ref

import

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

Loading required package: carData

Loading required package: ggplot2

Loading required package: lattice

Loading required package: Matrix

Loaded glmnet 4.1-7

── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──

✔ tibble  3.2.0     ✔ dplyr   1.1.0
✔ tidyr   1.3.0     ✔ stringr 1.5.0
✔ readr   2.1.4     ✔ forcats 1.0.0
✔ purrr   1.0.1     

── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ tidyr::expand() masks Matrix::expand()
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
✖ purrr::lift()   masks caret::lift()
✖ tidyr::pack()   masks Matrix::pack()
✖ dplyr::recode() masks car::recode()
✖ dplyr::select() masks MASS::select()
✖ purrr::some()   masks car::some()
✖ tidyr::unpack() masks Matrix::unpack()

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)

WAR: 1.84059685810784
연봉.2017.: 1.84059685810784

threshold <- 10

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

character(0)

threshold <- 15

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

character(0)

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.2017.	연봉.2018.
	<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	2.7347053	3.912893
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	1.3373033	3.266495
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	5.3298806	6.821679
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	3.3335919	2.620098
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	2.7347053	2.975617
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	0.7384167	2.135301

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 <- ㅍget_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=2775.03
연봉.2018. ~ +WAR + 연봉.2017.

             Df  Sum of Sq        RSS    AIC
<none>                     1.2403e+10 2775.0
- WAR         1 7.0421e+09 1.9445e+10 2841.4
- 연봉.2017.  1 4.1619e+10 5.4022e+10 2996.7


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(model_back)

WAR: 1.84059685810784
연봉.2017.: 1.84059685810784

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)

ERROR: Error in UseMethod("select"): no applicable method for 'select' applied to an object of class "ridgelm"

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

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 <- picher$"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 
-48253  -2002   -534   3472  43845 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) 2312.85178 1754.63797   1.318  0.19003    
승          1322.49243  533.83994   2.477  0.01467 *  
WAR         8040.03263 1345.09686   5.977 2.52e-08 ***
경기        -148.06296   57.54624  -2.573  0.01133 *  
선발        -522.51845  187.30514  -2.790  0.00616 ** 
연봉.2017.     0.88556    0.04671  18.957  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9453 on 117 degrees of freedom
Multiple R-squared:  0.9143,    Adjusted R-squared:  0.9106 
F-statistic: 249.6 on 5 and 117 DF,  p-value: < 2.2e-16

ㅎ므

X <- data.frame('승' = picher$"승",
                        WAR = picher$"WAR",
                        `경기` = picher$"경기",
                        `선발` = picher$"선발",
                        `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 × 23
	선수명	팀명	승	패	세	홀드	블론	경기	선발	이닝	⋯	BABIP	LOB.	ERA	RA9.WAR	FIP	kFIP	WAR	연봉.2018.	연봉.2017.	new_col
	<chr>	<chr>	<int>	<int>	<int>	<int>	<int>	<int>	<int>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<int>	<dbl>
1	켈리	SK	16	7	0	0	0	30	30	190.0	⋯	0.342	73.7	3.60	6.91	3.69	3.44	6.62	140000	85000	131853.25
2	소사	LG	11	11	1	0	0	30	29	185.1	⋯	0.319	67.1	3.88	6.80	3.52	3.41	6.08	120000	50000	90426.95
3	양현종	KIA	20	6	0	0	0	31	31	193.1	⋯	0.332	72.1	3.44	6.54	3.94	3.82	5.64	230000	150000	186155.07
4	차우찬	LG	10	7	0	0	0	28	28	175.2	⋯	0.298	75.0	3.43	6.11	4.20	4.03	4.63	100000	100000	122543.26
5	레일리	롯데	13	7	0	0	0	30	30	187.1	⋯	0.323	74.1	3.80	6.13	4.36	4.31	4.38	111000	85000	109876.10
6	피어밴드	KT	8	10	0	0	0	26	26	160.0	⋯	0.289	76.1	3.04	6.52	4.42	4.32	3.94	85000	35000	58130.15

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	131853	85000
2	소사	120000	90427	50000
3	양현종	230000	186155	150000
4	차우찬	100000	122543	100000
5	레일리	111000	109876	85000
6	피어밴드	85000	58130	35000
7	고영표	11500	32371	5200
8	장원준	100000	120891	100000
9	함덕주	16000	33083	7000
10	팻딘	70000	85876	70000
11	윤성환	80000	94613	80000
12	유희관	50000	64779	50000
13	임기영	13000	24736	3100
14	박세웅	25000	28684	10000
15	백정현	15500	27341	10000
16	송승준	40000	54034	40000
17	류제국	29000	44409	35000
18	우규민	70000	73705	70000
19	임찬규	11500	14822	6500
20	손승락	70000	71226	70000
21	정우람	120000	122776	120000
22	윤희상	13000	23102	15000
23	원종현	18500	22358	14000
24	배영수	50000	57019	55000
25	박종훈	20000	21139	10000
26	이상화	10000	13605	4500
27	김진성	23000	33080	18000
28	이민호	18800	23738	16000
29	이재학	19000	21005	20000
30	김강률	15000	16907	6200
⋮	⋮	⋮	⋮	⋮
123	정재원	4000	2817	4000
124	김민우	3600	3076	3800
125	이현호	5200	3064	6000
126	권혁	45000	36721	45000
127	배제성	3000	-295	2700
128	홍상삼	9000	10584	12500
129	이태양	7300	3544	8300
130	김진우	6000	7804	12000
131	이영하	4200	2615	2700
132	최성영	2900	2237	2900
133	김동호	6000	1649	5000
134	김윤동	15000	3978	4700
135	정인욱	5700	3413	7200
136	송창식	24000	17311	22000
137	배재환	3000	3039	4000
138	이정민	10000	14081	15000
139	최동환	6500	1837	6000
140	이종혁	3200	2970	2700
141	홍성용	6800	-360	6300
142	정영일	3000	2111	4000
143	김지용	9000	5556	10000
144	최금강	12500	5460	14000
145	김범수	3600	-2975	3300
146	이승현	7000	2469	6200
147	주권	7600	-176	7500
148	장민재	7100	853	8100
149	정용운	7500	-4363	3100
150	노경은	10000	9200	16000
151	김승현	4000	-6818	2900
152	류희운	4000	-8730	3000

k-fold

X <- dt[c('승', '경기', '선발', 'WAR', '연봉.2017.')]
y <- dt$"연봉.2018."

ERROR: Error in dt[c("승", "경기", "선발", "WAR", "연봉.2017.")]: object of type 'closure' is not subsettable

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 = 0.80293, p-value = 1.485e-11

귀무가설 기각

library(lmtest)

Loading required package: zoo


Attaching package: ‘zoo’


The following objects are masked from ‘package:base’:

    as.Date, as.Date.numeric

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


    studentized Breusch-Pagan test

data:  model
BP = 43.35, df = 5, p-value = 3.138e-08

잔차 이분산..

bptest(model)


    studentized Breusch-Pagan test

data:  model
BP = 43.35, df = 5, p-value = 3.138e-08

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: 131853.251722752
2: 90426.9473005226
3: 186155.073818348
4: 122543.256377936
5: 109876.101347654
6: 58130.1460693261
7: 32370.6338078238
8: 120891.419231451
9: 33082.9090122538
10: 85875.5646042552
11: 94612.907258451
12: 64779.2432182822
13: 24736.432167844
14: 28683.8050596197
15: 27341.0434374789
16: 54033.6089742136
17: 44409.0690815691
18: 73704.7935015169
19: 14822.4597236171
20: 71225.8489501107
21: 122776.430033276
22: 23102.4723102339
23: 22358.4004975124
24: 57019.0430915069
25: 21138.91207732
26: 13605.1026078606
27: 33080.433064936
28: 23738.2511333632
29: 21005.3510614688
30: 16907.230038373
31: 18149.4647698284
32: 8022.27721072489
33: 10555.5431004635
34: 22860.981530776
35: 9305.40472215851
36: 11392.9246005369
37: 57338.2157721655
38: 23904.7420284782
39: 15323.2191074946
40: 25799.8646455771
41: 15797.1830796868
42: 12386.7566462361
43: 11268.4374599085
44: 27181.6327954838
45: 58218.5631642926
46: 84.2491549617121
47: 6997.48046210642
48: 6623.06609223969
49: 37524.5209172796
50: 68252.8672643547
51: 5526.75772775975
52: 46011.0463688199
53: 13988.4104382785
54: 5669.59301443541
55: 9266.84557614415
56: 30415.6933317048
57: 2427.28629533588
58: 3523.97145639002
59: 9345.91329228837
60: 8522.14286154392
61: 7117.61695272959
62: 5826.76177364835
63: 20575.8304166946
64: -3248.10803524208
65: 1432.47361320697
66: 2851.50820535714
67: 4305.61668282123
68: 27789.0082687676
69: 9890.01282405876
70: 1628.47835528225
71: 20886.1978578739
72: 7039.25714045121
73: 4256.94270974835
74: 10755.7289381351
75: 8543.22556649082
76: 6443.23553034538
77: 6491.71113930571
78: 8023.19002679344
79: 1852.91236244955
80: 5204.00279116998
81: 4539.09996965536
82: 10388.5037497285
83: 4754.82557308093
84: 4606.76260822984
85: 1841.22291855011
86: 2122.67759069216
87: 4822.48821165541
88: 3669.56302759059
89: 5893.32120073109
90: 4750.24396797544
91: 5123.38648652916
92: 2185.01324555074
93: 3907.22819695754
94: 4420.48658027234
95: 6368.7275754839
96: 4555.8118574213
97: 4555.8118574213
98: 4998.59390178756
99: 1349.48963739276
100: 4198.77252155423
101: 2038.74145495265
102: 3970.30923042652
103: 4088.0680907676
104: 4475.41153114468
105: 5980.87048198998
106: 4741.08075776444
107: 3938.68971025506
108: 4322.76696118809
109: 2309.39200925058
110: 3405.05185250049
111: 16045.6585612658
112: 1784.80278842067
113: 7212.97988221046
114: 710.581165599726
115: 4161.96630863486
116: 3844.94660863389
117: 296.340101124663
118: 3734.08957927484
119: 3435.1499491986
120: 1648.47038365735
121: 3048.6997058917
122: 36138.5026118377
123: 2817.42271438994
124: 3075.90264334206
125: 3063.77546613714
126: 36720.9932854539
127: -294.771437209275
128: 10583.9599334096
129: 3544.07628683963
130: 7803.97039248833
131: 2614.93126241198
132: 2236.54036052891
133: 1648.88795289679
134: 3977.83231596103
135: 3413.20328574532
136: 17310.9499196651
137: 3039.19328780306
138: 14080.6714157531
139: 1836.91714437448
140: 2969.84408716327
141: -360.151744432489
142: 2110.53166566634
143: 5555.91285324796
144: 5459.60230519531
145: -2975.13715540324
146: 2468.83069055606
147: -176.047452043045
148: 853.420331233892
149: -4363.31532189832
150: 9199.85371406927
151: -6817.61675823917
152: -8729.68865531109

picher <- cbind(picher, new_data= y_pred)

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

A data.frame: 152 × 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_data
	<chr>	<chr>	<int>	<int>	<int>	<int>	<int>	<int>	<int>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<int>	<dbl>	<dbl>
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	186155.07	186155.07
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	131853.25	131853.25
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	90426.95	90426.95
21	정우람	한화	6	4	26	0	5	56	0	59.0	⋯	79.4	2.75	2.85	3.26	2.69	1.81	120000	120000	122776.43	122776.43
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	109876.10	109876.10
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	122543.26	122543.26
8	장원준	두산	14	9	0	0	0	29	29	180.1	⋯	75.8	3.14	7.28	4.26	4.35	3.85	100000	100000	120891.42	120891.42
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	58130.15	58130.15
11	윤성환	삼성	12	9	0	0	0	28	28	174.1	⋯	72.7	4.28	5.36	4.78	4.80	3.03	80000	80000	94612.91	94612.91
10	팻딘	KIA	9	7	0	0	0	30	29	176.0	⋯	76.5	4.14	5.66	4.65	4.61	3.64	70000	70000	85875.56	85875.56
18	우규민	삼성	7	10	0	0	0	27	25	133.0	⋯	60.6	5.21	1.48	4.95	4.98	2.14	70000	70000	73704.79	73704.79
20	손승락	롯데	1	3	37	0	5	61	0	62.0	⋯	89.9	2.18	3.91	3.69	3.37	1.82	70000	70000	71225.85	71225.85
45	이동현	LG	3	6	7	5	3	45	0	50.2	⋯	58.9	4.80	1.22	3.64	3.59	0.68	60000	60000	58218.56	58218.56
12	유희관	두산	11	6	0	1	0	30	29	188.2	⋯	69.7	4.53	4.79	4.78	4.97	2.89	50000	50000	64779.24	64779.24
24	배영수	한화	7	8	0	0	0	25	25	128.0	⋯	66.4	5.06	2.47	5.10	5.21	1.68	50000	55000	57019.04	57019.04
37	임창용	KIA	8	6	7	9	5	51	0	50.0	⋯	75.9	3.78	1.40	3.69	3.35	0.96	50000	50000	57338.22	57338.22
52	윤길현	롯데	1	4	0	13	2	40	0	39.1	⋯	60.5	6.41	-0.04	3.99	3.73	0.50	50000	50000	46011.05	46011.05
122	송은범	한화	0	4	1	0	1	13	6	37.1	⋯	62.7	6.51	0.10	6.33	6.79	-0.12	45000	45000	36138.50	36138.50
126	권혁	한화	1	3	0	11	1	37	0	31.1	⋯	67.3	6.32	0.04	6.48	6.78	-0.16	45000	45000	36720.99	36720.99
16	송승준	롯데	11	5	0	1	1	30	22	130.1	⋯	75.8	4.21	4.22	4.91	4.77	2.20	40000	40000	54033.61	54033.61
49	이현승	두산	3	2	5	9	7	57	0	52.0	⋯	77.2	3.98	1.69	4.25	4.30	0.53	40000	40000	37524.52	37524.52
41	안영명	한화	1	8	0	0	1	25	16	87.2	⋯	66.9	5.75	0.52	5.19	5.34	0.81	35000	20000	15797.18	15797.18
68	채병용	SK	6	4	0	6	3	43	0	50.0	⋯	58.1	6.84	-0.17	5.05	4.94	0.22	30000	25000	27789.01	27789.01
17	류제국	LG	8	6	0	0	0	25	25	131.1	⋯	63.5	5.35	1.53	4.79	4.84	2.15	29000	35000	44409.07	44409.07
14	박세웅	롯데	12	6	0	0	0	28	28	171.1	⋯	78.3	3.68	5.92	5.07	5.14	2.54	25000	10000	28683.81	28683.81
40	임창민	NC	4	3	29	0	6	60	0	66.0	⋯	81.4	3.68	2.68	4.83	4.60	0.89	25000	22500	25799.86	25799.86
56	박정진	한화	3	2	1	7	0	55	0	48.0	⋯	65.4	3.94	0.87	4.92	4.66	0.38	25000	33000	30415.69	30415.69
136	송창식	한화	5	6	0	15	6	63	0	73.1	⋯	61.0	6.63	-0.74	5.68	5.59	-0.22	24000	22000	17310.95	17310.95
27	김진성	NC	10	6	0	15	2	69	0	89.2	⋯	76.1	3.61	3.20	4.30	3.92	1.47	23000	18000	33080.43	33080.43
38	심창민	삼성	4	7	6	16	2	66	0	75.1	⋯	78.5	4.18	1.82	4.82	4.26	0.93	23000	21000	23904.74	23904.74
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋱	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
99	박치국	두산	1	1	0	0	0	21	3	32.0	⋯	60.6	6.75	-0.12	5.39	5.58	0.00	3400	2700	1349.4896	1349.4896
102	허건엽	SK	0	0	0	0	0	8	0	8.1	⋯	51.3	8.64	-0.20	5.29	5.64	-0.01	3400	3300	3970.3092	3970.3092
105	고봉재	두산	0	0	0	0	0	1	0	1.0	⋯	100.0	0.00	0.04	6.73	7.64	-0.01	3300	4400	5980.8705	5980.8705
112	김시현	삼성	0	0	0	0	0	17	0	21.1	⋯	69.3	7.59	0.08	7.06	7.18	-0.05	3300	2700	1784.8028	1784.8028
120	강장산	KT	0	0	0	0	0	17	0	26.1	⋯	69.4	5.47	0.54	6.16	6.46	-0.10	3300	3000	1648.4704	1648.4704
118	배민관	LG	0	0	0	0	0	4	0	3.2	⋯	69.8	9.82	-0.11	9.46	9.77	-0.08	3200	3000	3734.0896	3734.0896
140	이종혁	KT	2	0	0	0	0	16	0	19.0	⋯	67.0	6.63	-0.09	7.10	7.57	-0.25	3200	2700	2969.8441	2969.8441
70	최지광	삼성	0	2	0	0	0	11	6	25.0	⋯	64.3	6.48	-0.16	5.69	5.65	0.21	3100	2700	1628.4784	1628.4784
73	박세진	KT	0	2	0	0	0	4	3	11.1	⋯	50.0	9.53	-0.13	4.44	4.67	0.18	3100	3000	4256.9427	4256.9427
101	박상원	한화	0	0	0	1	0	18	0	21.2	⋯	73.4	4.15	0.32	5.30	5.42	0.00	3100	2700	2038.7415	2038.7415
81	김대유	SK	0	0	0	0	0	6	0	4.2	⋯	58.1	9.64	0.08	5.88	5.91	0.09	3000	2700	4539.1000	4539.1000
84	손주영	LG	0	0	0	0	0	5	0	6.0	⋯	62.5	4.50	0.06	3.07	3.08	0.08	3000	2700	4606.7626	4606.7626
87	김진영	한화	0	0	0	0	0	3	0	2.2	⋯	57.1	10.12	-0.02	2.98	2.29	0.07	3000	2700	4822.4882	4822.4882
98	임진우	두산	0	0	0	0	0	1	0	1.0	⋯	40.0	27.00	-0.11	4.73	4.61	0.00	3000	3200	4998.5939	4998.5939
109	서균	한화	0	0	0	0	0	14	0	14.1	⋯	79.2	4.40	0.25	5.41	5.58	-0.04	3000	2700	2309.3920	2309.3920
121	홍성무	KT	0	1	0	0	0	7	0	6.1	⋯	51.3	12.79	-0.29	7.37	7.58	-0.11	3000	3000	3048.6997	3048.6997
127	배제성	KT	0	0	0	0	0	21	1	32.0	⋯	59.6	8.72	-0.10	6.39	6.59	-0.17	3000	2700	-294.7714	-294.7714
137	배재환	NC	0	1	0	0	0	3	1	8.0	⋯	82.1	9.00	-0.16	11.48	11.73	-0.23	3000	4000	3039.1933	3039.1933
142	정영일	SK	0	0	0	0	0	9	0	8.0	⋯	47.3	10.12	-0.61	10.73	11.37	-0.30	3000	4000	2110.5317	2110.5317
96	김도영	KT	0	0	0	0	0	1	0	1.0	⋯	100.0	0.00	0.04	3.73	4.43	0.00	2900	2700	4555.8119	4555.8119
97	조근종	KT	0	0	0	0	0	1	0	2.0	⋯	35.7	22.50	-0.16	6.73	4.86	0.00	2900	2700	4555.8119	4555.8119
108	안규현	삼성	0	0	0	0	0	1	0	2.0	⋯	66.7	9.00	-0.04	8.73	9.67	-0.04	2900	2800	4322.7670	4322.7670
115	김종훈	KIA	0	0	0	0	0	1	0	1.0	⋯	43.5	36.00	-0.16	18.73	17.60	-0.06	2900	2800	4161.9663	4161.9663
132	최성영	NC	0	0	0	0	0	7	0	11.1	⋯	68.6	9.53	-0.26	9.29	9.48	-0.20	2900	2900	2236.5404	2236.5404
83	장지훈	삼성	0	0	0	0	0	4	0	2.1	⋯	100.0	0.00	0.09	0.73	-0.69	0.08	2800	2700	4754.8256	4754.8256
90	차재용	롯데	0	0	0	0	0	3	0	2.1	⋯	100.0	0.00	0.08	2.02	1.83	0.05	2800	2800	4750.2440	4750.2440
106	이수민	삼성	0	0	0	0	0	1	0	2.2	⋯	50.0	10.12	-0.15	5.23	5.95	-0.01	2800	3000	4741.0808	4741.0808
94	장민익	두산	0	0	0	0	0	3	0	2.0	⋯	100.0	0.00	0.08	4.73	4.61	0.02	2700	2700	4420.4866	4420.4866
104	성영훈	두산	0	0	0	0	0	1	0	1.0	⋯	100.0	0.00	0.04	6.73	7.64	-0.01	2700	2700	4475.4115	4475.4115
116	정동윤	SK	0	0	0	0	0	2	0	3.0	⋯	71.4	9.00	-0.03	9.40	10.05	-0.07	2700	2700	3844.9466	3844.9466

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

A data.frame: 128 × 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_data
	<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	131853.252	131853.252
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	90426.947	90426.947
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	186155.074	186155.074
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	109876.101	109876.101
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	58130.146	58130.146
7	고영표	KT	8	12	0	1	0	25	24	141.2	⋯	64.6	5.08	2.97	3.88	3.78	3.87	11500	5200	32370.634	32370.634
9	함덕주	두산	9	8	0	2	0	35	24	137.1	⋯	73.1	3.67	4.99	3.91	3.67	3.78	16000	7000	33082.909	33082.909
13	임기영	KIA	8	6	0	0	0	23	19	118.1	⋯	72.3	3.65	4.25	4.07	4.19	2.79	13000	3100	24736.432	24736.432
14	박세웅	롯데	12	6	0	0	0	28	28	171.1	⋯	78.3	3.68	5.92	5.07	5.14	2.54	25000	10000	28683.805	28683.805
15	백정현	삼성	8	4	0	3	0	35	14	100.2	⋯	73.2	4.38	3.01	4.51	4.34	2.25	15500	10000	27341.043	27341.043
17	류제국	LG	8	6	0	0	0	25	25	131.1	⋯	63.5	5.35	1.53	4.79	4.84	2.15	29000	35000	44409.069	44409.069
19	임찬규	LG	6	10	0	0	0	27	26	124.1	⋯	71.3	4.63	3.15	4.81	4.79	2.04	11500	6500	14822.460	14822.460
22	윤희상	SK	6	7	0	0	0	23	22	120.0	⋯	63.1	6.00	1.52	5.13	5.22	1.80	13000	15000	23102.472	23102.472
23	원종현	NC	3	6	0	22	0	68	0	80.0	⋯	63.9	4.39	2.02	3.60	3.52	1.71	18500	14000	22358.400	22358.400
24	배영수	한화	7	8	0	0	0	25	25	128.0	⋯	66.4	5.06	2.47	5.10	5.21	1.68	50000	55000	57019.043	57019.043
25	박종훈	SK	12	7	0	1	0	29	28	151.1	⋯	75.3	4.10	4.31	5.38	5.55	1.62	20000	10000	21138.912	21138.912
26	이상화	KT	4	3	6	4	1	70	0	66.0	⋯	68.0	3.95	2.43	3.57	3.45	1.54	10000	4500	13605.103	13605.103
27	김진성	NC	10	6	0	15	2	69	0	89.2	⋯	76.1	3.61	3.20	4.30	3.92	1.47	23000	18000	33080.433	33080.433
28	이민호	NC	5	1	3	6	1	60	3	88.2	⋯	71.4	4.06	1.97	4.41	4.22	1.38	18800	16000	23738.251	23738.251
29	이재학	NC	5	7	0	0	0	28	23	119.0	⋯	65.4	5.67	1.04	5.53	5.35	1.31	19000	20000	21005.351	21005.351
30	김강률	두산	7	2	7	12	1	70	0	89.0	⋯	73.5	3.44	2.68	4.15	4.09	1.27	15000	6200	16907.230	16907.230
31	김재윤	KT	3	5	15	0	4	41	0	37.1	⋯	54.3	5.79	0.73	3.15	3.05	1.24	11000	9000	18149.465	18149.465
32	김원중	롯데	7	8	0	0	0	24	24	107.1	⋯	70.3	5.70	2.22	5.53	5.56	1.23	6300	3000	8022.277	8022.277
33	박진형	롯데	4	4	2	10	3	45	9	88.0	⋯	68.9	5.11	1.70	4.43	4.14	1.12	10500	6000	10555.543	10555.543
34	윤규진	한화	8	7	0	2	0	36	18	119.0	⋯	72.1	5.22	2.23	5.46	5.42	1.09	21000	18000	22860.982	22860.982
35	김재영	한화	5	7	0	0	1	20	15	85.1	⋯	67.8	4.54	1.60	5.00	5.23	1.06	5300	3000	9305.405	9305.405
36	신정락	LG	3	5	10	12	3	63	0	59.0	⋯	59.3	5.34	0.51	4.23	4.12	0.97	10500	7500	11392.925	11392.925
38	심창민	삼성	4	7	6	16	2	66	0	75.1	⋯	78.5	4.18	1.82	4.82	4.26	0.93	23000	21000	23904.742	23904.742
39	정찬헌	LG	8	7	7	3	3	61	0	61.2	⋯	62.9	5.84	0.97	3.96	3.80	0.93	9500	4500	15323.219	15323.219
40	임창민	NC	4	3	29	0	6	60	0	66.0	⋯	81.4	3.68	2.68	4.83	4.60	0.89	25000	22500	25799.865	25799.865
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋱	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
118	배민관	LG	0	0	0	0	0	4	0	3.2	⋯	69.8	9.82	-0.11	9.46	9.77	-0.08	3200	3000	3734.0896	3734.0896
119	윤근영	KT	0	0	0	1	0	12	0	18.0	⋯	84.8	3.50	0.30	6.23	6.31	-0.08	4200	4000	3435.1499	3435.1499
120	강장산	KT	0	0	0	0	0	17	0	26.1	⋯	69.4	5.47	0.54	6.16	6.46	-0.10	3300	3000	1648.4704	1648.4704
124	김민우	한화	0	0	0	0	0	4	2	7.1	⋯	50.7	17.18	-0.52	7.83	8.32	-0.12	3600	3800	3075.9026	3075.9026
125	이현호	두산	1	0	0	0	0	24	2	30.0	⋯	65.3	5.70	-0.51	6.47	6.57	-0.16	5200	6000	3063.7755	3063.7755
127	배제성	KT	0	0	0	0	0	21	1	32.0	⋯	59.6	8.72	-0.10	6.39	6.59	-0.17	3000	2700	-294.7714	-294.7714
128	홍상삼	두산	1	1	0	0	0	11	2	17.0	⋯	53.0	7.94	-0.52	6.73	7.22	-0.18	9000	12500	10583.9599	10583.9599
129	이태양	한화	3	6	0	0	0	16	12	59.0	⋯	64.3	7.17	0.05	6.77	7.04	-0.18	7300	8300	3544.0763	3544.0763
130	김진우	KIA	2	6	0	0	1	14	8	36.1	⋯	65.3	7.93	-0.35	6.68	7.04	-0.19	6000	12000	7803.9704	7803.9704
131	이영하	두산	3	3	0	0	0	20	3	35.2	⋯	78.7	5.55	0.59	6.79	6.86	-0.19	4200	2700	2614.9313	2614.9313
133	김동호	삼성	0	1	0	0	0	20	1	36.0	⋯	67.0	6.75	-0.07	5.46	5.96	-0.20	6000	5000	1648.8880	1648.8880
134	김윤동	KIA	7	4	11	6	6	65	1	80.1	⋯	75.0	4.59	1.89	5.54	5.53	-0.20	15000	4700	3977.8323	3977.8323
135	정인욱	삼성	1	4	0	0	0	9	7	32.0	⋯	52.5	9.84	-0.43	7.39	7.36	-0.20	5700	7200	3413.2033	3413.2033
136	송창식	한화	5	6	0	15	6	63	0	73.1	⋯	61.0	6.63	-0.74	5.68	5.59	-0.22	24000	22000	17310.9499	17310.9499
137	배재환	NC	0	1	0	0	0	3	1	8.0	⋯	82.1	9.00	-0.16	11.48	11.73	-0.23	3000	4000	3039.1933	3039.1933
138	이정민	롯데	3	1	0	2	1	24	0	26.2	⋯	71.4	5.40	0.19	6.47	6.83	-0.24	10000	15000	14080.6714	14080.6714
139	최동환	LG	1	2	1	5	2	35	0	38.0	⋯	71.1	5.68	-0.05	6.76	6.77	-0.24	6500	6000	1836.9171	1836.9171
140	이종혁	KT	2	0	0	0	0	16	0	19.0	⋯	67.0	6.63	-0.09	7.10	7.57	-0.25	3200	2700	2969.8441	2969.8441
141	홍성용	KT	0	2	0	1	0	37	1	39.0	⋯	68.3	6.23	0.25	6.40	6.63	-0.28	6800	6300	-360.1517	-360.1517
142	정영일	SK	0	0	0	0	0	9	0	8.0	⋯	47.3	10.12	-0.61	10.73	11.37	-0.30	3000	4000	2110.5317	2110.5317
143	김지용	LG	4	3	3	8	4	53	0	53.0	⋯	73.9	5.09	0.28	6.30	6.27	-0.38	9000	10000	5555.9129	5555.9129
144	최금강	NC	5	3	0	0	0	39	13	89.2	⋯	57.4	7.33	-0.27	6.31	6.58	-0.41	12500	14000	5459.6023	5459.6023
145	김범수	한화	0	4	0	0	0	15	5	31.0	⋯	66.4	8.71	-0.42	8.15	8.52	-0.42	3600	3300	-2975.1372	-2975.1372
146	이승현	삼성	2	0	0	0	0	30	0	31.2	⋯	81.9	5.12	0.31	8.03	8.03	-0.44	7000	6200	2468.8307	2468.8307
147	주권	KT	5	6	1	3	2	39	12	81.2	⋯	63.2	6.61	-0.02	6.33	6.54	-0.46	7600	7500	-176.0475	-176.0475
148	장민재	한화	2	5	0	0	2	33	5	62.2	⋯	56.9	7.76	-1.21	6.21	6.48	-0.47	7100	8100	853.4203	853.4203
149	정용운	KIA	3	2	0	0	0	25	11	59.1	⋯	65.4	5.92	0.39	6.41	6.77	-0.49	7500	3100	-4363.3153	-4363.3153
150	노경은	롯데	0	2	0	0	0	9	2	14.2	⋯	52.8	11.66	-0.83	8.03	8.29	-0.61	10000	16000	9199.8537	9199.8537
151	김승현	삼성	0	3	0	1	0	41	0	43.2	⋯	73.9	5.77	-0.40	6.87	6.95	-0.70	4000	2900	-6817.6168	-6817.6168
152	류희운	KT	4	4	0	0	0	24	14	81.0	⋯	65.3	7.67	-0.68	7.60	7.81	-1.01	4000	3000	-8729.6887	-8729.6887

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	131853.252	85000
2	소사	120000	90426.947	50000
3	양현종	230000	186155.074	150000
5	레일리	111000	109876.101	85000
6	피어밴드	85000	58130.146	35000
7	고영표	11500	32370.634	5200
9	함덕주	16000	33082.909	7000
13	임기영	13000	24736.432	3100
14	박세웅	25000	28683.805	10000
15	백정현	15500	27341.043	10000
17	류제국	29000	44409.069	35000
19	임찬규	11500	14822.460	6500
22	윤희상	13000	23102.472	15000
23	원종현	18500	22358.400	14000
24	배영수	50000	57019.043	55000
25	박종훈	20000	21138.912	10000
26	이상화	10000	13605.103	4500
27	김진성	23000	33080.433	18000
28	이민호	18800	23738.251	16000
29	이재학	19000	21005.351	20000
30	김강률	15000	16907.230	6200
31	김재윤	11000	18149.465	9000
32	김원중	6300	8022.277	3000
33	박진형	10500	10555.543	6000
34	윤규진	21000	22860.982	18000
35	김재영	5300	9305.405	3000
36	신정락	10500	11392.925	7500
38	심창민	23000	23904.742	21000
39	정찬헌	9500	15323.219	4500
40	임창민	25000	25799.865	22500
⋮	⋮	⋮	⋮	⋮
118	배민관	3200	3734.0896	3000
119	윤근영	4200	3435.1499	4000
120	강장산	3300	1648.4704	3000
124	김민우	3600	3075.9026	3800
125	이현호	5200	3063.7755	6000
127	배제성	3000	-294.7714	2700
128	홍상삼	9000	10583.9599	12500
129	이태양	7300	3544.0763	8300
130	김진우	6000	7803.9704	12000
131	이영하	4200	2614.9313	2700
133	김동호	6000	1648.8880	5000
134	김윤동	15000	3977.8323	4700
135	정인욱	5700	3413.2033	7200
136	송창식	24000	17310.9499	22000
137	배재환	3000	3039.1933	4000
138	이정민	10000	14080.6714	15000
139	최동환	6500	1836.9171	6000
140	이종혁	3200	2969.8441	2700
141	홍성용	6800	-360.1517	6300
142	정영일	3000	2110.5317	4000
143	김지용	9000	5555.9129	10000
144	최금강	12500	5459.6023	14000
145	김범수	3600	-2975.1372	3300
146	이승현	7000	2468.8307	6200
147	주권	7600	-176.0475	7500
148	장민재	7100	853.4203	8100
149	정용운	7500	-4363.3153	3100
150	노경은	10000	9199.8537	16000
151	김승현	4000	-6817.6168	2900
152	류희운	4000	-8729.6887	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	186155.074	150000
1	켈리	140000	131853.252	85000
2	소사	120000	90426.947	50000
5	레일리	111000	109876.101	85000
6	피어밴드	85000	58130.146	35000
24	배영수	50000	57019.043	55000
41	안영명	35000	15797.183	20000
68	채병용	30000	27789.008	25000
17	류제국	29000	44409.069	35000
14	박세웅	25000	28683.805	10000
40	임창민	25000	25799.865	22500
56	박정진	25000	30415.693	33000
136	송창식	24000	17310.950	22000
27	김진성	23000	33080.433	18000
38	심창민	23000	23904.742	21000
34	윤규진	21000	22860.982	18000
25	박종훈	20000	21138.912	10000
44	심수창	20000	27181.633	25000
50	장원삼	20000	68252.867	75000
29	이재학	19000	21005.351	20000
43	진해수	19000	11268.437	11000
28	이민호	18800	23738.251	16000
23	원종현	18500	22358.400	14000
111	박희수	18500	16045.659	21000
9	함덕주	16000	33082.909	7000
15	백정현	15500	27341.043	10000
30	김강률	15000	16907.230	6200
60	권오준	15000	8522.143	10500
63	김사율	15000	20575.830	20000
134	김윤동	15000	3977.832	4700
⋮	⋮	⋮	⋮	⋮
79	황수범	3800	1852.9124	2700
124	김민우	3600	3075.9026	3800
145	김범수	3600	-2975.1372	3300
92	이형범	3500	2185.0132	2700
93	임현준	3500	3907.2282	3200
110	안성무	3500	3405.0519	2800
99	박치국	3400	1349.4896	2700
102	허건엽	3400	3970.3092	3300
105	고봉재	3300	5980.8705	4400
112	김시현	3300	1784.8028	2700
120	강장산	3300	1648.4704	3000
118	배민관	3200	3734.0896	3000
140	이종혁	3200	2969.8441	2700
70	최지광	3100	1628.4784	2700
73	박세진	3100	4256.9427	3000
101	박상원	3100	2038.7415	2700
81	김대유	3000	4539.1000	2700
84	손주영	3000	4606.7626	2700
87	김진영	3000	4822.4882	2700
98	임진우	3000	4998.5939	3200
109	서균	3000	2309.3920	2700
127	배제성	3000	-294.7714	2700
137	배재환	3000	3039.1933	4000
142	정영일	3000	2110.5317	4000
96	김도영	2900	4555.8119	2700
97	조근종	2900	4555.8119	2700
108	안규현	2900	4322.7670	2800
115	김종훈	2900	4161.9663	2800
83	장지훈	2800	4754.8256	2700
106	이수민	2800	4741.0808	3000

이상치 제거

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

picher2

A data.frame: 145 × 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_data
	<chr>	<chr>	<int>	<int>	<int>	<int>	<int>	<int>	<int>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<int>	<dbl>	<dbl>
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	122543.256	122543.256
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	109876.101	109876.101
7	고영표	KT	8	12	0	1	0	25	24	141.2	⋯	64.6	5.08	2.97	3.88	3.78	3.87	11500	5200	32370.634	32370.634
8	장원준	두산	14	9	0	0	0	29	29	180.1	⋯	75.8	3.14	7.28	4.26	4.35	3.85	100000	100000	120891.419	120891.419
9	함덕주	두산	9	8	0	2	0	35	24	137.1	⋯	73.1	3.67	4.99	3.91	3.67	3.78	16000	7000	33082.909	33082.909
10	팻딘	KIA	9	7	0	0	0	30	29	176.0	⋯	76.5	4.14	5.66	4.65	4.61	3.64	70000	70000	85875.565	85875.565
11	윤성환	삼성	12	9	0	0	0	28	28	174.1	⋯	72.7	4.28	5.36	4.78	4.80	3.03	80000	80000	94612.907	94612.907
12	유희관	두산	11	6	0	1	0	30	29	188.2	⋯	69.7	4.53	4.79	4.78	4.97	2.89	50000	50000	64779.243	64779.243
13	임기영	KIA	8	6	0	0	0	23	19	118.1	⋯	72.3	3.65	4.25	4.07	4.19	2.79	13000	3100	24736.432	24736.432
14	박세웅	롯데	12	6	0	0	0	28	28	171.1	⋯	78.3	3.68	5.92	5.07	5.14	2.54	25000	10000	28683.805	28683.805
15	백정현	삼성	8	4	0	3	0	35	14	100.2	⋯	73.2	4.38	3.01	4.51	4.34	2.25	15500	10000	27341.043	27341.043
16	송승준	롯데	11	5	0	1	1	30	22	130.1	⋯	75.8	4.21	4.22	4.91	4.77	2.20	40000	40000	54033.609	54033.609
17	류제국	LG	8	6	0	0	0	25	25	131.1	⋯	63.5	5.35	1.53	4.79	4.84	2.15	29000	35000	44409.069	44409.069
18	우규민	삼성	7	10	0	0	0	27	25	133.0	⋯	60.6	5.21	1.48	4.95	4.98	2.14	70000	70000	73704.794	73704.794
19	임찬규	LG	6	10	0	0	0	27	26	124.1	⋯	71.3	4.63	3.15	4.81	4.79	2.04	11500	6500	14822.460	14822.460
20	손승락	롯데	1	3	37	0	5	61	0	62.0	⋯	89.9	2.18	3.91	3.69	3.37	1.82	70000	70000	71225.849	71225.849
22	윤희상	SK	6	7	0	0	0	23	22	120.0	⋯	63.1	6.00	1.52	5.13	5.22	1.80	13000	15000	23102.472	23102.472
23	원종현	NC	3	6	0	22	0	68	0	80.0	⋯	63.9	4.39	2.02	3.60	3.52	1.71	18500	14000	22358.400	22358.400
24	배영수	한화	7	8	0	0	0	25	25	128.0	⋯	66.4	5.06	2.47	5.10	5.21	1.68	50000	55000	57019.043	57019.043
25	박종훈	SK	12	7	0	1	0	29	28	151.1	⋯	75.3	4.10	4.31	5.38	5.55	1.62	20000	10000	21138.912	21138.912
26	이상화	KT	4	3	6	4	1	70	0	66.0	⋯	68.0	3.95	2.43	3.57	3.45	1.54	10000	4500	13605.103	13605.103
27	김진성	NC	10	6	0	15	2	69	0	89.2	⋯	76.1	3.61	3.20	4.30	3.92	1.47	23000	18000	33080.433	33080.433
28	이민호	NC	5	1	3	6	1	60	3	88.2	⋯	71.4	4.06	1.97	4.41	4.22	1.38	18800	16000	23738.251	23738.251
29	이재학	NC	5	7	0	0	0	28	23	119.0	⋯	65.4	5.67	1.04	5.53	5.35	1.31	19000	20000	21005.351	21005.351
30	김강률	두산	7	2	7	12	1	70	0	89.0	⋯	73.5	3.44	2.68	4.15	4.09	1.27	15000	6200	16907.230	16907.230
31	김재윤	KT	3	5	15	0	4	41	0	37.1	⋯	54.3	5.79	0.73	3.15	3.05	1.24	11000	9000	18149.465	18149.465
32	김원중	롯데	7	8	0	0	0	24	24	107.1	⋯	70.3	5.70	2.22	5.53	5.56	1.23	6300	3000	8022.277	8022.277
33	박진형	롯데	4	4	2	10	3	45	9	88.0	⋯	68.9	5.11	1.70	4.43	4.14	1.12	10500	6000	10555.543	10555.543
34	윤규진	한화	8	7	0	2	0	36	18	119.0	⋯	72.1	5.22	2.23	5.46	5.42	1.09	21000	18000	22860.982	22860.982
35	김재영	한화	5	7	0	0	1	20	15	85.1	⋯	67.8	4.54	1.60	5.00	5.23	1.06	5300	3000	9305.405	9305.405
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋱	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
123	정재원	한화	0	2	0	1	1	14	0	21.0	⋯	69.2	3.43	0.12	5.16	5.73	-0.12	4000	4000	2817.4227	2817.4227
124	김민우	한화	0	0	0	0	0	4	2	7.1	⋯	50.7	17.18	-0.52	7.83	8.32	-0.12	3600	3800	3075.9026	3075.9026
125	이현호	두산	1	0	0	0	0	24	2	30.0	⋯	65.3	5.70	-0.51	6.47	6.57	-0.16	5200	6000	3063.7755	3063.7755
126	권혁	한화	1	3	0	11	1	37	0	31.1	⋯	67.3	6.32	0.04	6.48	6.78	-0.16	45000	45000	36720.9933	36720.9933
127	배제성	KT	0	0	0	0	0	21	1	32.0	⋯	59.6	8.72	-0.10	6.39	6.59	-0.17	3000	2700	-294.7714	-294.7714
128	홍상삼	두산	1	1	0	0	0	11	2	17.0	⋯	53.0	7.94	-0.52	6.73	7.22	-0.18	9000	12500	10583.9599	10583.9599
129	이태양	한화	3	6	0	0	0	16	12	59.0	⋯	64.3	7.17	0.05	6.77	7.04	-0.18	7300	8300	3544.0763	3544.0763
130	김진우	KIA	2	6	0	0	1	14	8	36.1	⋯	65.3	7.93	-0.35	6.68	7.04	-0.19	6000	12000	7803.9704	7803.9704
131	이영하	두산	3	3	0	0	0	20	3	35.2	⋯	78.7	5.55	0.59	6.79	6.86	-0.19	4200	2700	2614.9313	2614.9313
132	최성영	NC	0	0	0	0	0	7	0	11.1	⋯	68.6	9.53	-0.26	9.29	9.48	-0.20	2900	2900	2236.5404	2236.5404
133	김동호	삼성	0	1	0	0	0	20	1	36.0	⋯	67.0	6.75	-0.07	5.46	5.96	-0.20	6000	5000	1648.8880	1648.8880
134	김윤동	KIA	7	4	11	6	6	65	1	80.1	⋯	75.0	4.59	1.89	5.54	5.53	-0.20	15000	4700	3977.8323	3977.8323
135	정인욱	삼성	1	4	0	0	0	9	7	32.0	⋯	52.5	9.84	-0.43	7.39	7.36	-0.20	5700	7200	3413.2033	3413.2033
136	송창식	한화	5	6	0	15	6	63	0	73.1	⋯	61.0	6.63	-0.74	5.68	5.59	-0.22	24000	22000	17310.9499	17310.9499
137	배재환	NC	0	1	0	0	0	3	1	8.0	⋯	82.1	9.00	-0.16	11.48	11.73	-0.23	3000	4000	3039.1933	3039.1933
138	이정민	롯데	3	1	0	2	1	24	0	26.2	⋯	71.4	5.40	0.19	6.47	6.83	-0.24	10000	15000	14080.6714	14080.6714
139	최동환	LG	1	2	1	5	2	35	0	38.0	⋯	71.1	5.68	-0.05	6.76	6.77	-0.24	6500	6000	1836.9171	1836.9171
140	이종혁	KT	2	0	0	0	0	16	0	19.0	⋯	67.0	6.63	-0.09	7.10	7.57	-0.25	3200	2700	2969.8441	2969.8441
141	홍성용	KT	0	2	0	1	0	37	1	39.0	⋯	68.3	6.23	0.25	6.40	6.63	-0.28	6800	6300	-360.1517	-360.1517
142	정영일	SK	0	0	0	0	0	9	0	8.0	⋯	47.3	10.12	-0.61	10.73	11.37	-0.30	3000	4000	2110.5317	2110.5317
143	김지용	LG	4	3	3	8	4	53	0	53.0	⋯	73.9	5.09	0.28	6.30	6.27	-0.38	9000	10000	5555.9129	5555.9129
144	최금강	NC	5	3	0	0	0	39	13	89.2	⋯	57.4	7.33	-0.27	6.31	6.58	-0.41	12500	14000	5459.6023	5459.6023
145	김범수	한화	0	4	0	0	0	15	5	31.0	⋯	66.4	8.71	-0.42	8.15	8.52	-0.42	3600	3300	-2975.1372	-2975.1372
146	이승현	삼성	2	0	0	0	0	30	0	31.2	⋯	81.9	5.12	0.31	8.03	8.03	-0.44	7000	6200	2468.8307	2468.8307
147	주권	KT	5	6	1	3	2	39	12	81.2	⋯	63.2	6.61	-0.02	6.33	6.54	-0.46	7600	7500	-176.0475	-176.0475
148	장민재	한화	2	5	0	0	2	33	5	62.2	⋯	56.9	7.76	-1.21	6.21	6.48	-0.47	7100	8100	853.4203	853.4203
149	정용운	KIA	3	2	0	0	0	25	11	59.1	⋯	65.4	5.92	0.39	6.41	6.77	-0.49	7500	3100	-4363.3153	-4363.3153
150	노경은	롯데	0	2	0	0	0	9	2	14.2	⋯	52.8	11.66	-0.83	8.03	8.29	-0.61	10000	16000	9199.8537	9199.8537
151	김승현	삼성	0	3	0	1	0	41	0	43.2	⋯	73.9	5.77	-0.40	6.87	6.95	-0.70	4000	2900	-6817.6168	-6817.6168
152	류희운	KT	4	4	0	0	0	24	14	81.0	⋯	65.3	7.67	-0.68	7.60	7.81	-1.01	4000	3000	-8729.6887	-8729.6887

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: (2 not defined because of singularities)
              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 ***
new_col             NA         NA      NA       NA    
new_data            NA         NA      NA       NA    
---
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 <- data.frame('승' = picher$"승",
                        WAR = picher$"WAR",
                        `경기` = picher$"경기",
                        `선발` = picher$"선발",
                        `연봉.2017.` = picher$"연봉.2017.")

X <- picher2[c('승', 'WAR', '경기', '선발', '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 
-7594.6 -1045.4   335.8   777.8  8330.4 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -291.41119  436.61649  -0.667 0.505870    
승           439.94566  149.96710   2.934 0.004065 ** 
WAR         1528.78519  392.59368   3.894 0.000168 ***
경기          43.60185   15.92552   2.738 0.007195 ** 
선발         -81.74551   51.55867  -1.585 0.115676    
연봉.2017.     0.88666    0.01366  64.889  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2315 on 112 degrees of freedom
Multiple R-squared:  0.9871,    Adjusted R-squared:  0.9865 
F-statistic:  1710 on 5 and 112 DF,  p-value: < 2.2e-16

y_pred <- predict(model2, newdata = X_test)

plot(model2)

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


    Shapiro-Wilk normality test

data:  resid(model2)
W = 0.93815, p-value = 3.734e-05

귀무가설 기각

library(lmtest)

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


    studentized Breusch-Pagan test

data:  model2
BP = 10.625, df = 5, p-value = 0.05934

잔차 이분산..

bptest(model2)


    studentized Breusch-Pagan test

data:  model2
BP = 10.625, df = 5, p-value = 0.05934

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)

sorted_df

A data.frame: 122 × 4
	선수명	연봉.2018.	new_data	연봉.2017.
	<chr>	<int>	<dbl>	<int>
5	레일리	111000	109876.101	85000
24	배영수	50000	57019.043	55000
41	안영명	35000	15797.183	20000
68	채병용	30000	27789.008	25000
17	류제국	29000	44409.069	35000
14	박세웅	25000	28683.805	10000
40	임창민	25000	25799.865	22500
56	박정진	25000	30415.693	33000
136	송창식	24000	17310.950	22000
27	김진성	23000	33080.433	18000
38	심창민	23000	23904.742	21000
34	윤규진	21000	22860.982	18000
25	박종훈	20000	21138.912	10000
44	심수창	20000	27181.633	25000
29	이재학	19000	21005.351	20000
43	진해수	19000	11268.437	11000
28	이민호	18800	23738.251	16000
23	원종현	18500	22358.400	14000
111	박희수	18500	16045.659	21000
9	함덕주	16000	33082.909	7000
15	백정현	15500	27341.043	10000
30	김강률	15000	16907.230	6200
60	권오준	15000	8522.143	10500
63	김사율	15000	20575.830	20000
134	김윤동	15000	3977.832	4700
71	임정우	14000	20886.198	22000
78	박정배	14000	8023.190	8000
13	임기영	13000	24736.432	3100
22	윤희상	13000	23102.472	15000
42	심동섭	13000	12386.757	11000
⋮	⋮	⋮	⋮	⋮
152	류희운	4000	-8729.6887	3000
79	황수범	3800	1852.9124	2700
124	김민우	3600	3075.9026	3800
145	김범수	3600	-2975.1372	3300
92	이형범	3500	2185.0132	2700
93	임현준	3500	3907.2282	3200
110	안성무	3500	3405.0519	2800
99	박치국	3400	1349.4896	2700
102	허건엽	3400	3970.3092	3300
105	고봉재	3300	5980.8705	4400
112	김시현	3300	1784.8028	2700
120	강장산	3300	1648.4704	3000
118	배민관	3200	3734.0896	3000
140	이종혁	3200	2969.8441	2700
70	최지광	3100	1628.4784	2700
73	박세진	3100	4256.9427	3000
101	박상원	3100	2038.7415	2700
81	김대유	3000	4539.1000	2700
84	손주영	3000	4606.7626	2700
87	김진영	3000	4822.4882	2700
109	서균	3000	2309.3920	2700
127	배제성	3000	-294.7714	2700
137	배재환	3000	3039.1933	4000
142	정영일	3000	2110.5317	4000
96	김도영	2900	4555.8119	2700
97	조근종	2900	4555.8119	2700
108	안규현	2900	4322.7670	2800
115	김종훈	2900	4161.9663	2800
83	장지훈	2800	4754.8256	2700
106	이수민	2800	4741.0808	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.