 - kFIP - RA9.WAR - 
    선발, data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-46776  -2395    374   2597  50018 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  7221.2085 10138.7800   0.712   0.4775    
승            558.2422   451.0986   1.238   0.2180    
패           -758.5773   359.9930  -2.107   0.0369 *  
세            -12.1963   241.3026  -0.051   0.9598    
홀드          106.5326   283.0186   0.376   0.7072    
블론          843.4665   734.3349   1.149   0.2527    
경기          -69.6278    86.5803  -0.804   0.4227    
삼진.9       -270.1732   342.5480  -0.789   0.4316    
볼넷.9        431.0859   452.3679   0.953   0.3423    
홈런.9        983.4449  1119.0004   0.879   0.3810    
BABIP       -8863.3423 14648.1787  -0.605   0.5461    
LOB.          -57.5239   120.1320  -0.479   0.6328    
ERA           -88.2397   554.2171  -0.159   0.8737    
WAR          7825.6419  1264.4051   6.189 6.57e-09 ***
연봉.2017.      0.8792     0.0440  19.981  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9178 on 137 degrees of freedom
Multiple R-squared:  0.9202,    Adjusted R-squared:  0.912 
F-statistic: 112.8 on 14 and 137 DF,  p-value: < 2.2e-16

승: 5.44563629770577
패: 2.27744620091112
세: 2.41391273581397
홀드: 2.9278580003899
블론: 2.58069224802437
경기: 5.04287223750904
삼진.9: 1.68181308100372
볼넷.9: 2.04813245831198
홈런.9: 2.32207970272157
BABIP: 3.04592151858475
LOB.: 3.47629848428834
ERA: 9.55974332977644
WAR: 5.01053061622992
연봉.2017.: 2.17719632600132

유의미한 변수는 ’WAR’과 ’연봉(2017)’이다.

정규화

normalize

normalize <- function(x) {
  return((x - mean(x)) / sd(x))
}

df_normalized <- as.data.frame(lapply(dt, normalize))

head(df_normalized)

A data.frame: 6 × 20
	승	패	세	홀드	블론	경기	선발	이닝	삼진.9	볼넷.9	홈런.9	BABIP	LOB.	ERA	RA9.WAR	FIP	kFIP	WAR	연봉.2018.	연봉.2017.
	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
1	3.313623	1.2271453	-0.3064519	-0.5857052	-0.5435919	0.05943348	2.452068	2.645175	0.6720988	-0.8689998	-0.44238194	0.01678276	0.4466146	-0.5870557	3.174630	-0.9710297	-1.0581252	4.503142	3.912893	2.7347053
2	2.019505	2.5047212	-0.0985024	-0.5857052	-0.5435919	0.05943348	2.349505	2.547755	0.1345315	-0.9875023	-0.66852133	-0.24168646	-0.1227637	-0.5198553	3.114968	-1.0618879	-1.0732645	4.094734	3.266495	1.3373033
3	4.348918	0.9077513	-0.3064519	-0.5857052	-0.5435919	0.11105570	2.554632	2.706808	0.1097751	-0.8859287	-0.41288550	-0.09559517	0.3085835	-0.6254559	2.973948	-0.8374147	-0.8663606	3.761956	6.821679	5.3298806
4	1.760682	1.2271453	-0.3064519	-0.5857052	-0.5435919	-0.04381097	2.246942	2.350927	0.3502657	-0.9451800	-0.18674611	-0.47768010	0.5587649	-0.6278559	2.740722	-0.6984550	-0.7603854	2.998081	2.620098	3.3335919
5	2.537153	1.2271453	-0.3064519	-0.5857052	-0.5435919	0.05943348	2.452068	2.587518	0.1557512	-0.8774643	-0.29489973	-0.19673529	0.4811224	-0.5390554	2.751570	-0.6129414	-0.6190851	2.809003	2.975617	2.7347053
6	1.243035	2.1853272	-0.3064519	-0.5857052	-0.5435919	-0.14705541	2.041816	2.048726	0.1309948	-1.0340569	-0.08842464	-0.57882022	0.6536613	-0.7214564	2.963100	-0.5808738	-0.6140386	2.476226	2.135301	0.7384167

model4 <- lm(연봉.2018. ~ ., df_normalized)
summary(model4)


Call:
lm(formula = 연봉.2018. ~ ., data = df_normalized)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.50382 -0.07816  0.01372  0.08561  1.54402 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -5.061e-16  2.411e-02   0.000   1.0000    
승           1.254e-01  6.712e-02   1.869   0.0639 .  
패          -1.858e-02  5.569e-02  -0.334   0.7392    
세          -3.282e-03  4.216e-02  -0.078   0.9381    
홀드        -2.652e-03  4.613e-02  -0.057   0.9542    
블론         2.395e-02  4.019e-02   0.596   0.5522    
경기        -1.102e-01  9.116e-02  -1.209   0.2289    
선발        -2.117e-01  1.455e-01  -1.456   0.1479    
이닝         1.207e-01  1.879e-01   0.642   0.5217    
삼진.9      -4.207e-02  2.146e-01  -0.196   0.8449    
볼넷.9       9.115e-02  1.723e-01   0.529   0.5976    
홈런.9       1.602e-01  4.643e-01   0.345   0.7306    
BABIP       -2.875e-02  4.273e-02  -0.673   0.5022    
LOB.        -1.630e-02  4.866e-02  -0.335   0.7382    
ERA         -9.982e-03  7.667e-02  -0.130   0.8966    
RA9.WAR     -4.519e-02  8.862e-02  -0.510   0.6109    
FIP         -3.892e-01  2.707e+00  -0.144   0.8859    
kFIP         2.437e-01  2.301e+00   0.106   0.9158    
WAR          3.657e-01  7.647e-02   4.783 4.55e-06 ***
연봉.2017.   7.087e-01  3.598e-02  19.698  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2973 on 132 degrees of freedom
Multiple R-squared:  0.9228,    Adjusted R-squared:  0.9116 
F-statistic: 82.99 on 19 and 132 DF,  p-value: < 2.2e-16

threshold <- 10

high_vif_vars <- get_high_vif_variables(model4, threshold)
print(high_vif_vars)

 [1] "경기"    "선발"    "이닝"    "삼진.9"  "볼넷.9"  "홈런.9"  "ERA"    
 [8] "RA9.WAR" "FIP"     "kFIP"

vif(model4)

승: 7.6993466963604
패: 5.30032799820294
세: 3.03718565967898
홀드: 3.63605161357941
블론: 2.75956034802382
경기: 14.2011271199764
선발: 36.160187873294
이닝: 60.3244538179135
삼진.9: 78.7161704890434
볼넷.9: 50.7257985014939
홈런.9: 368.399308167005
BABIP: 3.11936893312485
LOB.: 4.04602533224442
ERA: 10.044173823258
RA9.WAR: 13.4198973514472
FIP: 12525.2424058262
kFIP: 9046.04880481494
WAR: 9.99177856815799
연봉.2017.: 2.2118694256429

###

변수선택

model3(AIC)

- AIC(Step)

m0 = lm(연봉.2018. ~ 1, data = dt)

model3 = step(
 m0,
 scope = 연봉.2018. ~연봉.2017.+승+패+세+홀드+블론+경기+선발+이닝+삼진.9+볼넷.9+홈런.9+BABIP+LOB.+ERA+RA9.WAR+FIP+kFIP+WAR,
 direction = "both")

Start:  AIC=3144.3
연봉.2018. ~ 1

             Df  Sum of Sq        RSS    AIC
+ 연봉.2017.  1 1.2511e+11 1.9445e+10 2841.4
+ WAR         1 9.0535e+10 5.4022e+10 2996.7
+ RA9.WAR     1 7.9230e+10 6.5326e+10 3025.6
+ 승          1 7.3377e+10 7.1179e+10 3038.6
+ 이닝        1 6.2759e+10 8.1797e+10 3059.8
+ 선발        1 4.5409e+10 9.9147e+10 3089.0
+ 패          1 3.1910e+10 1.1265e+11 3108.4
+ 볼넷.9      1 1.5661e+10 1.2890e+11 3128.9
+ kFIP        1 1.2591e+10 1.3197e+11 3132.4
+ FIP         1 1.1403e+10 1.3315e+11 3133.8
+ ERA         1 6.7332e+09 1.3782e+11 3139.1
+ 세          1 6.4461e+09 1.3811e+11 3139.4
+ 경기        1 6.3714e+09 1.3819e+11 3139.4
+ LOB.        1 2.2831e+09 1.4227e+11 3143.9
+ 홈런.9      1 1.9575e+09 1.4260e+11 3144.2
<none>                     1.4456e+11 3144.3
+ 삼진.9      1 1.5567e+09 1.4300e+11 3144.7
+ BABIP       1 1.5139e+09 1.4304e+11 3144.7
+ 블론        1 1.3815e+09 1.4318e+11 3144.8
+ 홀드        1 4.3499e+07 1.4451e+11 3146.3

Step:  AIC=2841.38
연봉.2018. ~ 연봉.2017.

             Df  Sum of Sq        RSS    AIC
+ WAR         1 7.0421e+09 1.2403e+10 2775.0
+ RA9.WAR     1 4.9589e+09 1.4486e+10 2798.6
+ 승          1 3.8414e+09 1.5604e+10 2809.9
+ 이닝        1 2.8118e+09 1.6633e+10 2819.6
+ 선발        1 2.1318e+09 1.7313e+10 2825.7
+ 패          1 8.8114e+08 1.8564e+10 2836.3
<none>                     1.9445e+10 2841.4
+ 블론        1 2.2022e+08 1.9225e+10 2841.7
+ 세          1 1.7105e+08 1.9274e+10 2842.0
+ kFIP        1 1.6254e+08 1.9283e+10 2842.1
+ FIP         1 1.5483e+08 1.9290e+10 2842.2
+ ERA         1 1.0735e+08 1.9338e+10 2842.5
+ LOB.        1 7.7049e+07 1.9368e+10 2842.8
+ 홈런.9      1 7.3957e+07 1.9371e+10 2842.8
+ 볼넷.9      1 6.4565e+07 1.9381e+10 2842.9
+ BABIP       1 5.6938e+07 1.9388e+10 2842.9
+ 홀드        1 3.8024e+07 1.9407e+10 2843.1
+ 삼진.9      1 5.5081e+06 1.9440e+10 2843.3
+ 경기        1 1.2651e+04 1.9445e+10 2843.4
- 연봉.2017.  1 1.2511e+11 1.4456e+11 3144.3

Step:  AIC=2775.03
연봉.2018. ~ 연봉.2017. + WAR

             Df  Sum of Sq        RSS    AIC
+ 패          1 2.1336e+08 1.2190e+10 2774.4
+ kFIP        1 1.8769e+08 1.2215e+10 2774.7
+ 선발        1 1.7153e+08 1.2232e+10 2774.9
+ FIP         1 1.6877e+08 1.2234e+10 2774.9
+ 볼넷.9      1 1.6419e+08 1.2239e+10 2775.0
<none>                     1.2403e+10 2775.0
+ 이닝        1 1.4704e+08 1.2256e+10 2775.2
+ 홈런.9      1 5.1612e+07 1.2351e+10 2776.4
+ 삼진.9      1 4.8349e+07 1.2355e+10 2776.4
+ 승          1 3.0076e+07 1.2373e+10 2776.7
+ 경기        1 2.7246e+07 1.2376e+10 2776.7
+ BABIP       1 2.4182e+07 1.2379e+10 2776.7
+ ERA         1 1.7077e+07 1.2386e+10 2776.8
+ 블론        1 1.1153e+07 1.2392e+10 2776.9
+ RA9.WAR     1 6.6509e+06 1.2396e+10 2776.9
+ 세          1 4.3325e+06 1.2399e+10 2777.0
+ 홀드        1 3.4824e+06 1.2400e+10 2777.0
+ LOB.        1 6.6018e+05 1.2402e+10 2777.0
- WAR         1 7.0421e+09 1.9445e+10 2841.4
- 연봉.2017.  1 4.1619e+10 5.4022e+10 2996.7

Step:  AIC=2774.4
연봉.2018. ~ 연봉.2017. + WAR + 패

             Df  Sum of Sq        RSS    AIC
+ kFIP        1 1.9738e+08 1.1992e+10 2773.9
+ 승          1 1.8072e+08 1.2009e+10 2774.1
+ FIP         1 1.7496e+08 1.2015e+10 2774.2
<none>                     1.2190e+10 2774.4
- 패          1 2.1336e+08 1.2403e+10 2775.0
+ 볼넷.9      1 1.0330e+08 1.2086e+10 2775.1
+ 홈런.9      1 7.1015e+07 1.2119e+10 2775.5
+ 삼진.9      1 6.6895e+07 1.2123e+10 2775.6
+ 블론        1 4.2173e+07 1.2148e+10 2775.9
+ BABIP       1 4.1954e+07 1.2148e+10 2775.9
+ 선발        1 3.1474e+07 1.2158e+10 2776.0
+ ERA         1 1.3441e+07 1.2176e+10 2776.2
+ 이닝        1 5.8966e+06 1.2184e+10 2776.3
+ 세          1 3.4705e+06 1.2186e+10 2776.3
+ RA9.WAR     1 2.4143e+06 1.2187e+10 2776.4
+ LOB.        1 1.7129e+06 1.2188e+10 2776.4
+ 경기        1 1.1252e+06 1.2189e+10 2776.4
+ 홀드        1 1.8992e+05 1.2190e+10 2776.4
- WAR         1 6.3743e+09 1.8564e+10 2836.3
- 연봉.2017.  1 4.1680e+10 5.3870e+10 2998.3

Step:  AIC=2773.92
연봉.2018. ~ 연봉.2017. + WAR + 패 + kFIP

             Df  Sum of Sq        RSS    AIC
+ 승          1 1.6741e+08 1.1825e+10 2773.8
<none>                     1.1992e+10 2773.9
+ 블론        1 1.2836e+08 1.1864e+10 2774.3
- kFIP        1 1.9738e+08 1.2190e+10 2774.4
+ 선발        1 1.1764e+08 1.1875e+10 2774.4
- 패          1 2.2305e+08 1.2215e+10 2774.7
+ BABIP       1 7.5190e+07 1.1917e+10 2775.0
+ ERA         1 2.1818e+07 1.1971e+10 2775.6
+ 홀드        1 2.1404e+07 1.1971e+10 2775.6
+ 삼진.9      1 1.9275e+07 1.1973e+10 2775.7
+ 경기        1 1.7028e+07 1.1975e+10 2775.7
+ 이닝        1 1.3041e+07 1.1979e+10 2775.8
+ FIP         1 9.3610e+06 1.1983e+10 2775.8
+ 볼넷.9      1 8.8432e+06 1.1983e+10 2775.8
+ 홈런.9      1 8.7223e+06 1.1984e+10 2775.8
+ LOB.        1 4.0316e+06 1.1988e+10 2775.9
+ RA9.WAR     1 2.0131e+06 1.1990e+10 2775.9
+ 세          1 1.4454e+06 1.1991e+10 2775.9
- WAR         1 6.4941e+09 1.8486e+10 2837.7
- 연봉.2017.  1 4.1735e+10 5.3727e+10 2999.9

Step:  AIC=2773.78
연봉.2018. ~ 연봉.2017. + WAR + 패 + kFIP + 승

             Df  Sum of Sq        RSS    AIC
+ 이닝        1 2.1565e+08 1.1609e+10 2773.0
+ 선발        1 1.9668e+08 1.1628e+10 2773.2
<none>                     1.1825e+10 2773.8
- 승          1 1.6741e+08 1.1992e+10 2773.9
- kFIP        1 1.8408e+08 1.2009e+10 2774.1
+ 블론        1 8.3012e+07 1.1742e+10 2774.7
+ RA9.WAR     1 6.3182e+07 1.1762e+10 2775.0
+ BABIP       1 4.5875e+07 1.1779e+10 2775.2
+ 볼넷.9      1 1.7921e+07 1.1807e+10 2775.6
+ 삼진.9      1 1.4564e+07 1.1810e+10 2775.6
+ 홈런.9      1 1.2160e+07 1.1813e+10 2775.6
+ ERA         1 8.8026e+06 1.1816e+10 2775.7
+ FIP         1 8.1221e+06 1.1817e+10 2775.7
+ 세          1 5.8214e+06 1.1819e+10 2775.7
+ 홀드        1 5.2671e+06 1.1820e+10 2775.7
+ LOB.        1 3.9758e+05 1.1825e+10 2775.8
+ 경기        1 3.3176e+05 1.1825e+10 2775.8
- 패          1 3.6648e+08 1.2191e+10 2776.4
- WAR         1 3.6353e+09 1.5460e+10 2812.5
- 연봉.2017.  1 3.9188e+10 5.1013e+10 2994.0

Step:  AIC=2772.98
연봉.2018. ~ 연봉.2017. + WAR + 패 + kFIP + 승 + 이닝

             Df  Sum of Sq        RSS    AIC
- 패          1 3.1923e+07 1.1641e+10 2771.4
<none>                     1.1609e+10 2773.0
- kFIP        1 2.1496e+08 1.1824e+10 2773.8
- 이닝        1 2.1565e+08 1.1825e+10 2773.8
+ BABIP       1 8.7592e+07 1.1522e+10 2773.8
+ 선발        1 5.0414e+07 1.1559e+10 2774.3
+ 블론        1 3.9472e+07 1.1570e+10 2774.5
+ 삼진.9      1 3.3863e+07 1.1575e+10 2774.5
+ ERA         1 3.3525e+07 1.1576e+10 2774.5
+ FIP         1 1.8310e+07 1.1591e+10 2774.7
+ 홈런.9      1 1.2031e+07 1.1597e+10 2774.8
+ RA9.WAR     1 1.0398e+07 1.1599e+10 2774.8
+ LOB.        1 3.1362e+06 1.1606e+10 2774.9
+ 경기        1 1.9500e+06 1.1607e+10 2775.0
+ 볼넷.9      1 1.2880e+06 1.1608e+10 2775.0
+ 세          1 2.2726e+05 1.1609e+10 2775.0
+ 홀드        1 9.3003e+04 1.1609e+10 2775.0
- 승          1 3.7002e+08 1.1979e+10 2775.8
- WAR         1 3.7546e+09 1.5364e+10 2813.6
- 연봉.2017.  1 3.8723e+10 5.0333e+10 2993.9

Step:  AIC=2771.4
연봉.2018. ~ 연봉.2017. + WAR + kFIP + 승 + 이닝

             Df  Sum of Sq        RSS    AIC
<none>                     1.1641e+10 2771.4
+ BABIP       1 9.5915e+07 1.1545e+10 2772.1
- kFIP        1 2.2291e+08 1.1864e+10 2772.3
+ 선발        1 6.0820e+07 1.1580e+10 2772.6
+ ERA         1 4.1760e+07 1.1599e+10 2772.8
+ 삼진.9      1 3.6788e+07 1.1604e+10 2772.9
+ 패          1 3.1923e+07 1.1609e+10 2773.0
+ 블론        1 2.3680e+07 1.1618e+10 2773.1
+ FIP         1 2.0239e+07 1.1621e+10 2773.1
+ 홈런.9      1 1.4166e+07 1.1627e+10 2773.2
+ LOB.        1 7.7349e+06 1.1633e+10 2773.3
+ 경기        1 1.5351e+06 1.1640e+10 2773.4
+ RA9.WAR     1 1.4350e+06 1.1640e+10 2773.4
+ 볼넷.9      1 1.4095e+06 1.1640e+10 2773.4
+ 홀드        1 2.5525e+05 1.1641e+10 2773.4
+ 세          1 6.8181e+04 1.1641e+10 2773.4
- 승          1 4.0011e+08 1.2041e+10 2774.5
- 이닝        1 5.5021e+08 1.2191e+10 2776.4
- WAR         1 3.9604e+09 1.5602e+10 2813.9
- 연봉.2017.  1 3.8795e+10 5.0436e+10 2992.2

summary

summary(model3)


Call:
lm(formula = 연봉.2018. ~ 연봉.2017. + WAR + kFIP + 승 + 
    이닝, data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-48717  -2879    204   3083  48961 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -2.691e+03  2.658e+03  -1.012  0.31310    
연봉.2017.   8.862e-01  4.018e-02  22.058  < 2e-16 ***
WAR          8.118e+03  1.152e+03   7.048 6.68e-11 ***
kFIP         6.737e+02  4.029e+02   1.672  0.09666 .  
승           1.059e+03  4.727e+02   2.240  0.02659 *  
이닝        -9.701e+01  3.693e+01  -2.627  0.00954 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8929 on 146 degrees of freedom
Multiple R-squared:  0.9195,    Adjusted R-squared:  0.9167 
F-statistic: 333.4 on 5 and 146 DF,  p-value: < 2.2e-16

AIC를 이용하면 최종 모형은 “연봉.2018. ~ 연봉.2017. + WAR + kFIP+승+이닝” 이다.

vif(model3)

연봉.2017.: 1.91752518192932
WAR: 4.3927072113068
kFIP: 1.20722030237251
승: 6.3165168650018
이닝: 6.53436057823665

연봉.2018. ~ 연봉.2017. + WAR + kFIP + 승 + 이닝

후진

model_back = step(model1, direction = "backward")
summary(model_back)

Start:  AIC=2793.07
연봉.2018. ~ 승 + 패 + 세 + 홀드 + 블론 + 경기 + 선발 + 
    이닝 + 삼진.9 + 볼넷.9 + 홈런.9 + BABIP + LOB. + 
    ERA + RA9.WAR + FIP + kFIP + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- 홀드        1 2.7964e+05 1.1167e+10 2791.1
- 세          1 5.1274e+05 1.1167e+10 2791.1
- kFIP        1 9.4914e+05 1.1168e+10 2791.1
- ERA         1 1.4342e+06 1.1168e+10 2791.1
- FIP         1 1.7480e+06 1.1168e+10 2791.1
- 삼진.9      1 3.2496e+06 1.1170e+10 2791.1
- 패          1 9.4169e+06 1.1176e+10 2791.2
- LOB.        1 9.4883e+06 1.1176e+10 2791.2
- 홈런.9      1 1.0071e+07 1.1177e+10 2791.2
- RA9.WAR     1 2.1998e+07 1.1189e+10 2791.4
- 볼넷.9      1 2.3679e+07 1.1190e+10 2791.4
- 블론        1 3.0047e+07 1.1197e+10 2791.5
- 이닝        1 3.4909e+07 1.1201e+10 2791.6
- BABIP       1 3.8305e+07 1.1205e+10 2791.6
- 경기        1 1.2360e+08 1.1290e+10 2792.7
<none>                     1.1167e+10 2793.1
- 선발        1 1.7922e+08 1.1346e+10 2793.5
- 승          1 2.9538e+08 1.1462e+10 2795.0
- WAR         1 1.9353e+09 1.3102e+10 2815.4
- 연봉.2017.  1 3.2824e+10 4.3991e+10 2999.5

Step:  AIC=2791.07
연봉.2018. ~ 승 + 패 + 세 + 블론 + 경기 + 선발 + 이닝 + 
    삼진.9 + 볼넷.9 + 홈런.9 + BABIP + LOB. + ERA + RA9.WAR + 
    FIP + kFIP + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- 세          1 2.6213e+05 1.1167e+10 2789.1
- kFIP        1 9.3814e+05 1.1168e+10 2789.1
- ERA         1 1.5378e+06 1.1168e+10 2789.1
- FIP         1 1.7362e+06 1.1169e+10 2789.1
- 삼진.9      1 3.2908e+06 1.1170e+10 2789.1
- LOB.        1 9.8104e+06 1.1177e+10 2789.2
- 홈런.9      1 1.0084e+07 1.1177e+10 2789.2
- 패          1 1.1289e+07 1.1178e+10 2789.2
- 볼넷.9      1 2.3701e+07 1.1191e+10 2789.4
- RA9.WAR     1 2.3959e+07 1.1191e+10 2789.4
- 블론        1 2.9856e+07 1.1197e+10 2789.5
- BABIP       1 3.8334e+07 1.1205e+10 2789.6
- 이닝        1 3.9219e+07 1.1206e+10 2789.6
<none>                     1.1167e+10 2791.1
- 선발        1 1.7952e+08 1.1346e+10 2791.5
- 경기        1 1.8031e+08 1.1347e+10 2791.5
- 승          1 2.9677e+08 1.1464e+10 2793.1
- WAR         1 1.9405e+09 1.3107e+10 2813.4
- 연봉.2017.  1 3.2987e+10 4.4154e+10 2998.0

Step:  AIC=2789.08
연봉.2018. ~ 승 + 패 + 블론 + 경기 + 선발 + 이닝 + 
    삼진.9 + 볼넷.9 + 홈런.9 + BABIP + LOB. + ERA + RA9.WAR + 
    FIP + kFIP + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- kFIP        1 9.9324e+05 1.1168e+10 2787.1
- ERA         1 1.6052e+06 1.1169e+10 2787.1
- FIP         1 1.8109e+06 1.1169e+10 2787.1
- 삼진.9      1 3.2005e+06 1.1170e+10 2787.1
- LOB.        1 9.9171e+06 1.1177e+10 2787.2
- 홈런.9      1 1.0260e+07 1.1177e+10 2787.2
- 패          1 1.1827e+07 1.1179e+10 2787.2
- 볼넷.9      1 2.3993e+07 1.1191e+10 2787.4
- RA9.WAR     1 2.8604e+07 1.1196e+10 2787.5
- 블론        1 3.3423e+07 1.1201e+10 2787.5
- BABIP       1 3.8245e+07 1.1205e+10 2787.6
- 이닝        1 4.1983e+07 1.1209e+10 2787.7
<none>                     1.1167e+10 2789.1
- 선발        1 1.8297e+08 1.1350e+10 2789.6
- 경기        1 1.9004e+08 1.1357e+10 2789.6
- 승          1 3.2363e+08 1.1491e+10 2791.4
- WAR         1 1.9440e+09 1.3111e+10 2811.5
- 연봉.2017.  1 3.4986e+10 4.6153e+10 3002.8

Step:  AIC=2787.09
연봉.2018. ~ 승 + 패 + 블론 + 경기 + 선발 + 이닝 + 
    삼진.9 + 볼넷.9 + 홈런.9 + BABIP + LOB. + ERA + RA9.WAR + 
    FIP + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- ERA         1 1.8214e+06 1.1170e+10 2785.1
- LOB.        1 1.0407e+07 1.1179e+10 2785.2
- 패          1 1.1087e+07 1.1179e+10 2785.2
- FIP         1 2.8081e+07 1.1196e+10 2785.5
- RA9.WAR     1 2.8212e+07 1.1196e+10 2785.5
- 블론        1 3.3436e+07 1.1202e+10 2785.6
- BABIP       1 3.7443e+07 1.1206e+10 2785.6
- 이닝        1 4.1025e+07 1.1209e+10 2785.7
- 홈런.9      1 5.5367e+07 1.1223e+10 2785.8
- 삼진.9      1 6.7478e+07 1.1236e+10 2786.0
- 볼넷.9      1 7.1385e+07 1.1239e+10 2786.1
<none>                     1.1168e+10 2787.1
- 선발        1 1.8242e+08 1.1351e+10 2787.6
- 경기        1 1.8950e+08 1.1358e+10 2787.7
- 승          1 3.2639e+08 1.1494e+10 2789.5
- WAR         1 1.9444e+09 1.3112e+10 2809.5
- 연봉.2017.  1 3.5014e+10 4.6182e+10 3000.9

Step:  AIC=2785.12
연봉.2018. ~ 승 + 패 + 블론 + 경기 + 선발 + 이닝 + 
    삼진.9 + 볼넷.9 + 홈런.9 + BABIP + LOB. + RA9.WAR + 
    FIP + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- LOB.        1 1.0813e+07 1.1181e+10 2783.3
- 패          1 1.1584e+07 1.1181e+10 2783.3
- FIP         1 2.9304e+07 1.1199e+10 2783.5
- 블론        1 3.2749e+07 1.1203e+10 2783.6
- RA9.WAR     1 3.2883e+07 1.1203e+10 2783.6
- 이닝        1 4.0932e+07 1.1211e+10 2783.7
- 홈런.9      1 5.3929e+07 1.1224e+10 2783.8
- BABIP       1 6.8000e+07 1.1238e+10 2784.0
- 삼진.9      1 6.9211e+07 1.1239e+10 2784.1
- 볼넷.9      1 6.9566e+07 1.1239e+10 2784.1
<none>                     1.1170e+10 2785.1
- 선발        1 1.8070e+08 1.1351e+10 2785.6
- 경기        1 1.8826e+08 1.1358e+10 2785.7
- 승          1 3.2533e+08 1.1495e+10 2787.5
- WAR         1 1.9871e+09 1.3157e+10 2808.0
- 연봉.2017.  1 3.5061e+10 4.6231e+10 2999.0

Step:  AIC=2783.26
연봉.2018. ~ 승 + 패 + 블론 + 경기 + 선발 + 이닝 + 
    삼진.9 + 볼넷.9 + 홈런.9 + BABIP + RA9.WAR + FIP + 
    WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- 패          1 1.0204e+07 1.1191e+10 2781.4
- FIP         1 2.3196e+07 1.1204e+10 2781.6
- 블론        1 3.0781e+07 1.1212e+10 2781.7
- 이닝        1 4.3368e+07 1.1224e+10 2781.8
- 홈런.9      1 4.6793e+07 1.1228e+10 2781.9
- RA9.WAR     1 5.5284e+07 1.1236e+10 2782.0
- BABIP       1 5.7524e+07 1.1238e+10 2782.0
- 볼넷.9      1 6.1767e+07 1.1242e+10 2782.1
- 삼진.9      1 6.4118e+07 1.1245e+10 2782.1
<none>                     1.1181e+10 2783.3
- 선발        1 1.8271e+08 1.1363e+10 2783.7
- 경기        1 1.8379e+08 1.1365e+10 2783.7
- 승          1 3.3073e+08 1.1511e+10 2785.7
- WAR         1 2.1202e+09 1.3301e+10 2807.7
- 연봉.2017.  1 3.5097e+10 4.6278e+10 2997.2

Step:  AIC=2781.4
연봉.2018. ~ 승 + 블론 + 경기 + 선발 + 이닝 + 삼진.9 + 
    볼넷.9 + 홈런.9 + BABIP + RA9.WAR + FIP + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- FIP         1 2.2440e+07 1.1213e+10 2779.7
- 블론        1 2.3243e+07 1.1214e+10 2779.7
- 이닝        1 4.1401e+07 1.1232e+10 2780.0
- 홈런.9      1 4.5529e+07 1.1236e+10 2780.0
- RA9.WAR     1 4.6219e+07 1.1237e+10 2780.0
- BABIP       1 5.8410e+07 1.1249e+10 2780.2
- 볼넷.9      1 6.1274e+07 1.1252e+10 2780.2
- 삼진.9      1 6.2728e+07 1.1254e+10 2780.2
<none>                     1.1191e+10 2781.4
- 경기        1 2.1328e+08 1.1404e+10 2782.3
- 선발        1 2.3948e+08 1.1430e+10 2782.6
- 승          1 3.4606e+08 1.1537e+10 2784.0
- WAR         1 2.1342e+09 1.3325e+10 2805.9
- 연봉.2017.  1 3.5334e+10 4.6525e+10 2996.0

Step:  AIC=2779.71
연봉.2018. ~ 승 + 블론 + 경기 + 선발 + 이닝 + 삼진.9 + 
    볼넷.9 + 홈런.9 + BABIP + RA9.WAR + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- 블론        1 2.8280e+07 1.1242e+10 2778.1
- 이닝        1 4.0706e+07 1.1254e+10 2778.3
- RA9.WAR     1 4.3431e+07 1.1257e+10 2778.3
- BABIP       1 6.5327e+07 1.1279e+10 2778.6
- 삼진.9      1 6.9757e+07 1.1283e+10 2778.7
- 볼넷.9      1 8.4569e+07 1.1298e+10 2778.8
- 홈런.9      1 1.0518e+08 1.1319e+10 2779.1
<none>                     1.1213e+10 2779.7
- 경기        1 2.0863e+08 1.1422e+10 2780.5
- 선발        1 2.4225e+08 1.1456e+10 2781.0
- 승          1 3.4542e+08 1.1559e+10 2782.3
- WAR         1 2.1544e+09 1.3368e+10 2804.4
- 연봉.2017.  1 3.5313e+10 4.6526e+10 2994.0

Step:  AIC=2778.09
연봉.2018. ~ 승 + 경기 + 선발 + 이닝 + 삼진.9 + 볼넷.9 + 
    홈런.9 + BABIP + RA9.WAR + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- 이닝        1 3.5553e+07 1.1277e+10 2776.6
- RA9.WAR     1 4.1773e+07 1.1283e+10 2776.7
- 삼진.9      1 6.2788e+07 1.1304e+10 2776.9
- BABIP       1 6.6047e+07 1.1308e+10 2777.0
- 볼넷.9      1 8.6190e+07 1.1328e+10 2777.2
- 홈런.9      1 9.9781e+07 1.1341e+10 2777.4
<none>                     1.1242e+10 2778.1
- 경기        1 1.8104e+08 1.1423e+10 2778.5
- 선발        1 2.4212e+08 1.1484e+10 2779.3
- 승          1 3.7616e+08 1.1618e+10 2781.1
- WAR         1 2.1262e+09 1.3368e+10 2802.4
- 연봉.2017.  1 3.7489e+10 4.8731e+10 2999.0

Step:  AIC=2776.57
연봉.2018. ~ 승 + 경기 + 선발 + 삼진.9 + 볼넷.9 + 
    홈런.9 + BABIP + RA9.WAR + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- RA9.WAR     1 2.7446e+07 1.1305e+10 2774.9
- BABIP       1 6.5912e+07 1.1343e+10 2775.5
- 삼진.9      1 7.3754e+07 1.1351e+10 2775.6
- 볼넷.9      1 7.9195e+07 1.1356e+10 2775.6
- 홈런.9      1 1.1893e+08 1.1396e+10 2776.2
<none>                     1.1277e+10 2776.6
- 경기        1 2.5407e+08 1.1531e+10 2778.0
- 승          1 4.4284e+08 1.1720e+10 2780.4
- 선발        1 7.1295e+08 1.1990e+10 2783.9
- WAR         1 2.3107e+09 1.3588e+10 2802.9
- 연봉.2017.  1 3.7540e+10 4.8818e+10 2997.3

Step:  AIC=2774.94
연봉.2018. ~ 승 + 경기 + 선발 + 삼진.9 + 볼넷.9 + 
    홈런.9 + BABIP + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- BABIP       1 5.1810e+07 1.1356e+10 2773.6
- 삼진.9      1 7.6555e+07 1.1381e+10 2774.0
- 볼넷.9      1 7.6805e+07 1.1381e+10 2774.0
- 홈런.9      1 1.1502e+08 1.1420e+10 2774.5
<none>                     1.1305e+10 2774.9
- 경기        1 2.6687e+08 1.1572e+10 2776.5
- 승          1 4.1542e+08 1.1720e+10 2778.4
- 선발        1 7.2929e+08 1.2034e+10 2782.4
- WAR         1 3.6036e+09 1.4908e+10 2815.0
- 연봉.2017.  1 3.7533e+10 4.8837e+10 2995.4

Step:  AIC=2773.63
연봉.2018. ~ 승 + 경기 + 선발 + 삼진.9 + 볼넷.9 + 
    홈런.9 + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- 볼넷.9      1 7.2317e+07 1.1429e+10 2772.6
- 홈런.9      1 8.5360e+07 1.1442e+10 2772.8
<none>                     1.1356e+10 2773.6
- 삼진.9      1 1.8112e+08 1.1538e+10 2774.0
- 경기        1 2.2627e+08 1.1583e+10 2774.6
- 승          1 4.2114e+08 1.1778e+10 2777.2
- 선발        1 7.1482e+08 1.2071e+10 2780.9
- WAR         1 3.5773e+09 1.4934e+10 2813.3
- 연봉.2017.  1 3.7607e+10 4.8964e+10 2993.8

Step:  AIC=2772.6
연봉.2018. ~ 승 + 경기 + 선발 + 삼진.9 + 홈런.9 + 
    WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- 홈런.9      1 1.2421e+08 1.1553e+10 2772.2
- 삼진.9      1 1.4867e+08 1.1577e+10 2772.6
<none>                     1.1429e+10 2772.6
- 경기        1 3.5597e+08 1.1785e+10 2775.3
- 승          1 4.5207e+08 1.1881e+10 2776.5
- 선발        1 7.9752e+08 1.2226e+10 2780.8
- WAR         1 3.5112e+09 1.4940e+10 2811.3
- 연봉.2017.  1 3.7614e+10 4.9042e+10 2992.0

Step:  AIC=2772.24
연봉.2018. ~ 승 + 경기 + 선발 + 삼진.9 + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
- 삼진.9      1 8.2804e+07 1.1636e+10 2771.3
<none>                     1.1553e+10 2772.2
- 경기        1 4.0633e+08 1.1959e+10 2775.5
- 승          1 4.9123e+08 1.2044e+10 2776.6
- 선발        1 7.3028e+08 1.2283e+10 2779.6
- WAR         1 3.4409e+09 1.4994e+10 2809.9
- 연봉.2017.  1 3.8020e+10 4.9573e+10 2991.6

Step:  AIC=2771.33
연봉.2018. ~ 승 + 경기 + 선발 + WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
<none>                     1.1636e+10 2771.3
- 경기        1 4.4893e+08 1.2085e+10 2775.1
- 승          1 5.0693e+08 1.2143e+10 2775.8
- 선발        1 6.7070e+08 1.2306e+10 2777.8
- WAR         1 3.3777e+09 1.5014e+10 2808.1
- 연봉.2017.  1 3.8082e+10 4.9718e+10 2990.1


Call:
lm(formula = 연봉.2018. ~ 승 + 경기 + 선발 + WAR + 연봉.2017., 
    data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-48420  -1976    -56   2829  48859 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1969.51173 1500.85489   1.312   0.1915    
승          1174.23883  465.58916   2.522   0.0127 *  
경기        -120.60886   50.81729  -2.373   0.0189 *  
선발        -440.87646  151.97589  -2.901   0.0043 ** 
WAR         7220.36610 1109.09601   6.510 1.13e-09 ***
연봉.2017.     0.88247    0.04037  21.860  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8927 on 146 degrees of freedom
Multiple R-squared:  0.9195,    Adjusted R-squared:  0.9168 
F-statistic: 333.6 on 5 and 146 DF,  p-value: < 2.2e-16

vif(model_back)

승: 6.13100501411465
경기: 1.83604531782849
선발: 4.16007029774887
WAR: 4.07445827346373
연봉.2017.: 1.93705640010866

연봉.2018. ~ 승 + 경기 + 선발 + WAR + 연봉.2017.

전진

m0 = lm(연봉.2018. ~ 1, data = dt)

model_forward = step(
 m0,
 scope = 연봉.2018. ~연봉.2017.+승+패+세+홀드+블론+경기+선발+이닝+삼진.9+볼넷.9+홈런.9+BABIP+LOB.+ERA+RA9.WAR+FIP+kFIP+WAR,
 direction = "forward")
summary(model_forward)

Start:  AIC=3144.3
연봉.2018. ~ 1

             Df  Sum of Sq        RSS    AIC
+ 연봉.2017.  1 1.2511e+11 1.9445e+10 2841.4
+ WAR         1 9.0535e+10 5.4022e+10 2996.7
+ RA9.WAR     1 7.9230e+10 6.5326e+10 3025.6
+ 승          1 7.3377e+10 7.1179e+10 3038.6
+ 이닝        1 6.2759e+10 8.1797e+10 3059.8
+ 선발        1 4.5409e+10 9.9147e+10 3089.0
+ 패          1 3.1910e+10 1.1265e+11 3108.4
+ 볼넷.9      1 1.5661e+10 1.2890e+11 3128.9
+ kFIP        1 1.2591e+10 1.3197e+11 3132.4
+ FIP         1 1.1403e+10 1.3315e+11 3133.8
+ ERA         1 6.7332e+09 1.3782e+11 3139.1
+ 세          1 6.4461e+09 1.3811e+11 3139.4
+ 경기        1 6.3714e+09 1.3819e+11 3139.4
+ LOB.        1 2.2831e+09 1.4227e+11 3143.9
+ 홈런.9      1 1.9575e+09 1.4260e+11 3144.2
<none>                     1.4456e+11 3144.3
+ 삼진.9      1 1.5567e+09 1.4300e+11 3144.7
+ BABIP       1 1.5139e+09 1.4304e+11 3144.7
+ 블론        1 1.3815e+09 1.4318e+11 3144.8
+ 홀드        1 4.3499e+07 1.4451e+11 3146.3

Step:  AIC=2841.38
연봉.2018. ~ 연봉.2017.

          Df  Sum of Sq        RSS    AIC
+ WAR      1 7042094427 1.2403e+10 2775.0
+ RA9.WAR  1 4958914952 1.4486e+10 2798.6
+ 승       1 3841387936 1.5604e+10 2809.9
+ 이닝     1 2811807174 1.6633e+10 2819.6
+ 선발     1 2131826098 1.7313e+10 2825.7
+ 패       1  881138122 1.8564e+10 2836.3
<none>                  1.9445e+10 2841.4
+ 블론     1  220224080 1.9225e+10 2841.7
+ 세       1  171052899 1.9274e+10 2842.0
+ kFIP     1  162536872 1.9283e+10 2842.1
+ FIP      1  154825743 1.9290e+10 2842.2
+ ERA      1  107350094 1.9338e+10 2842.5
+ LOB.     1   77049296 1.9368e+10 2842.8
+ 홈런.9   1   73957140 1.9371e+10 2842.8
+ 볼넷.9   1   64564811 1.9381e+10 2842.9
+ BABIP    1   56938420 1.9388e+10 2842.9
+ 홀드     1   38023685 1.9407e+10 2843.1
+ 삼진.9   1    5508109 1.9440e+10 2843.3
+ 경기     1      12651 1.9445e+10 2843.4

Step:  AIC=2775.03
연봉.2018. ~ 연봉.2017. + WAR

          Df Sum of Sq        RSS    AIC
+ 패       1 213356827 1.2190e+10 2774.4
+ kFIP     1 187694356 1.2215e+10 2774.7
+ 선발     1 171531569 1.2232e+10 2774.9
+ FIP      1 168772833 1.2234e+10 2774.9
+ 볼넷.9   1 164189202 1.2239e+10 2775.0
<none>                 1.2403e+10 2775.0
+ 이닝     1 147039192 1.2256e+10 2775.2
+ 홈런.9   1  51612430 1.2351e+10 2776.4
+ 삼진.9   1  48348966 1.2355e+10 2776.4
+ 승       1  30075743 1.2373e+10 2776.7
+ 경기     1  27245510 1.2376e+10 2776.7
+ BABIP    1  24181791 1.2379e+10 2776.7
+ ERA      1  17077047 1.2386e+10 2776.8
+ 블론     1  11153112 1.2392e+10 2776.9
+ RA9.WAR  1   6650871 1.2396e+10 2776.9
+ 세       1   4332494 1.2399e+10 2777.0
+ 홀드     1   3482363 1.2400e+10 2777.0
+ LOB.     1    660176 1.2402e+10 2777.0

Step:  AIC=2774.4
연봉.2018. ~ 연봉.2017. + WAR + 패

          Df Sum of Sq        RSS    AIC
+ kFIP     1 197383620 1.1992e+10 2773.9
+ 승       1 180715640 1.2009e+10 2774.1
+ FIP      1 174958135 1.2015e+10 2774.2
<none>                 1.2190e+10 2774.4
+ 볼넷.9   1 103300993 1.2086e+10 2775.1
+ 홈런.9   1  71014626 1.2119e+10 2775.5
+ 삼진.9   1  66895356 1.2123e+10 2775.6
+ 블론     1  42172679 1.2148e+10 2775.9
+ BABIP    1  41953578 1.2148e+10 2775.9
+ 선발     1  31473684 1.2158e+10 2776.0
+ ERA      1  13441234 1.2176e+10 2776.2
+ 이닝     1   5896647 1.2184e+10 2776.3
+ 세       1   3470456 1.2186e+10 2776.3
+ RA9.WAR  1   2414340 1.2187e+10 2776.4
+ LOB.     1   1712854 1.2188e+10 2776.4
+ 경기     1   1125166 1.2189e+10 2776.4
+ 홀드     1    189917 1.2190e+10 2776.4

Step:  AIC=2773.92
연봉.2018. ~ 연봉.2017. + WAR + 패 + kFIP

          Df Sum of Sq        RSS    AIC
+ 승       1 167413120 1.1825e+10 2773.8
<none>                 1.1992e+10 2773.9
+ 블론     1 128359041 1.1864e+10 2774.3
+ 선발     1 117641927 1.1875e+10 2774.4
+ BABIP    1  75190355 1.1917e+10 2775.0
+ ERA      1  21818455 1.1971e+10 2775.6
+ 홀드     1  21403854 1.1971e+10 2775.6
+ 삼진.9   1  19275489 1.1973e+10 2775.7
+ 경기     1  17028183 1.1975e+10 2775.7
+ 이닝     1  13040981 1.1979e+10 2775.8
+ FIP      1   9361041 1.1983e+10 2775.8
+ 볼넷.9   1   8843181 1.1983e+10 2775.8
+ 홈런.9   1   8722328 1.1984e+10 2775.8
+ LOB.     1   4031616 1.1988e+10 2775.9
+ RA9.WAR  1   2013063 1.1990e+10 2775.9
+ 세       1   1445393 1.1991e+10 2775.9

Step:  AIC=2773.78
연봉.2018. ~ 연봉.2017. + WAR + 패 + kFIP + 승

          Df Sum of Sq        RSS    AIC
+ 이닝     1 215650124 1.1609e+10 2773.0
+ 선발     1 196677432 1.1628e+10 2773.2
<none>                 1.1825e+10 2773.8
+ 블론     1  83011867 1.1742e+10 2774.7
+ RA9.WAR  1  63182313 1.1762e+10 2775.0
+ BABIP    1  45874866 1.1779e+10 2775.2
+ 볼넷.9   1  17920561 1.1807e+10 2775.6
+ 삼진.9   1  14563944 1.1810e+10 2775.6
+ 홈런.9   1  12160231 1.1813e+10 2775.6
+ ERA      1   8802604 1.1816e+10 2775.7
+ FIP      1   8122100 1.1817e+10 2775.7
+ 세       1   5821352 1.1819e+10 2775.7
+ 홀드     1   5267064 1.1820e+10 2775.7
+ LOB.     1    397579 1.1825e+10 2775.8
+ 경기     1    331762 1.1825e+10 2775.8

Step:  AIC=2772.98
연봉.2018. ~ 연봉.2017. + WAR + 패 + kFIP + 승 + 이닝

          Df Sum of Sq        RSS    AIC
<none>                 1.1609e+10 2773.0
+ BABIP    1  87591503 1.1522e+10 2773.8
+ 선발     1  50413708 1.1559e+10 2774.3
+ 블론     1  39472232 1.1570e+10 2774.5
+ 삼진.9   1  33863019 1.1575e+10 2774.5
+ ERA      1  33524887 1.1576e+10 2774.5
+ FIP      1  18310110 1.1591e+10 2774.7
+ 홈런.9   1  12031455 1.1597e+10 2774.8
+ RA9.WAR  1  10397930 1.1599e+10 2774.8
+ LOB.     1   3136209 1.1606e+10 2774.9
+ 경기     1   1950014 1.1607e+10 2775.0
+ 볼넷.9   1   1288038 1.1608e+10 2775.0
+ 세       1    227255 1.1609e+10 2775.0
+ 홀드     1     93003 1.1609e+10 2775.0


Call:
lm(formula = 연봉.2018. ~ 연봉.2017. + WAR + 패 + kFIP + 
    승 + 이닝, data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-48378  -2526    133   2563  48361 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -2.653e+03  2.664e+03  -0.996   0.3209    
연봉.2017.   8.856e-01  4.027e-02  21.992  < 2e-16 ***
WAR          8.003e+03  1.169e+03   6.848 1.97e-10 ***
패          -2.708e+02  4.288e+02  -0.631   0.5287    
kFIP         6.622e+02  4.042e+02   1.639   0.1035    
승           1.025e+03  4.767e+02   2.150   0.0332 *  
이닝        -7.811e+01  4.760e+01  -1.641   0.1029    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8948 on 145 degrees of freedom
Multiple R-squared:  0.9197,    Adjusted R-squared:  0.9164 
F-statistic: 276.8 on 6 and 145 DF,  p-value: < 2.2e-16

vif(model_forward)

연봉.2017.: 1.9185269678088
WAR: 4.50275401281816
패: 3.39937428417761
kFIP: 1.20965408072733
승: 6.3982769107728
이닝: 10.8086888355271

연봉.2018. ~ 연봉.2017. + WAR + 패 + kFIP + 승 + 이닝

PCA(주성분분석)

서로 상관성이 높은 변수들의 선형 결합으로 만들어 기존의 상관성이 높은 변수들을 요약, 축소하는 기법

dt2 <- dt[,1:19] # 설명변수

dt3 <- dt[,20] # 종속변수

procomp.result2 <- prcomp(dt2, center=T, scale=T)
summary(procomp.result2)

Importance of components:
                          PC1    PC2    PC3     PC4     PC5     PC6     PC7
Standard deviation     2.6109 1.8528 1.5587 1.27735 1.07673 0.94635 0.77437
Proportion of Variance 0.3588 0.1807 0.1279 0.08588 0.06102 0.04714 0.03156
Cumulative Proportion  0.3588 0.5395 0.6673 0.75322 0.81424 0.86137 0.89293
                           PC8     PC9    PC10    PC11    PC12    PC13    PC14
Standard deviation     0.75305 0.60013 0.57118 0.51280 0.43707 0.31874 0.28648
Proportion of Variance 0.02985 0.01896 0.01717 0.01384 0.01005 0.00535 0.00432
Cumulative Proportion  0.92278 0.94173 0.95890 0.97274 0.98280 0.98815 0.99247
                          PC15    PC16   PC17    PC18     PC19
Standard deviation     0.27007 0.21161 0.1236 0.10061 0.006742
Proportion of Variance 0.00384 0.00236 0.0008 0.00053 0.000000
Cumulative Proportion  0.99630 0.99866 0.9995 1.00000 1.000000

dt.pca <- princomp(dt2, cor=TRUE)

summary(dt.pca)

Importance of components:
                          Comp.1    Comp.2    Comp.3    Comp.4     Comp.5
Standard deviation     2.6109027 1.8528422 1.5587351 1.2773530 1.07672785
Proportion of Variance 0.3587796 0.1806855 0.1278766 0.0858753 0.06101805
Cumulative Proportion  0.3587796 0.5394651 0.6673417 0.7532170 0.81423504
                           Comp.6     Comp.7     Comp.8     Comp.9    Comp.10
Standard deviation     0.94635475 0.77436931 0.75305028 0.60012648 0.57117946
Proportion of Variance 0.04713617 0.03156041 0.02984656 0.01895536 0.01717084
Cumulative Proportion  0.86137122 0.89293163 0.92277819 0.94173355 0.95890439
                          Comp.11   Comp.12    Comp.13     Comp.14     Comp.15
Standard deviation     0.51280325 0.4370697 0.31874103 0.286476368 0.270069813
Proportion of Variance 0.01384038 0.0100542 0.00534715 0.004319406 0.003838827
Cumulative Proportion  0.97274477 0.9827990 0.98814612 0.992465529 0.996304355
                           Comp.16      Comp.17      Comp.18      Comp.19
Standard deviation     0.211606675 0.1235839263 0.1006053051 6.741848e-03
Proportion of Variance 0.002356704 0.0008038414 0.0005327067 2.392237e-06
Cumulative Proportion  0.998661060 0.9994649011 0.9999976078 1.000000e+00

제 1주성분과 제6주성분까지의 누적 분산비율은 대략 85.71%로 6개의 주성분 변수를 활용해 전체 데이터의 85.71%를 설명할 수 있다.

screeplot(dt.pca, npcs=8, type="lines")

주성분들에 의해 설명되는 변동 비율

loadings(dt.pca)


Loadings:
           Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
승          0.322  0.201                              0.105              
패          0.272  0.198         0.108  0.236 -0.108        -0.477 -0.294
세                -0.202  0.289  0.126 -0.512 -0.426        -0.192  0.360
홀드              -0.253  0.336  0.141  0.417  0.343  0.154  0.296       
블론              -0.274  0.396  0.204        -0.208  0.116 -0.183 -0.354
경기        0.191 -0.220  0.372  0.222  0.227                       0.236
선발        0.261  0.350 -0.123                             -0.250 -0.105
이닝        0.329  0.235                0.109               -0.134       
삼진.9                    0.393 -0.404 -0.229  0.455 -0.171 -0.204 -0.211
볼넷.9     -0.250  0.116               -0.236  0.289  0.752 -0.178       
홈런.9     -0.173  0.286  0.276  0.268         0.154 -0.535              
BABIP      -0.142  0.207  0.292 -0.444                              0.146
LOB.        0.131 -0.209 -0.230  0.228 -0.416  0.495 -0.174              
ERA        -0.235  0.294  0.288 -0.156        -0.133  0.106         0.107
RA9.WAR     0.327  0.176               -0.181  0.124         0.119  0.391
FIP        -0.259  0.284         0.378                                   
kFIP       -0.257  0.268         0.423                                   
WAR         0.318  0.213               -0.126         0.113  0.165  0.235
연봉.2017.  0.252  0.130  0.103        -0.296 -0.181         0.629 -0.535
           Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16 Comp.17
승                  0.383   0.237   0.542   0.550   0.102                 
패                 -0.478  -0.137           0.321  -0.270  -0.229         
세         -0.134  -0.328           0.242           0.206   0.105         
홀드        0.128  -0.339  -0.335   0.264  -0.113   0.240                 
블론        0.363   0.513  -0.251  -0.150  -0.121                         
경기       -0.183           0.560  -0.322          -0.240                 
선발                                0.154  -0.463   0.328   0.249         
이닝                        0.213          -0.370           0.151         
삼진.9     -0.380                                                   0.376 
볼넷.9     -0.105           0.128                                  -0.359 
홈런.9                                                             -0.614 
BABIP       0.665  -0.171   0.296  -0.149           0.187                 
LOB.        0.414  -0.155           0.112          -0.328   0.216         
ERA                        -0.141   0.336  -0.206  -0.663   0.296         
RA9.WAR             0.123  -0.243          -0.247  -0.163  -0.683         
FIP                                                                 0.323 
kFIP                                                                0.492 
WAR                        -0.398  -0.499   0.305           0.473         
연봉.2017.         -0.229   0.174                                         
           Comp.18 Comp.19
승                        
패                        
세                        
홀드                      
블론                      
경기        0.318         
선발        0.553         
이닝       -0.758         
삼진.9                    
볼넷.9                    
홈런.9             -0.125 
BABIP                     
LOB.                      
ERA                       
RA9.WAR                   
FIP                 0.754 
kFIP               -0.641 
WAR                       
연봉.2017.                

               Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
SS loadings     1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000
Proportion Var  0.053  0.053  0.053  0.053  0.053  0.053  0.053  0.053  0.053
Cumulative Var  0.053  0.105  0.158  0.211  0.263  0.316  0.368  0.421  0.474
               Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16 Comp.17
SS loadings      1.000   1.000   1.000   1.000   1.000   1.000   1.000   1.000
Proportion Var   0.053   0.053   0.053   0.053   0.053   0.053   0.053   0.053
Cumulative Var   0.526   0.579   0.632   0.684   0.737   0.789   0.842   0.895
               Comp.18 Comp.19
SS loadings      1.000   1.000
Proportion Var   0.053   0.053
Cumulative Var   0.947   1.000

능형회귀

rfit <- lm.ridge(연봉.2018.~., dt, lambda=seq(0.01,20,0.1))

select(rfit)

modified HKB estimator is 1.552458 
modified L-W estimator is 1.638756 
smallest value of GCV  at 4.11

round(rfit$coef[,rfit$lam=='4.11'],3)

승: 3659.317
패: -737.614
세: -93.401
홀드: -155.777
블론: 859.526
경기: -1932.839
선발: -3234.453
이닝: 441.579
삼진.9: -934.786
볼넷.9: 1047.402
홈런.9: 1328.778
BABIP: -755.31
LOB.: -578.691
ERA: -288.368
RA9.WAR: 516.127
FIP: -176.744
kFIP: -420.71
WAR: 9904.312
연봉.2017.: 21113.076

matplot(rfit$lambda, t(rfit$coef), type='l',
        xlab=expression(lambda),
        ylab=expression(bold(beta)(lambda)), lwd=2) 
abline(h=0, col="grey", lty=2)
abline(v=14.91, col="black", lty=2)

glm


X <- model.matrix(연봉.2018.~., dt)[,-1] 
y <- dt$연봉.2018.

head(X)

A matrix: 6 × 19 of type dbl
	승	패	세	경기	선발	이닝	삼진.9	볼넷.9	홈런.9	BABIP	LOB.	ERA	RA9.WAR	FIP	kFIP	WAR	연봉.2017.
1	16	7	0	30	30	190.0	8.95	2.13	0.76	0.342	73.7	3.60	6.91	3.69	3.44	6.62	85000
2	11	11	1	30	29	185.1	7.43	1.85	0.53	0.319	67.1	3.88	6.80	3.52	3.41	6.08	50000
3	20	6	0	31	31	193.1	7.36	2.09	0.79	0.332	72.1	3.44	6.54	3.94	3.82	5.64	150000
4	10	7	0	28	28	175.2	8.04	1.95	1.02	0.298	75.0	3.43	6.11	4.20	4.03	4.63	100000
5	13	7	0	30	30	187.1	7.49	2.11	0.91	0.323	74.1	3.80	6.13	4.36	4.31	4.38	85000
6	8	10	0	26	26	160.0	7.42	1.74	1.12	0.289	76.1	3.04	6.52	4.42	4.32	3.94	35000

ridge.fit<-glmnet(X,y,alpha=0, lambda=seq(0,100,10)) ##ridge : alpha=0 
plot(ridge.fit, label=TRUE)
abline(h=0, col="grey", lty=2)

summary(ridge.fit)

          Length Class     Mode   
a0         11    -none-    numeric
beta      209    dgCMatrix S4     
df         11    -none-    numeric
dim         2    -none-    numeric
lambda     11    -none-    numeric
dev.ratio  11    -none-    numeric
nulldev     1    -none-    numeric
npasses     1    -none-    numeric
jerr        1    -none-    numeric
offset      1    -none-    logical
call        5    -none-    call   
nobs        1    -none-    numeric

cv.fit<-cv.glmnet(X,y,alpha=0,nfolds=length(y))

Warning message:
“Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold”

cv.fit


Call:  cv.glmnet(x = X, y = y, nfolds = length(y), alpha = 0) 

Measure: Mean-Squared Error 

    Lambda Index   Measure       SE Nonzero
min   2869   100 117171048 49876335      19
1se  12711    84 166795504 78214517      19

plot(cv.fit)

예측

WAR이라는 변수가 다른 설명변수의 곱으로 이루어진 변수니까, 인터넷에서 나오는 WAR계산법에 들어가는 변수들을 제거해보자.(근데 인터넷에 말이 다 다름 ㅎㅎ)

ERA, 이닝수, FIP는 일단 빼야함.

FIP자체가 홈런, 삼진, 볼넷 등의 값인데..

step, 전진: 연봉.2017.이랑 kFIP, 볼넷.9, 삼진.9를ㄴ넣어보자.

연봉.2018. ~ 연봉.2017. + WAR + kFIP + 승 + 이닝

후진: 연봉.2018. ~ 연봉.2017. + WAR + 패 + kFIP + 승 + 이닝

연봉.2018. ~ 연봉.2017. + WAR + 패 + kFIP + 승 + 이닝

model3 <- lm(연봉.2018. ~ 연봉.2017.+kFIP+볼넷.9+삼진.9, dt)
summary(model3)


Call:
lm(formula = 연봉.2018. ~ 연봉.2017. + kFIP + 볼넷.9 + 
    삼진.9, data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-65987  -2665    -72   1406  61788 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) 3604.44247 4650.08368   0.775    0.440    
연봉.2017.     1.13680    0.03994  28.461   <2e-16 ***
kFIP        -552.00216  675.96374  -0.817    0.415    
볼넷.9       -19.23606  556.28780  -0.035    0.972    
삼진.9       -42.36062  381.57885  -0.111    0.912    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 11450 on 147 degrees of freedom
Multiple R-squared:  0.8666,    Adjusted R-squared:  0.863 
F-statistic: 238.8 on 4 and 147 DF,  p-value: < 2.2e-16

X <- data.frame(FIP = dt$"FIP",
                        WAR = dt$"WAR",
                        `볼넷/9` = dt$"볼넷.9",
                        `삼진/9` = dt$"삼진.9",
                        `연봉.2017.` = dt$"연봉.2017.")

y <- dt$"연봉.2018."

set.seed(19)
train_indices <- createDataPartition(y, p = 0.8, list = FALSE)
X_train <- X[train_indices, ]
X_test <- X[-train_indices, ]
y_train <- y[train_indices]
y_test <- y[-train_indices]

model <- lm(y_train ~ ., data = cbind(X_train, y_train))

summary(model)


Call:
lm(formula = y_train ~ ., data = cbind(X_train, y_train))

Residuals:
   Min     1Q Median     3Q    Max 
-49900  -1887    574   2975  49836 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.261e+03  4.037e+03  -0.312    0.755    
FIP          1.395e+02  6.349e+02   0.220    0.826    
WAR          8.148e+03  9.161e+02   8.894 8.65e-15 ***
볼넷.9       5.772e+02  5.144e+02   1.122    0.264    
삼진.9      -4.929e+02  3.528e+02  -1.397    0.165    
연봉.2017.   9.156e-01  4.691e-02  19.518  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9667 on 117 degrees of freedom
Multiple R-squared:  0.9104,    Adjusted R-squared:  0.9065 
F-statistic: 237.7 on 5 and 117 DF,  p-value: < 2.2e-16

ㅎ므

X <- data.frame(FIP = picher$"FIP",
                        WAR = picher$"WAR",
                        `볼넷/9` = picher$"볼넷.9",
                        `삼진/9` = picher$"삼진.9",
                        `연봉.2017.` = picher$"연봉.2017.")

predict_2018_salary <- predict(model, newdata = X)

picher <- cbind(picher, new_col = predict_2018_salary)

head(picher)

A data.frame: 6 × 24
	선수명	팀명	승	패	세	홀드	블론	경기	선발	이닝	⋯	LOB.	ERA	RA9.WAR	FIP	kFIP	WAR	연봉.2018.	연봉.2017.	new_col	new_col.1
	<chr>	<chr>	<int>	<int>	<int>	<int>	<int>	<int>	<int>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<int>	<dbl>	<dbl>
1	켈리	SK	16	7	0	0	0	30	30	190.0	⋯	73.7	3.60	6.91	3.69	3.44	6.62	140000	85000	63003.59	127838.00
2	소사	LG	11	11	1	0	0	30	29	185.1	⋯	67.1	3.88	6.80	3.52	3.41	6.08	120000	50000	37061.64	91955.34
3	양현종	KIA	20	6	0	0	0	31	31	193.1	⋯	72.1	3.44	6.54	3.94	3.82	5.64	230000	150000	111180.99	180164.16
4	차우찬	LG	10	7	0	0	0	28	28	175.2	⋯	75.0	3.43	6.11	4.20	4.03	4.63	100000	100000	74120.86	125774.08
5	레일리	롯데	13	7	0	0	0	30	30	187.1	⋯	74.1	3.80	6.13	4.36	4.31	4.38	111000	85000	63002.89	110388.58
6	피어밴드	KT	8	10	0	0	0	26	26	160.0	⋯	76.1	3.04	6.52	4.42	4.32	3.94	85000	35000	25942.97	60851.77

predictsalart <- round(predict_2018_salary,0)

result1 <- picher$"선수명"
result2 <- picher$"연봉.2018."
result3 <- predictsalart
result4 <- picher$"연봉.2017."
result <- cbind(result1,result2,result3,result4)

result

A matrix: 152 × 4 of type chr
	result1	result2	result3	result4
1	켈리	140000	127838	85000
2	소사	120000	91955	50000
3	양현종	230000	180164	150000
4	차우찬	100000	125774	100000
5	레일리	111000	110389	85000
6	피어밴드	85000	60852	35000
7	고영표	11500	32249	5200
8	장원준	100000	120661	100000
9	함덕주	16000	34421	7000
10	팻딘	70000	90685	70000
11	윤성환	80000	95139	80000
12	유희관	50000	67371	50000
13	임기영	13000	22933	3100
14	박세웅	25000	27964	10000
15	백정현	15500	24575	10000
16	송승준	40000	51763	40000
17	류제국	29000	47535	35000
18	우규민	70000	78523	70000
19	임찬규	11500	19833	6500
20	손승락	70000	74664	70000
21	정우람	120000	119624	120000
22	윤희상	13000	26255	15000
23	원종현	18500	23403	14000
24	배영수	50000	61694	55000
25	박종훈	20000	20806	10000
26	이상화	10000	13334	4500
27	김진성	23000	24511	18000
28	이민호	18800	22706	16000
29	이재학	19000	25924	20000
30	김강률	15000	13575	6200
⋮	⋮	⋮	⋮	⋮
123	정재원	4000	2960	4000
124	김민우	3600	3555	3800
125	이현호	5200	3447	6000
126	권혁	45000	38632	45000
127	배제성	3000	1539	2700
128	홍상삼	9000	11187	12500
129	이태양	7300	5930	8300
130	김진우	6000	9837	12000
131	이영하	4200	-291	2700
132	최성영	2900	1140	2900
133	김동호	6000	3508	5000
134	김윤동	15000	1585	4700
135	정인욱	5700	3266	7200
136	송창식	24000	16351	22000
137	배재환	3000	3807	4000
138	이정민	10000	11150	15000
139	최동환	6500	1652	6000
140	이종혁	3200	564	2700
141	홍성용	6800	2878	6300
142	정영일	3000	4241	4000
143	김지용	9000	3789	10000
144	최금강	12500	8542	14000
145	김범수	3600	1207	3300
146	이승현	7000	2054	6200
147	주권	7600	2162	7500
148	장민재	7100	2973	8100
149	정용운	7500	-673	3100
150	노경은	10000	9953	16000
151	김승현	4000	-3065	2900
152	류희운	4000	-5132	3000

k-fold

X <- dt[c('FIP', 'WAR', '볼넷.9', '삼진.9', '연봉.2017.')]
y <- dt$"연봉.2018."

ctrl <- trainControl(method = "cv", 
                     number = 10, 
                     verboseIter = TRUE)

print(model)

Linear Regression 

152 samples
  5 predictor

No pre-processing
Resampling: Cross-Validated (10 fold) 
Summary of sample sizes: 136, 139, 137, 136, 137, 136, ... 
Resampling results:

  RMSE      Rsquared   MAE     
  8775.345  0.9234182  5096.303

Tuning parameter 'intercept' was held constant at a value of TRUE

createDataPartition


set.seed(20) 
train_indices <- createDataPartition(y, p = 0.8, list = FALSE)  # 80%를 훈련 세트로 사용
X_train <- X[train_indices, ]  # X 훈련 세트
y_train <- y[train_indices]  # y 훈련 세트
X_test <- X[-train_indices, ]  # X 테스트 세트
y_test <- y[-train_indices]  # y 테스트 세트

model <- lm(y_train ~ ., data = cbind(X_train, y_train))

summary(model)


Call:
lm(formula = y_train ~ ., data = cbind(X_train, y_train))

Residuals:
   Min     1Q Median     3Q    Max 
-51628  -1742    835   2679  54478 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -3.132e+03  3.752e+03  -0.835    0.406    
FIP          3.656e+02  6.383e+02   0.573    0.568    
WAR          6.521e+03  9.510e+02   6.857 3.53e-10 ***
볼넷.9       4.095e+02  4.922e+02   0.832    0.407    
삼진.9      -2.664e+02  3.220e+02  -0.827    0.410    
연봉.2017.   9.436e-01  4.885e-02  19.314  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9407 on 117 degrees of freedom
Multiple R-squared:  0.9084,    Adjusted R-squared:  0.9045 
F-statistic: 232.1 on 5 and 117 DF,  p-value: < 2.2e-16

y_pred <- predict(model, newdata = X_test)

y_pred

2: 83760.5036635398
11: 92856.5551719829
16: 49834.1350433709
20: 74394.6037441324
21: 121111.857311619
23: 21354.3954407502
30: 11877.9200631754
31: 13693.1214770523
36: 10957.9331638088
39: 7904.67772835263
41: 22618.8632801464
47: 3977.22428640269
51: 4759.88345127168
58: 5598.23942115724
62: 2384.85845607467
64: 3520.11810139773
67: 3352.59845508957
68: 22782.5629218232
73: 2753.45775461199
77: 8019.61080626648
80: 5122.41200499673
83: -3354.1873156885
90: -1479.51353608508
98: 2904.84077333906
118: 5349.37841885841
121: 3656.12420217399
132: 2282.13105827633
141: 3578.68637161238
142: 4774.13856910488

plot(model)

## Shapiro-Wilk Test
## H0 : normal distribution vs. H1 : not H0
shapiro.test(resid(model))


    Shapiro-Wilk normality test

data:  resid(model)
W = 0.69671, p-value = 1.316e-14

귀무가설 기각

library(lmtest)

### 등분산성
## H0 : 등분산 vs. H1 : 이분산 (Heteroscedasticity)
bptest(model)


    studentized Breusch-Pagan test

data:  model
BP = 48.48, df = 5, p-value = 2.834e-09

잔차 이분산..

bptest(model)


    studentized Breusch-Pagan test

data:  model
BP = 48.48, df = 5, p-value = 2.834e-09

기각..

rmse <- sqrt(mean((y_pred - y_test)^2))
rmse

8169.95343721918

r_squared <- 1 - sum((y_test - y_pred)^2) / sum((y_test - mean(y_test))^2)
r_squared

0.937905268099376

y_pred <- predict(model, newdata = X)
y_pred

1: 120079.644407696
2: 83760.5036635398
3: 175521.573203863
4: 121612.06220557
5: 106098.40123629
6: 55938.3360303223
7: 26731.8079691304
8: 117272.89045312
9: 28840.8622273183
10: 87223.7553189251
11: 92856.5551719829
12: 64095.7326866766
13: 18557.1211875583
14: 24286.457756089
15: 21705.8561903346
16: 49834.1350433709
17: 45256.3857125534
18: 77519.7451159889
19: 17218.5428165066
20: 74394.6037441324
21: 121111.857311619
22: 24012.4794639814
23: 21354.3954407502
24: 60809.3599020221
25: 18627.1334642915
26: 11284.3959821959
27: 23499.0012034168
28: 21500.0921981219
29: 25216.0463766418
30: 11877.9200631754
31: 13693.1214770523
32: 9721.37978877243
33: 10832.9902724258
34: 22447.697009164
35: 7824.80860177616
36: 10957.9331638088
37: 50497.4525617583
38: 23384.8597822882
39: 7904.67772835263
40: 24703.2223966378
41: 22618.8632801464
42: 13201.8856253739
43: 12816.7508124466
44: 26147.3170424822
45: 58131.6087102705
46: 7523.01225446262
47: 3977.22428640269
48: 4591.4093894283
49: 39003.2211855645
50: 71627.7765552946
51: 4759.88345127168
52: 47644.4841594123
53: 10530.7891568554
54: 5199.11439751501
55: 9368.46795181711
56: 31579.4491180105
57: 4231.50693696113
58: 5598.23942115724
59: 5136.52005559622
60: 9102.06897972658
61: 6984.12598013427
62: 2384.85845607467
63: 18303.363177317
64: 3520.11810139773
65: 3322.44698945243
66: 1989.42705473082
67: 3352.59845508957
68: 22782.5629218232
69: 10769.628209866
70: 3902.99550968491
71: 19176.2096780485
72: 5598.20242176528
73: 2753.45775461199
74: 10039.0367084241
75: 7357.93890125183
76: 5058.81091390124
77: 8019.61080626648
78: 7277.46775096933
79: 2999.80648325582
80: 5122.41200499673
81: 2190.6374430789
82: 9310.17406653524
83: -3354.1873156885
84: -324.080566112093
85: 3952.58752085951
86: 3631.83930171537
87: 129.350963084188
88: 2855.73595792648
89: 3556.52749004506
90: -1479.51353608508
91: 9288.2135748458
92: 2179.48869530268
93: 2274.22153090663
94: 2563.46139539266
95: 4225.95510985668
96: 779.354766372629
97: -2275.06753560988
98: 2904.84077333906
99: 1276.18575681504
100: 1278.77949800168
101: 1106.52488833093
102: 1872.11890217375
103: 2491.20505069081
104: 5496.81554757196
105: 7100.93204974382
106: 2029.42471093689
107: 6086.50404299722
108: 6770.85899230805
109: 229.654419792656
110: 3410.59366971035
111: 18753.9298630808
112: 2464.93783388577
113: 9614.92030264136
114: 1084.00882682257
115: 8543.2323809515
116: 2825.44788089157
117: 3470.9785470481
118: 5349.37841885841
119: 1957.02838737825
120: 1942.46056909266
121: 3656.12420217399
122: 42166.0786594782
123: 2646.91201627154
124: 3912.29633727664
125: 4053.21273794936
126: 40416.3088155261
127: 1718.55530132255
128: 11344.8355840123
129: 6449.57632010468
130: 10343.4503716666
131: 566.080172487302
132: 2282.13105827633
133: 3362.37196892649
134: 2213.60459015082
135: 4651.09395657194
136: 17836.449861336
137: 4905.41919551359
138: 11939.7833450429
139: 2934.46752999489
140: 1059.70613969482
141: 3578.68637161238
142: 4774.13856910488
143: 5340.39499497243
144: 9744.24047688514
145: 1838.44630518678
146: 3450.35582952913
147: 3280.22844632236
148: 3919.93354796755
149: -53.2035118929793
150: 11626.3868566865
151: -1610.41555450545
152: -3236.44776099906

picher <- cbind(picher, new_data= y_pred)

sorted_picher <- picher[order(-picher$"연봉.2018."), ]
sorted_picher

A data.frame: 152 × 25
	선수명	팀명	승	패	세	홀드	블론	경기	선발	이닝	⋯	ERA	RA9.WAR	FIP	kFIP	WAR	연봉.2018.	연봉.2017.	new_col	new_col.1	new_data
	<chr>	<chr>	<int>	<int>	<int>	<int>	<int>	<int>	<int>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<int>	<dbl>	<dbl>	<dbl>
3	양현종	KIA	20	6	0	0	0	31	31	193.1	⋯	3.44	6.54	3.94	3.82	5.64	230000	150000	111180.99	180164.16	175521.57
1	켈리	SK	16	7	0	0	0	30	30	190.0	⋯	3.60	6.91	3.69	3.44	6.62	140000	85000	63003.59	127838.00	120079.64
2	소사	LG	11	11	1	0	0	30	29	185.1	⋯	3.88	6.80	3.52	3.41	6.08	120000	50000	37061.64	91955.34	83760.50
21	정우람	한화	6	4	26	0	5	56	0	59.0	⋯	2.75	2.85	3.26	2.69	1.81	120000	120000	88943.64	119624.39	121111.86
5	레일리	롯데	13	7	0	0	0	30	30	187.1	⋯	3.80	6.13	4.36	4.31	4.38	111000	85000	63002.89	110388.58	106098.40
4	차우찬	LG	10	7	0	0	0	28	28	175.2	⋯	3.43	6.11	4.20	4.03	4.63	100000	100000	74120.86	125774.08	121612.06
8	장원준	두산	14	9	0	0	0	29	29	180.1	⋯	3.14	7.28	4.26	4.35	3.85	100000	100000	74120.70	120660.77	117272.89
6	피어밴드	KT	8	10	0	0	0	26	26	160.0	⋯	3.04	6.52	4.42	4.32	3.94	85000	35000	25942.97	60851.77	55938.34
11	윤성환	삼성	12	9	0	0	0	28	28	174.1	⋯	4.28	5.36	4.78	4.80	3.03	80000	80000	59296.47	95138.61	92856.56
10	팻딘	KIA	9	7	0	0	0	30	29	176.0	⋯	4.14	5.66	4.65	4.61	3.64	70000	70000	51884.71	90684.81	87223.76
18	우규민	삼성	7	10	0	0	0	27	25	133.0	⋯	5.21	1.48	4.95	4.98	2.14	70000	70000	51884.20	78523.00	77519.75
20	손승락	롯데	1	3	37	0	5	61	0	62.0	⋯	2.18	3.91	3.69	3.37	1.82	70000	70000	51883.97	74663.86	74394.60
45	이동현	LG	3	6	7	5	3	45	0	50.2	⋯	4.80	1.22	3.64	3.59	0.68	60000	60000	44471.73	57336.45	58131.61
12	유희관	두산	11	6	0	1	0	30	29	188.2	⋯	4.53	4.79	4.78	4.97	2.89	50000	50000	37060.65	67371.43	64095.73
24	배영수	한화	7	8	0	0	0	25	25	128.0	⋯	5.06	2.47	5.10	5.21	1.68	50000	55000	40766.17	61693.57	60809.36
37	임창용	KIA	8	6	7	9	5	51	0	50.0	⋯	3.78	1.40	3.69	3.35	0.96	50000	50000	37059.82	49996.69	50497.45
52	윤길현	롯데	1	4	0	13	2	40	0	39.1	⋯	6.41	-0.04	3.99	3.73	0.50	50000	50000	37059.67	46413.16	47644.48
122	송은범	한화	0	4	1	0	1	13	6	37.1	⋯	6.51	0.10	6.33	6.79	-0.12	45000	45000	33353.86	41260.88	42166.08
126	권혁	한화	1	3	0	11	1	37	0	31.1	⋯	6.32	0.04	6.48	6.78	-0.16	45000	45000	33353.67	38632.11	40416.31
16	송승준	롯데	11	5	0	1	1	30	22	130.1	⋯	4.21	4.22	4.91	4.77	2.20	40000	40000	29648.38	51762.94	49834.14
49	이현승	두산	3	2	5	9	7	57	0	52.0	⋯	3.98	1.69	4.25	4.30	0.53	40000	40000	29647.84	38630.86	39003.22
41	안영명	한화	1	8	0	0	1	25	16	87.2	⋯	5.75	0.52	5.19	5.34	0.81	35000	20000	14824.10	23301.25	22618.86
68	채병용	SK	6	4	0	6	3	43	0	50.0	⋯	6.84	-0.17	5.05	4.94	0.22	30000	25000	18529.76	21870.11	22782.56
17	류제국	LG	8	6	0	0	0	25	25	131.1	⋯	5.35	1.53	4.79	4.84	2.15	29000	35000	25942.45	47534.93	45256.39
14	박세웅	롯데	12	6	0	0	0	28	28	171.1	⋯	3.68	5.92	5.07	5.14	2.54	25000	10000	7412.73	27963.63	24286.46
40	임창민	NC	4	3	29	0	6	60	0	66.0	⋯	3.68	2.68	4.83	4.60	0.89	25000	22500	16677.00	24913.36	24703.22
56	박정진	한화	3	2	1	7	0	55	0	48.0	⋯	3.94	0.87	4.92	4.66	0.38	25000	33000	24459.37	30622.42	31579.45
136	송창식	한화	5	6	0	15	6	63	0	73.1	⋯	6.63	-0.74	5.68	5.59	-0.22	24000	22000	16306.09	16351.07	17836.45
27	김진성	NC	10	6	0	15	2	69	0	89.2	⋯	3.61	3.20	4.30	3.92	1.47	23000	18000	13341.73	24511.49	23499.00
38	심창민	삼성	4	7	6	16	2	66	0	75.1	⋯	4.18	1.82	4.82	4.26	0.93	23000	21000	15565.14	23185.40	23384.86
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋱	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
99	박치국	두산	1	1	0	0	0	21	3	32.0	⋯	6.75	-0.12	5.39	5.58	0.00	3400	2700	2001.156	1048.3622	1276.1858
102	허건엽	SK	0	0	0	0	0	8	0	8.1	⋯	8.64	-0.20	5.29	5.64	-0.01	3400	3300	2445.935	2067.0516	1872.1189
105	고봉재	두산	0	0	0	0	0	1	0	1.0	⋯	0.00	0.04	6.73	7.64	-0.01	3300	4400	3261.709	8820.0864	7100.9320
112	김시현	삼성	0	0	0	0	0	17	0	21.1	⋯	7.59	0.08	7.06	7.18	-0.05	3300	2700	2001.245	2115.3516	2464.9378
120	강장산	KT	0	0	0	0	0	17	0	26.1	⋯	5.47	0.54	6.16	6.46	-0.10	3300	3000	2223.583	1795.4384	1942.4606
118	배민관	LG	0	0	0	0	0	4	0	3.2	⋯	9.82	-0.11	9.46	9.77	-0.08	3200	3000	2223.850	5401.6928	5349.3784
140	이종혁	KT	2	0	0	0	0	16	0	19.0	⋯	6.63	-0.09	7.10	7.57	-0.25	3200	2700	2001.196	564.4227	1059.7061
70	최지광	삼성	0	2	0	0	0	11	6	25.0	⋯	6.48	-0.16	5.69	5.65	0.21	3100	2700	2001.325	4206.2468	3902.9955
73	박세진	KT	0	2	0	0	0	4	3	11.1	⋯	9.53	-0.13	4.44	4.67	0.18	3100	3000	2223.610	3189.5874	2753.4578
101	박상원	한화	0	0	0	1	0	18	0	21.2	⋯	4.15	0.32	5.30	5.42	0.00	3100	2700	2001.158	968.7329	1106.5249
81	김대유	SK	0	0	0	0	0	6	0	4.2	⋯	9.64	0.08	5.88	5.91	0.09	3000	2700	2001.218	2139.0137	2190.6374
84	손주영	LG	0	0	0	0	0	5	0	6.0	⋯	4.50	0.06	3.07	3.08	0.08	3000	2700	2001.010	-539.4368	-324.0806
87	김진영	한화	0	0	0	0	0	3	0	2.2	⋯	10.12	-0.02	2.98	2.29	0.07	3000	2700	2000.967	-560.7629	129.3510
98	임진우	두산	0	0	0	0	0	1	0	1.0	⋯	27.00	-0.11	4.73	4.61	0.00	3000	3200	2371.857	3087.5908	2904.8408
109	서균	한화	0	0	0	0	0	14	0	14.1	⋯	4.40	0.25	5.41	5.58	-0.04	3000	2700	2001.060	-370.1056	229.6544
121	홍성무	KT	0	1	0	0	0	7	0	6.1	⋯	12.79	-0.29	7.37	7.58	-0.11	3000	3000	2223.730	3741.6415	3656.1242
127	배제성	KT	0	0	0	0	0	21	1	32.0	⋯	8.72	-0.10	6.39	6.59	-0.17	3000	2700	2001.242	1539.0311	1718.5553
137	배재환	NC	0	1	0	0	0	3	1	8.0	⋯	9.00	-0.16	11.48	11.73	-0.23	3000	4000	2964.893	3807.0275	4905.4192
142	정영일	SK	0	0	0	0	0	9	0	8.0	⋯	10.12	-0.61	10.73	11.37	-0.30	3000	4000	2964.964	4241.1480	4774.1386
96	김도영	KT	0	0	0	0	0	1	0	1.0	⋯	0.00	0.04	3.73	4.43	0.00	2900	2700	2001.259	1731.9157	779.3548
97	조근종	KT	0	0	0	0	0	1	0	2.0	⋯	22.50	-0.16	6.73	4.86	0.00	2900	2700	2000.470	-6343.0220	-2275.0675
108	안규현	삼성	0	0	0	0	0	1	0	2.0	⋯	9.00	-0.04	8.73	9.67	-0.04	2900	2800	2075.799	7768.8014	6770.8590
115	김종훈	KIA	0	0	0	0	0	1	0	1.0	⋯	36.00	-0.16	18.73	17.60	-0.06	2900	2800	2075.467	4943.5065	8543.2324
132	최성영	NC	0	0	0	0	0	7	0	11.1	⋯	9.53	-0.26	9.29	9.48	-0.20	2900	2900	2149.435	1140.0750	2282.1311
83	장지훈	삼성	0	0	0	0	0	4	0	2.1	⋯	0.00	0.09	0.73	-0.69	0.08	2800	2700	2000.563	-5315.1733	-3354.1873
90	차재용	롯데	0	0	0	0	0	3	0	2.1	⋯	0.00	0.08	2.02	1.83	0.05	2800	2800	2075.035	-1808.0465	-1479.5135
106	이수민	삼성	0	0	0	0	0	1	0	2.2	⋯	10.12	-0.15	5.23	5.95	-0.01	2800	3000	2223.624	2419.1537	2029.4247
94	장민익	두산	0	0	0	0	0	3	0	2.0	⋯	0.00	0.08	4.73	4.61	0.02	2700	2700	2001.266	2792.7349	2563.4614
104	성영훈	두산	0	0	0	0	0	1	0	1.0	⋯	0.00	0.04	6.73	7.64	-0.01	2700	2700	2001.678	7263.5285	5496.8155
116	정동윤	SK	0	0	0	0	0	2	0	3.0	⋯	9.00	-0.03	9.40	10.05	-0.07	2700	2700	2001.280	2205.1885	2825.4479

filtered_df <- picher[picher$"연봉.2018." != picher$"연봉.2017.", ]
filtered_df

A data.frame: 128 × 25
	선수명	팀명	승	패	세	홀드	블론	경기	선발	이닝	⋯	ERA	RA9.WAR	FIP	kFIP	WAR	연봉.2018.	연봉.2017.	new_col	new_col.1	new_data
	<chr>	<chr>	<int>	<int>	<int>	<int>	<int>	<int>	<int>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<int>	<dbl>	<dbl>	<dbl>
1	켈리	SK	16	7	0	0	0	30	30	190.0	⋯	3.60	6.91	3.69	3.44	6.62	140000	85000	63003.595	127837.996	120079.644
2	소사	LG	11	11	1	0	0	30	29	185.1	⋯	3.88	6.80	3.52	3.41	6.08	120000	50000	37061.640	91955.341	83760.504
3	양현종	KIA	20	6	0	0	0	31	31	193.1	⋯	3.44	6.54	3.94	3.82	5.64	230000	150000	111180.994	180164.163	175521.573
5	레일리	롯데	13	7	0	0	0	30	30	187.1	⋯	3.80	6.13	4.36	4.31	4.38	111000	85000	63002.886	110388.580	106098.401
6	피어밴드	KT	8	10	0	0	0	26	26	160.0	⋯	3.04	6.52	4.42	4.32	3.94	85000	35000	25942.975	60851.766	55938.336
7	고영표	KT	8	12	0	1	0	25	24	141.2	⋯	5.08	2.97	3.88	3.78	3.87	11500	5200	3855.283	32248.671	26731.808
9	함덕주	두산	9	8	0	2	0	35	24	137.1	⋯	3.67	4.99	3.91	3.67	3.78	16000	7000	5189.489	34420.638	28840.862
13	임기영	KIA	8	6	0	0	0	23	19	118.1	⋯	3.65	4.25	4.07	4.19	2.79	13000	3100	2298.522	22932.876	18557.121
14	박세웅	롯데	12	6	0	0	0	28	28	171.1	⋯	3.68	5.92	5.07	5.14	2.54	25000	10000	7412.730	27963.633	24286.458
15	백정현	삼성	8	4	0	3	0	35	14	100.2	⋯	4.38	3.01	4.51	4.34	2.25	15500	10000	7412.536	24575.219	21705.856
17	류제국	LG	8	6	0	0	0	25	25	131.1	⋯	5.35	1.53	4.79	4.84	2.15	29000	35000	25942.448	47534.929	45256.386
19	임찬규	LG	6	10	0	0	0	27	26	124.1	⋯	4.63	3.15	4.81	4.79	2.04	11500	6500	4818.295	19832.884	17218.543
22	윤희상	SK	6	7	0	0	0	23	22	120.0	⋯	6.00	1.52	5.13	5.22	1.80	13000	15000	11118.427	26255.265	24012.479
23	원종현	NC	3	6	0	22	0	68	0	80.0	⋯	4.39	2.02	3.60	3.52	1.71	18500	14000	10377.101	23403.105	21354.395
24	배영수	한화	7	8	0	0	0	25	25	128.0	⋯	5.06	2.47	5.10	5.21	1.68	50000	55000	40766.167	61693.571	60809.360
25	박종훈	SK	12	7	0	1	0	29	28	151.1	⋯	4.10	4.31	5.38	5.55	1.62	20000	10000	7412.434	20805.675	18627.133
26	이상화	KT	4	3	6	4	1	70	0	66.0	⋯	3.95	2.43	3.57	3.45	1.54	10000	4500	3335.691	13333.548	11284.396
27	김진성	NC	10	6	0	15	2	69	0	89.2	⋯	3.61	3.20	4.30	3.92	1.47	23000	18000	13341.734	24511.486	23499.001
28	이민호	NC	5	1	3	6	1	60	3	88.2	⋯	4.06	1.97	4.41	4.22	1.38	18800	16000	11859.379	22705.669	21500.092
29	이재학	NC	5	7	0	0	0	28	23	119.0	⋯	5.67	1.04	5.53	5.35	1.31	19000	20000	14824.140	25923.735	25216.046
30	김강률	두산	7	2	7	12	1	70	0	89.0	⋯	3.44	2.68	4.15	4.09	1.27	15000	6200	4595.698	13575.161	11877.920
31	김재윤	KT	3	5	15	0	4	41	0	37.1	⋯	5.79	0.73	3.15	3.05	1.24	11000	9000	6670.994	15370.094	13693.121
32	김원중	롯데	7	8	0	0	0	24	24	107.1	⋯	5.70	2.22	5.53	5.56	1.23	6300	3000	2223.940	11393.858	9721.380
33	박진형	롯데	4	4	2	10	3	45	9	88.0	⋯	5.11	1.70	4.43	4.14	1.12	10500	6000	4447.373	11961.674	10832.990
34	윤규진	한화	8	7	0	2	0	36	18	119.0	⋯	5.22	2.23	5.46	5.42	1.09	21000	18000	13341.766	23320.087	22447.697
35	김재영	한화	5	7	0	0	1	20	15	85.1	⋯	4.54	1.60	5.00	5.23	1.06	5300	3000	2223.843	9322.823	7824.809
36	신정락	LG	3	5	10	12	3	63	0	59.0	⋯	5.34	0.51	4.23	4.12	0.97	10500	7500	5559.100	11850.125	10957.933
38	심창민	삼성	4	7	6	16	2	66	0	75.1	⋯	4.18	1.82	4.82	4.26	0.93	23000	21000	15565.136	23185.400	23384.860
39	정찬헌	LG	8	7	7	3	3	61	0	61.2	⋯	5.84	0.97	3.96	3.80	0.93	9500	4500	3335.522	8995.166	7904.678
40	임창민	NC	4	3	29	0	6	60	0	66.0	⋯	3.68	2.68	4.83	4.60	0.89	25000	22500	16676.995	24913.355	24703.222
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋱	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
118	배민관	LG	0	0	0	0	0	4	0	3.2	⋯	9.82	-0.11	9.46	9.77	-0.08	3200	3000	2223.850	5401.6928	5349.37842
119	윤근영	KT	0	0	0	1	0	12	0	18.0	⋯	3.50	0.30	6.23	6.31	-0.08	4200	4000	2964.668	1350.9942	1957.02839
120	강장산	KT	0	0	0	0	0	17	0	26.1	⋯	5.47	0.54	6.16	6.46	-0.10	3300	3000	2223.583	1795.4384	1942.46057
124	김민우	한화	0	0	0	0	0	4	2	7.1	⋯	17.18	-0.52	7.83	8.32	-0.12	3600	3800	2816.614	3554.7700	3912.29634
125	이현호	두산	1	0	0	0	0	24	2	30.0	⋯	5.70	-0.51	6.47	6.57	-0.16	5200	6000	4447.098	3446.5228	4053.21274
127	배제성	KT	0	0	0	0	0	21	1	32.0	⋯	8.72	-0.10	6.39	6.59	-0.17	3000	2700	2001.242	1539.0311	1718.55530
128	홍상삼	두산	1	1	0	0	0	11	2	17.0	⋯	7.94	-0.52	6.73	7.22	-0.18	9000	12500	9265.021	11187.3262	11344.83558
129	이태양	한화	3	6	0	0	0	16	12	59.0	⋯	7.17	0.05	6.77	7.04	-0.18	7300	8300	6151.890	5929.5258	6449.57632
130	김진우	KIA	2	6	0	0	1	14	8	36.1	⋯	7.93	-0.35	6.68	7.04	-0.19	6000	12000	8894.348	9837.3511	10343.45037
131	이영하	두산	3	3	0	0	0	20	3	35.2	⋯	5.55	0.59	6.79	6.86	-0.19	4200	2700	2001.102	-291.0924	566.08017
133	김동호	삼성	0	1	0	0	0	20	1	36.0	⋯	6.75	-0.07	5.46	5.96	-0.20	6000	5000	3706.004	3508.1291	3362.37197
134	김윤동	KIA	7	4	11	6	6	65	1	80.1	⋯	4.59	1.89	5.54	5.53	-0.20	15000	4700	3483.494	1585.1461	2213.60459
135	정인욱	삼성	1	4	0	0	0	9	7	32.0	⋯	9.84	-0.43	7.39	7.36	-0.20	5700	7200	5336.429	3265.9890	4651.09396
136	송창식	한화	5	6	0	15	6	63	0	73.1	⋯	6.63	-0.74	5.68	5.59	-0.22	24000	22000	16306.086	16351.0737	17836.44986
137	배재환	NC	0	1	0	0	0	3	1	8.0	⋯	9.00	-0.16	11.48	11.73	-0.23	3000	4000	2964.893	3807.0275	4905.41920
138	이정민	롯데	3	1	0	2	1	24	0	26.2	⋯	5.40	0.19	6.47	6.83	-0.24	10000	15000	11117.848	11150.4349	11939.78335
139	최동환	LG	1	2	1	5	2	35	0	38.0	⋯	5.68	-0.05	6.76	6.77	-0.24	6500	6000	4446.970	1651.5907	2934.46753
140	이종혁	KT	2	0	0	0	0	16	0	19.0	⋯	6.63	-0.09	7.10	7.57	-0.25	3200	2700	2001.196	564.4227	1059.70614
141	홍성용	KT	0	2	0	1	0	37	1	39.0	⋯	6.23	0.25	6.40	6.63	-0.28	6800	6300	4669.430	2877.7134	3578.68637
142	정영일	SK	0	0	0	0	0	9	0	8.0	⋯	10.12	-0.61	10.73	11.37	-0.30	3000	4000	2964.964	4241.1480	4774.13857
143	김지용	LG	4	3	3	8	4	53	0	53.0	⋯	5.09	0.28	6.30	6.27	-0.38	9000	10000	7411.678	3788.8307	5340.39499
144	최금강	NC	5	3	0	0	0	39	13	89.2	⋯	7.33	-0.27	6.31	6.58	-0.41	12500	14000	10376.560	8542.1622	9744.24048
145	김범수	한화	0	4	0	0	0	15	5	31.0	⋯	8.71	-0.42	8.15	8.52	-0.42	3600	3300	2445.965	1206.6108	1838.44631
146	이승현	삼성	2	0	0	0	0	30	0	31.2	⋯	5.12	0.31	8.03	8.03	-0.44	7000	6200	4595.280	2054.0673	3450.35583
147	주권	KT	5	6	1	3	2	39	12	81.2	⋯	6.61	-0.02	6.33	6.54	-0.46	7600	7500	5558.774	2162.2155	3280.22845
148	장민재	한화	2	5	0	0	2	33	5	62.2	⋯	7.76	-1.21	6.21	6.48	-0.47	7100	8100	6003.520	2972.9523	3919.93355
149	정용운	KIA	3	2	0	0	0	25	11	59.1	⋯	5.92	0.39	6.41	6.77	-0.49	7500	3100	2297.618	-673.0981	-53.20351
150	노경은	롯데	0	2	0	0	0	9	2	14.2	⋯	11.66	-0.83	8.03	8.29	-0.61	10000	16000	11858.971	9953.0416	11626.38686
151	김승현	삼성	0	3	0	1	0	41	0	43.2	⋯	5.77	-0.40	6.87	6.95	-0.70	4000	2900	2149.246	-3065.3516	-1610.41555
152	류희운	KT	4	4	0	0	0	24	14	81.0	⋯	7.67	-0.68	7.60	7.81	-1.01	4000	3000	2223.298	-5132.3247	-3236.44776

df <- filtered_df[,c("선수명","연봉.2018.","new_data","연봉.2017.")]

df

A data.frame: 128 × 4
	선수명	연봉.2018.	new_data	연봉.2017.
	<chr>	<int>	<dbl>	<int>
1	켈리	140000	120079.644	85000
2	소사	120000	83760.504	50000
3	양현종	230000	175521.573	150000
5	레일리	111000	106098.401	85000
6	피어밴드	85000	55938.336	35000
7	고영표	11500	26731.808	5200
9	함덕주	16000	28840.862	7000
13	임기영	13000	18557.121	3100
14	박세웅	25000	24286.458	10000
15	백정현	15500	21705.856	10000
17	류제국	29000	45256.386	35000
19	임찬규	11500	17218.543	6500
22	윤희상	13000	24012.479	15000
23	원종현	18500	21354.395	14000
24	배영수	50000	60809.360	55000
25	박종훈	20000	18627.133	10000
26	이상화	10000	11284.396	4500
27	김진성	23000	23499.001	18000
28	이민호	18800	21500.092	16000
29	이재학	19000	25216.046	20000
30	김강률	15000	11877.920	6200
31	김재윤	11000	13693.121	9000
32	김원중	6300	9721.380	3000
33	박진형	10500	10832.990	6000
34	윤규진	21000	22447.697	18000
35	김재영	5300	7824.809	3000
36	신정락	10500	10957.933	7500
38	심창민	23000	23384.860	21000
39	정찬헌	9500	7904.678	4500
40	임창민	25000	24703.222	22500
⋮	⋮	⋮	⋮	⋮
118	배민관	3200	5349.37842	3000
119	윤근영	4200	1957.02839	4000
120	강장산	3300	1942.46057	3000
124	김민우	3600	3912.29634	3800
125	이현호	5200	4053.21274	6000
127	배제성	3000	1718.55530	2700
128	홍상삼	9000	11344.83558	12500
129	이태양	7300	6449.57632	8300
130	김진우	6000	10343.45037	12000
131	이영하	4200	566.08017	2700
133	김동호	6000	3362.37197	5000
134	김윤동	15000	2213.60459	4700
135	정인욱	5700	4651.09396	7200
136	송창식	24000	17836.44986	22000
137	배재환	3000	4905.41920	4000
138	이정민	10000	11939.78335	15000
139	최동환	6500	2934.46753	6000
140	이종혁	3200	1059.70614	2700
141	홍성용	6800	3578.68637	6300
142	정영일	3000	4774.13857	4000
143	김지용	9000	5340.39499	10000
144	최금강	12500	9744.24048	14000
145	김범수	3600	1838.44631	3300
146	이승현	7000	3450.35583	6200
147	주권	7600	3280.22845	7500
148	장민재	7100	3919.93355	8100
149	정용운	7500	-53.20351	3100
150	노경은	10000	11626.38686	16000
151	김승현	4000	-1610.41555	2900
152	류희운	4000	-3236.44776	3000

sorted_df <- df[order(df$"연봉.2018.", decreasing = TRUE), ]

sorted_df

A data.frame: 128 × 4
	선수명	연봉.2018.	new_data	연봉.2017.
	<chr>	<int>	<dbl>	<int>
3	양현종	230000	175521.573	150000
1	켈리	140000	120079.644	85000
2	소사	120000	83760.504	50000
5	레일리	111000	106098.401	85000
6	피어밴드	85000	55938.336	35000
24	배영수	50000	60809.360	55000
41	안영명	35000	22618.863	20000
68	채병용	30000	22782.563	25000
17	류제국	29000	45256.386	35000
14	박세웅	25000	24286.458	10000
40	임창민	25000	24703.222	22500
56	박정진	25000	31579.449	33000
136	송창식	24000	17836.450	22000
27	김진성	23000	23499.001	18000
38	심창민	23000	23384.860	21000
34	윤규진	21000	22447.697	18000
25	박종훈	20000	18627.133	10000
44	심수창	20000	26147.317	25000
50	장원삼	20000	71627.777	75000
29	이재학	19000	25216.046	20000
43	진해수	19000	12816.751	11000
28	이민호	18800	21500.092	16000
23	원종현	18500	21354.395	14000
111	박희수	18500	18753.930	21000
9	함덕주	16000	28840.862	7000
15	백정현	15500	21705.856	10000
30	김강률	15000	11877.920	6200
60	권오준	15000	9102.069	10500
63	김사율	15000	18303.363	20000
134	김윤동	15000	2213.605	4700
⋮	⋮	⋮	⋮	⋮
79	황수범	3800	2999.8065	2700
124	김민우	3600	3912.2963	3800
145	김범수	3600	1838.4463	3300
92	이형범	3500	2179.4887	2700
93	임현준	3500	2274.2215	3200
110	안성무	3500	3410.5937	2800
99	박치국	3400	1276.1858	2700
102	허건엽	3400	1872.1189	3300
105	고봉재	3300	7100.9320	4400
112	김시현	3300	2464.9378	2700
120	강장산	3300	1942.4606	3000
118	배민관	3200	5349.3784	3000
140	이종혁	3200	1059.7061	2700
70	최지광	3100	3902.9955	2700
73	박세진	3100	2753.4578	3000
101	박상원	3100	1106.5249	2700
81	김대유	3000	2190.6374	2700
84	손주영	3000	-324.0806	2700
87	김진영	3000	129.3510	2700
98	임진우	3000	2904.8408	3200
109	서균	3000	229.6544	2700
127	배제성	3000	1718.5553	2700
137	배재환	3000	4905.4192	4000
142	정영일	3000	4774.1386	4000
96	김도영	2900	779.3548	2700
97	조근종	2900	-2275.0675	2700
108	안규현	2900	6770.8590	2800
115	김종훈	2900	8543.2324	2800
83	장지훈	2800	-3354.1873	2700
106	이수민	2800	2029.4247	3000

이상치 제거

picher2 <- picher[-c(1,2,3,6,21,50,98),]

picher2

A data.frame: 145 × 22
	선수명	팀명	승	패	세	홀드	블론	경기	선발	이닝	⋯	홈런.9	BABIP	LOB.	ERA	RA9.WAR	FIP	kFIP	WAR	연봉.2018.	연봉.2017.
	<chr>	<chr>	<int>	<int>	<int>	<int>	<int>	<int>	<int>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<int>
4	차우찬	LG	10	7	0	0	0	28	28	175.2	⋯	1.02	0.298	75.0	3.43	6.11	4.20	4.03	4.63	100000	100000
5	레일리	롯데	13	7	0	0	0	30	30	187.1	⋯	0.91	0.323	74.1	3.80	6.13	4.36	4.31	4.38	111000	85000
7	고영표	KT	8	12	0	1	0	25	24	141.2	⋯	0.83	0.362	64.6	5.08	2.97	3.88	3.78	3.87	11500	5200
8	장원준	두산	14	9	0	0	0	29	29	180.1	⋯	0.60	0.293	75.8	3.14	7.28	4.26	4.35	3.85	100000	100000
9	함덕주	두산	9	8	0	2	0	35	24	137.1	⋯	0.52	0.321	73.1	3.67	4.99	3.91	3.67	3.78	16000	7000
10	팻딘	KIA	9	7	0	0	0	30	29	176.0	⋯	1.12	0.353	76.5	4.14	5.66	4.65	4.61	3.64	70000	70000
11	윤성환	삼성	12	9	0	0	0	28	28	174.1	⋯	1.14	0.305	72.7	4.28	5.36	4.78	4.80	3.03	80000	80000
12	유희관	두산	11	6	0	1	0	30	29	188.2	⋯	0.95	0.329	69.7	4.53	4.79	4.78	4.97	2.89	50000	50000
13	임기영	KIA	8	6	0	0	0	23	19	118.1	⋯	0.68	0.331	72.3	3.65	4.25	4.07	4.19	2.79	13000	3100
14	박세웅	롯데	12	6	0	0	0	28	28	171.1	⋯	1.10	0.290	78.3	3.68	5.92	5.07	5.14	2.54	25000	10000
15	백정현	삼성	8	4	0	3	0	35	14	100.2	⋯	0.98	0.336	73.2	4.38	3.01	4.51	4.34	2.25	15500	10000
16	송승준	롯데	11	5	0	1	1	30	22	130.1	⋯	1.31	0.298	75.8	4.21	4.22	4.91	4.77	2.20	40000	40000
17	류제국	LG	8	6	0	0	0	25	25	131.1	⋯	0.69	0.327	63.5	5.35	1.53	4.79	4.84	2.15	29000	35000
18	우규민	삼성	7	10	0	0	0	27	25	133.0	⋯	1.29	0.334	60.6	5.21	1.48	4.95	4.98	2.14	70000	70000
19	임찬규	LG	6	10	0	0	0	27	26	124.1	⋯	0.87	0.335	71.3	4.63	3.15	4.81	4.79	2.04	11500	6500
20	손승락	롯데	1	3	37	0	5	61	0	62.0	⋯	1.02	0.311	89.9	2.18	3.91	3.69	3.37	1.82	70000	70000
22	윤희상	SK	6	7	0	0	0	23	22	120.0	⋯	1.20	0.340	63.1	6.00	1.52	5.13	5.22	1.80	13000	15000
23	원종현	NC	3	6	0	22	0	68	0	80.0	⋯	0.45	0.336	63.9	4.39	2.02	3.60	3.52	1.71	18500	14000
24	배영수	한화	7	8	0	0	0	25	25	128.0	⋯	1.20	0.328	66.4	5.06	2.47	5.10	5.21	1.68	50000	55000
25	박종훈	SK	12	7	0	1	0	29	28	151.1	⋯	0.95	0.287	75.3	4.10	4.31	5.38	5.55	1.62	20000	10000
26	이상화	KT	4	3	6	4	1	70	0	66.0	⋯	0.55	0.337	68.0	3.95	2.43	3.57	3.45	1.54	10000	4500
27	김진성	NC	10	6	0	15	2	69	0	89.2	⋯	1.30	0.268	76.1	3.61	3.20	4.30	3.92	1.47	23000	18000
28	이민호	NC	5	1	3	6	1	60	3	88.2	⋯	1.02	0.312	71.4	4.06	1.97	4.41	4.22	1.38	18800	16000
29	이재학	NC	5	7	0	0	0	28	23	119.0	⋯	1.66	0.350	65.4	5.67	1.04	5.53	5.35	1.31	19000	20000
30	김강률	두산	7	2	7	12	1	70	0	89.0	⋯	0.61	0.316	73.5	3.44	2.68	4.15	4.09	1.27	15000	6200
31	김재윤	KT	3	5	15	0	4	41	0	37.1	⋯	0.24	0.348	54.3	5.79	0.73	3.15	3.05	1.24	11000	9000
32	김원중	롯데	7	8	0	0	0	24	24	107.1	⋯	1.09	0.347	70.3	5.70	2.22	5.53	5.56	1.23	6300	3000
33	박진형	롯데	4	4	2	10	3	45	9	88.0	⋯	0.82	0.349	68.9	5.11	1.70	4.43	4.14	1.12	10500	6000
34	윤규진	한화	8	7	0	2	0	36	18	119.0	⋯	1.44	0.328	72.1	5.22	2.23	5.46	5.42	1.09	21000	18000
35	김재영	한화	5	7	0	0	1	20	15	85.1	⋯	0.95	0.337	67.8	4.54	1.60	5.00	5.23	1.06	5300	3000
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋱	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
123	정재원	한화	0	2	0	1	1	14	0	21.0	⋯	0.00	0.315	69.2	3.43	0.12	5.16	5.73	-0.12	4000	4000
124	김민우	한화	0	0	0	0	0	4	2	7.1	⋯	1.23	0.613	50.7	17.18	-0.52	7.83	8.32	-0.12	3600	3800
125	이현호	두산	1	0	0	0	0	24	2	30.0	⋯	1.80	0.389	65.3	5.70	-0.51	6.47	6.57	-0.16	5200	6000
126	권혁	한화	1	3	0	11	1	37	0	31.1	⋯	1.72	0.311	67.3	6.32	0.04	6.48	6.78	-0.16	45000	45000
127	배제성	KT	0	0	0	0	0	21	1	32.0	⋯	1.12	0.378	59.6	8.72	-0.10	6.39	6.59	-0.17	3000	2700
128	홍상삼	두산	1	1	0	0	0	11	2	17.0	⋯	1.06	0.300	53.0	7.94	-0.52	6.73	7.22	-0.18	9000	12500
129	이태양	한화	3	6	0	0	0	16	12	59.0	⋯	1.83	0.330	64.3	7.17	0.05	6.77	7.04	-0.18	7300	8300
130	김진우	KIA	2	6	0	0	1	14	8	36.1	⋯	1.24	0.376	65.3	7.93	-0.35	6.68	7.04	-0.19	6000	12000
131	이영하	두산	3	3	0	0	0	20	3	35.2	⋯	2.02	0.333	78.7	5.55	0.59	6.79	6.86	-0.19	4200	2700
132	최성영	NC	0	0	0	0	0	7	0	11.1	⋯	3.18	0.361	68.6	9.53	-0.26	9.29	9.48	-0.20	2900	2900
133	김동호	삼성	0	1	0	0	0	20	1	36.0	⋯	0.25	0.381	67.0	6.75	-0.07	5.46	5.96	-0.20	6000	5000
134	김윤동	KIA	7	4	11	6	6	65	1	80.1	⋯	1.12	0.267	75.0	4.59	1.89	5.54	5.53	-0.20	15000	4700
135	정인욱	삼성	1	4	0	0	0	9	7	32.0	⋯	2.53	0.359	52.5	9.84	-0.43	7.39	7.36	-0.20	5700	7200
136	송창식	한화	5	6	0	15	6	63	0	73.1	⋯	1.60	0.303	61.0	6.63	-0.74	5.68	5.59	-0.22	24000	22000
137	배재환	NC	0	1	0	0	0	3	1	8.0	⋯	4.50	0.346	82.1	9.00	-0.16	11.48	11.73	-0.23	3000	4000
138	이정민	롯데	3	1	0	2	1	24	0	26.2	⋯	1.69	0.307	71.4	5.40	0.19	6.47	6.83	-0.24	10000	15000
139	최동환	LG	1	2	1	5	2	35	0	38.0	⋯	2.13	0.273	71.1	5.68	-0.05	6.76	6.77	-0.24	6500	6000
140	이종혁	KT	2	0	0	0	0	16	0	19.0	⋯	1.42	0.324	67.0	6.63	-0.09	7.10	7.57	-0.25	3200	2700
141	홍성용	KT	0	2	0	1	0	37	1	39.0	⋯	1.62	0.294	68.3	6.23	0.25	6.40	6.63	-0.28	6800	6300
142	정영일	SK	0	0	0	0	0	9	0	8.0	⋯	3.38	0.281	47.3	10.12	-0.61	10.73	11.37	-0.30	3000	4000
143	김지용	LG	4	3	3	8	4	53	0	53.0	⋯	2.21	0.280	73.9	5.09	0.28	6.30	6.27	-0.38	9000	10000
144	최금강	NC	5	3	0	0	0	39	13	89.2	⋯	1.51	0.320	57.4	7.33	-0.27	6.31	6.58	-0.41	12500	14000
145	김범수	한화	0	4	0	0	0	15	5	31.0	⋯	2.03	0.340	66.4	8.71	-0.42	8.15	8.52	-0.42	3600	3300
146	이승현	삼성	2	0	0	0	0	30	0	31.2	⋯	2.56	0.276	81.9	5.12	0.31	8.03	8.03	-0.44	7000	6200
147	주권	KT	5	6	1	3	2	39	12	81.2	⋯	1.65	0.314	63.2	6.61	-0.02	6.33	6.54	-0.46	7600	7500
148	장민재	한화	2	5	0	0	2	33	5	62.2	⋯	1.58	0.355	56.9	7.76	-1.21	6.21	6.48	-0.47	7100	8100
149	정용운	KIA	3	2	0	0	0	25	11	59.1	⋯	1.06	0.263	65.4	5.92	0.39	6.41	6.77	-0.49	7500	3100
150	노경은	롯데	0	2	0	0	0	9	2	14.2	⋯	2.45	0.382	52.8	11.66	-0.83	8.03	8.29	-0.61	10000	16000
151	김승현	삼성	0	3	0	1	0	41	0	43.2	⋯	1.44	0.341	73.9	5.77	-0.40	6.87	6.95	-0.70	4000	2900
152	류희운	KT	4	4	0	0	0	24	14	81.0	⋯	2.00	0.312	65.3	7.67	-0.68	7.60	7.81	-1.01	4000	3000

aa <- lm(연봉.2018. ~ .-팀명-선수명, data=picher2)

summary(aa)


Call:
lm(formula = 연봉.2018. ~ . - 팀명 - 선수명, data = picher2)

Residuals:
    Min      1Q  Median      3Q     Max 
-6719.3 -1077.4    65.0   796.1 21824.2 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1180.5580  6767.2703  -0.174    0.862    
승            -11.5761   219.0412  -0.053    0.958    
패             81.9489   210.8035   0.389    0.698    
세            -37.2721   103.6610  -0.360    0.720    
홀드           80.5730   116.2315   0.693    0.489    
블론          370.1732   278.5525   1.329    0.186    
경기          -32.2197    53.8240  -0.599    0.551    
선발         -174.3314   168.9477  -1.032    0.304    
이닝           52.2789    42.2955   1.236    0.219    
삼진.9        201.3240   879.7268   0.229    0.819    
볼넷.9        340.5238   826.0454   0.412    0.681    
홈런.9       1665.6462  5202.1586   0.320    0.749    
BABIP         114.3823  5557.0488   0.021    0.984    
LOB.           27.0594    55.5030   0.488    0.627    
ERA           188.2818   297.7530   0.632    0.528    
RA9.WAR      1323.6685   595.3892   2.223    0.028 *  
FIP         -6291.3374 16484.2058  -0.382    0.703    
kFIP         4975.4255 13255.6236   0.375    0.708    
WAR           477.9530   756.5703   0.632    0.529    
연봉.2017.      0.8897     0.0197  45.155   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3321 on 125 degrees of freedom
Multiple R-squared:  0.9762,    Adjusted R-squared:  0.9726 
F-statistic: 269.9 on 19 and 125 DF,  p-value: < 2.2e-16

X <- picher2[c('FIP', 'WAR', '볼넷.9', '삼진.9', '연봉.2017.')]
y <- picher2$"연봉.2018."


set.seed(20) 
train_indices <- createDataPartition(y, p = 0.8, list = FALSE)  # 80%를 훈련 세트로 사용
X_train <- X[train_indices, ]  # X 훈련 세트
y_train <- y[train_indices]  # y 훈련 세트
X_test <- X[-train_indices, ]  # X 테스트 세트
y_test <- y[-train_indices]  # y 테스트 세트

model2 <- lm(y_train ~ ., data = cbind(X_train, y_train))
summary(model2)


Call:
lm(formula = y_train ~ ., data = cbind(X_train, y_train))

Residuals:
    Min      1Q  Median      3Q     Max 
-8171.3 -1022.5  -169.3  1009.7  9835.0 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1947.46270 1101.98299   1.767   0.0799 .  
FIP         -130.36447  180.71549  -0.721   0.4722    
WAR         1933.30721  331.27392   5.836 5.29e-08 ***
볼넷.9       -95.23174  143.48508  -0.664   0.5082    
삼진.9        81.85525   94.20305   0.869   0.3867    
연봉.2017.     0.89859    0.01633  55.034  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2764 on 112 degrees of freedom
Multiple R-squared:  0.9816,    Adjusted R-squared:  0.9808 
F-statistic:  1194 on 5 and 112 DF,  p-value: < 2.2e-16

y_pred <- predict(model2, newdata = X_test)

summary(model2)


Call:
lm(formula = y_train ~ ., data = cbind(X_train, y_train))

Residuals:
    Min      1Q  Median      3Q     Max 
-8171.3 -1022.5  -169.3  1009.7  9835.0 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1947.46270 1101.98299   1.767   0.0799 .  
FIP         -130.36447  180.71549  -0.721   0.4722    
WAR         1933.30721  331.27392   5.836 5.29e-08 ***
볼넷.9       -95.23174  143.48508  -0.664   0.5082    
삼진.9        81.85525   94.20305   0.869   0.3867    
연봉.2017.     0.89859    0.01633  55.034  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2764 on 112 degrees of freedom
Multiple R-squared:  0.9816,    Adjusted R-squared:  0.9808 
F-statistic:  1194 on 5 and 112 DF,  p-value: < 2.2e-16

plot(model2)

## Shapiro-Wilk Test
## H0 : normal distribution vs. H1 : not H0
shapiro.test(resid(model2))


    Shapiro-Wilk normality test

data:  resid(model2)
W = 0.92186, p-value = 3.661e-06

귀무가설 기각

library(lmtest)

### 등분산성
## H0 : 등분산 vs. H1 : 이분산 (Heteroscedasticity)
bptest(model2)


    studentized Breusch-Pagan test

data:  model2
BP = 2.7624, df = 5, p-value = 0.7366

잔차 이분산..

bptest(model2)


    studentized Breusch-Pagan test

data:  model2
BP = 2.7624, df = 5, p-value = 0.7366

y_pred <- predict(model2, newdata = X)

picher2 <- cbind(picher2, new_data= y_pred)

sorted_picher2 <- picher[order(-picher2$"연봉.2018."), ]

filtered_df2 <- picher2[picher2$"연봉.2018." != picher2$"연봉.2017.", ]

df <- filtered_df2[,c("선수명","연봉.2018.","new_data","연봉.2017.")]

sorted_df <- df[order(df$"연봉.2018.", decreasing = TRUE), ]

summary(model2)


Call:
lm(formula = y_train ~ ., data = cbind(X_train, y_train))

Residuals:
    Min      1Q  Median      3Q     Max 
-8171.3 -1022.5  -169.3  1009.7  9835.0 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1947.46270 1101.98299   1.767   0.0799 .  
FIP         -130.36447  180.71549  -0.721   0.4722    
WAR         1933.30721  331.27392   5.836 5.29e-08 ***
볼넷.9       -95.23174  143.48508  -0.664   0.5082    
삼진.9        81.85525   94.20305   0.869   0.3867    
연봉.2017.     0.89859    0.01633  55.034  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2764 on 112 degrees of freedom
Multiple R-squared:  0.9816,    Adjusted R-squared:  0.9808 
F-statistic:  1194 on 5 and 112 DF,  p-value: < 2.2e-16

sorted_df

A data.frame: 122 × 4
	선수명	연봉.2018.	new_data	연봉.2017.
	<chr>	<int>	<dbl>	<int>
5	레일리	111000	86639.501	85000
24	배영수	50000	54254.114	55000
41	안영명	35000	20988.868	20000
68	채병용	30000	24555.703	25000
17	류제국	29000	37171.350	35000
14	박세웅	25000	15406.471	10000
40	임창민	25000	23649.432	22500
56	박정진	25000	32048.281	33000
136	송창식	24000	20807.581	22000
27	김진성	23000	20950.905	18000
38	심창민	23000	22494.249	21000
34	윤규진	21000	19775.968	18000
25	박종훈	20000	13538.895	10000
44	심수창	20000	25556.492	25000
29	이재학	19000	22160.236	20000
43	진해수	19000	13232.667	11000
28	이민호	18800	18842.143	16000
23	원종현	18500	17795.806	14000
111	박희수	18500	20005.072	21000
9	함덕주	16000	15382.469	7000
15	백정현	15500	15076.326	10000
30	김강률	15000	9728.566	6200
60	권오준	15000	11743.714	10500
63	김사율	15000	20080.039	20000
134	김윤동	15000	5165.007	4700
71	임정우	14000	22059.786	22000
78	박정배	14000	8806.466	8000
13	임기영	13000	9920.273	3100
22	윤희상	13000	18504.773	15000
42	심동섭	13000	13188.418	11000
⋮	⋮	⋮	⋮	⋮
152	류희운	4000	1612.039	3000
79	황수범	3800	3785.906	2700
124	김민우	3600	3911.050	3800
145	김범수	3600	2755.221	3300
92	이형범	3500	3704.690	2700
93	임현준	3500	4226.944	3200
110	안성무	3500	3170.363	2800
99	박치국	3400	3825.389	2700
102	허건엽	3400	4263.368	3300
105	고봉재	3300	4147.499	4400
112	김시현	3300	3306.331	2700
120	강장산	3300	3606.075	3000
118	배민관	3200	2722.062	3000
140	이종혁	3200	2901.344	2700
70	최지광	3100	3961.410	2700
73	박세진	3100	4478.896	3000
101	박상원	3100	3847.625	2700
81	김대유	3000	3887.465	2700
84	손주영	3000	4599.176	2700
87	김진영	3000	4582.740	2700
109	서균	3000	3926.074	2700
127	배제성	3000	3079.587	2700
137	배재환	3000	3326.123	4000
142	정영일	3000	3104.391	4000
96	김도영	2900	3887.404	2700
97	조근종	2900	4909.511	2700
108	안규현	2900	2330.828	2800
115	김종훈	2900	1665.021	2800
83	장지훈	2800	5644.555	2700
106	이수민	2800	3896.889	3000

다 안되노

번외 (WAR을 y로)

model_ <- lm(WAR ~ ., dt)
summary(model_)


Call:
lm(formula = WAR ~ ., data = dt)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.25837 -0.18387 -0.00443  0.17470  1.58012 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  8.632e-01  8.184e-01   1.055   0.2935    
승           7.000e-04  2.446e-02   0.029   0.9772    
패           3.924e-02  2.449e-02   1.602   0.1115    
세           1.444e-03  1.218e-02   0.119   0.9058    
홀드         1.016e-02  1.417e-02   0.717   0.4747    
블론        -5.186e-02  3.392e-02  -1.529   0.1287    
경기        -1.216e-02  6.489e-03  -1.874   0.0631 .  
선발        -2.104e-02  2.081e-02  -1.011   0.3139    
이닝         7.125e-03  5.161e-03   1.381   0.1698    
삼진.9       2.483e-02  1.055e-01   0.235   0.8142    
볼넷.9       1.254e-02  1.014e-01   0.124   0.9017    
홈런.9      -3.549e-03  6.346e-01  -0.006   0.9955    
BABIP        9.050e-01  6.636e-01   1.364   0.1749    
LOB.        -1.276e-02  5.728e-03  -2.227   0.0277 *  
ERA         -3.164e-02  2.542e-02  -1.245   0.2154    
RA9.WAR      4.259e-01  5.563e-02   7.655 3.63e-12 ***
FIP         -2.926e-02  2.011e+00  -0.015   0.9884    
kFIP        -2.821e-02  1.613e+00  -0.017   0.9861    
연봉.2017.  -9.617e-06  3.872e-06  -2.484   0.0143 *  
연봉.2018.   1.726e-05  3.608e-06   4.783 4.55e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.413 on 132 degrees of freedom
Multiple R-squared:  0.9147,    Adjusted R-squared:  0.9024 
F-statistic:  74.5 on 19 and 132 DF,  p-value: < 2.2e-16

vif(model_)

승: 7.90295946434333
패: 5.20359428013343
세: 3.03700161686219
홀드: 3.62204119070082
블론: 2.71884077341594
경기: 13.9861481235637
선발: 36.4583393437973
이닝: 59.6518045536396
삼진.9: 78.7060221382563
볼넷.9: 50.827473231828
홈런.9: 368.731473824191
BABIP: 3.08657710689232
LOB.: 3.90285091455687
ERA: 9.92892504245132
RA9.WAR: 9.31215347437081
FIP: 12527.1829609619
kFIP: 9046.79675535442
연봉.2017.: 8.32457422927786
연봉.2018.: 11.033305518369

WAR로 돌린 모델의 \(R^2\)값이 연봉으로 돌린 것보다 높게 나왔다.