Ridge Regression의 장점
- 규제항을 통해 회귀계수를 “0”에 가깝게 추정한다.
- 회귀계수 추정치의 분산을 감소시켜
Training Dataset의 변화에도 회귀계수 추정치가 크게 변하지 않는다.
- 회귀계수 추정치의 분산을 감소시켜
Ridge Regression의 단점
- \(\lambda = \infty\)가 아닌 한 회귀계수를 정확하게 “0”으로 추정하지 못한다.
- 변수 선택을 수행할 수 없다.
- 예측변수가 많을 경우 해석이 어렵다.
실습 자료 : 유니버셜 은행의 고객 2,500명에 대한 자료(출처 : Data Mining for Business Intelligence, Shmueli et al. 2010)이며, 총 13개의 변수를 포함하고 있다. 이 자료에서 Target은
Personal Loan이다.
1. 데이터 불러오기
pacman::p_load("data.table",
"tidyverse",
"dplyr",
"ggplot2", "GGally",
"caret",
"glmnet") # For glmnet
UB <- fread("../Universal Bank_Main.csv") # 데이터 불러오기
UB %>%
as_tibble# A tibble: 2,500 × 14
ID Age Experience Income `ZIP Code` Family CCAvg Education
<int> <int> <int> <int> <int> <int> <dbl> <int>
1 1 25 1 49 91107 4 1.6 1
2 2 45 19 34 90089 3 1.5 1
3 3 39 15 11 94720 1 1 1
4 4 35 9 100 94112 1 2.7 2
5 5 35 8 45 91330 4 1 2
6 6 37 13 29 92121 4 0.4 2
7 7 53 27 72 91711 2 1.5 2
8 8 50 24 22 93943 1 0.3 3
9 9 35 10 81 90089 3 0.6 2
10 10 34 9 180 93023 1 8.9 3
# ℹ 2,490 more rows
# ℹ 6 more variables: Mortgage <int>, `Personal Loan` <int>,
# `Securities Account` <int>, `CD Account` <int>, Online <int>,
# CreditCard <int>2. 데이터 전처리 I
UB %<>%
data.frame() %>% # Data Frame 형태로 변환
mutate(Personal.Loan = ifelse(Personal.Loan == 1, "yes", "no")) %>% # Target을 문자형 변수로 변환
select(-1) # ID 변수 제거
# Convert to Factor
fac.col <- c("Family", "Education", "Securities.Account",
"CD.Account", "Online", "CreditCard",
# Target
"Personal.Loan")
UB <- UB %>%
mutate_at(fac.col, as.factor) # 범주형으로 변환
glimpse(UB) # 데이터 구조 확인Rows: 2,500
Columns: 13
$ Age <int> 25, 45, 39, 35, 35, 37, 53, 50, 35, 34, 6…
$ Experience <int> 1, 19, 15, 9, 8, 13, 27, 24, 10, 9, 39, 5…
$ Income <int> 49, 34, 11, 100, 45, 29, 72, 22, 81, 180,…
$ ZIP.Code <int> 91107, 90089, 94720, 94112, 91330, 92121,…
$ Family <fct> 4, 3, 1, 1, 4, 4, 2, 1, 3, 1, 4, 3, 2, 4,…
$ CCAvg <dbl> 1.6, 1.5, 1.0, 2.7, 1.0, 0.4, 1.5, 0.3, 0…
$ Education <fct> 1, 1, 1, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2,…
$ Mortgage <int> 0, 0, 0, 0, 0, 155, 0, 0, 104, 0, 0, 0, 0…
$ Personal.Loan <fct> no, no, no, no, no, no, no, no, no, yes, …
$ Securities.Account <fct> 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,…
$ CD.Account <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ Online <fct> 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1,…
$ CreditCard <fct> 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,…3. 데이터 탐색
ggpairs(UB,
columns = c("Age", "Experience", "Income", # 수치형 예측 변수
"ZIP.Code", "CCAvg", "Mortgage"),
aes(colour = Personal.Loan)) + # Target의 범주에 따라 색깔을 다르게 표현
theme_bw() 
ggpairs(UB,
columns = c("Age", "Experience", "Income", # 수치형 예측 변수
"ZIP.Code", "CCAvg", "Mortgage"),
aes(colour = Personal.Loan)) + # Target의 범주에 따라 색깔을 다르게 표현
scale_colour_manual(values = c("#00798c", "#d1495b")) + # 특정 색깔 지정
scale_fill_manual(values = c("#00798c", "#d1495b")) + # 특정 색깔 지정
theme_bw()
ggpairs(UB,
columns = c("Age", "Income", # 수치형 예측 변수
"Family", "Education"), # 범주형 예측 변수
aes(colour = Personal.Loan, alpha = 0.8)) + # Target의 범주에 따라 색깔을 다르게 표현
scale_colour_manual(values = c("#E69F00", "#56B4E9")) + # 특정 색깔 지정
scale_fill_manual(values = c("#E69F00", "#56B4E9")) + # 특정 색깔 지정
theme_bw()
4. 데이터 분할
# Partition (Training Dataset : Test Dataset = 7:3)
y <- UB$Personal.Loan # Target
set.seed(200)
ind <- createDataPartition(y, p = 0.7, list = T) # Index를 이용하여 7:3으로 분할
UB.trd <- UB[ind$Resample1,] # Training Dataset
UB.ted <- UB[-ind$Resample1,] # Test Dataset5. 데이터 전처리 II
# 1. Standardization
preProcValues <- preProcess(UB.trd,
method = c("center", "scale")) # Training Dataset에 대한 평균과 표준편차 계산
UB.trd <- predict(preProcValues, UB.trd) # 표준화 for Training Dataset
UB.ted <- predict(preProcValues, UB.ted) # 표준화 for Test Dataset
glimpse(UB.trd) # 데이터 구조 확인Rows: 1,751
Columns: 13
$ Age <dbl> -0.05431273, -0.57446728, -0.92123699, -0…
$ Experience <dbl> -0.12175295, -0.46882565, -0.98943471, -1…
$ Income <dbl> -0.85867297, -1.35649686, 0.56986515, -0.…
$ ZIP.Code <dbl> -1.75250883, 0.88354520, 0.53745994, -1.0…
$ Family <fct> 3, 1, 1, 4, 2, 1, 3, 1, 4, 3, 2, 4, 1, 4,…
$ CCAvg <dbl> -0.25119120, -0.53150921, 0.42157204, -0.…
$ Education <fct> 1, 1, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 1, 3,…
$ Mortgage <dbl> -0.5664192, -0.5664192, -0.5664192, -0.56…
$ Personal.Loan <fct> no, no, no, no, no, no, no, yes, no, no, …
$ Securities.Account <fct> 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0,…
$ CD.Account <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ Online <fct> 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0,…
$ CreditCard <fct> 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,…glimpse(UB.ted) # 데이터 구조 확인Rows: 749
Columns: 13
$ Age <dbl> -1.7881612, -0.7478521, 1.2460737, 0.8126…
$ Experience <dbl> -1.68358012, -0.64236200, 0.83269699, 0.6…
$ Income <dbl> -0.53400522, -0.96689556, -1.11840718, -1…
$ ZIP.Code <dbl> -1.17304370, -0.59585545, 1.07366441, 0.8…
$ Family <fct> 4, 4, 1, 1, 4, 1, 4, 4, 3, 3, 1, 3, 1, 4,…
$ CCAvg <dbl> -0.19512759, -0.86789083, -0.25119120, -0…
$ Education <fct> 1, 2, 3, 2, 2, 3, 3, 3, 3, 2, 1, 2, 1, 2,…
$ Mortgage <dbl> -0.5664192, 0.9609885, -0.5664192, -0.566…
$ Personal.Loan <fct> no, no, no, no, no, no, no, no, no, no, n…
$ Securities.Account <fct> 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0,…
$ CD.Account <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,…
$ Online <fct> 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1,…
$ CreditCard <fct> 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,…# 2. Convert Factor Var. into Dummy Var.
train.x <- model.matrix(Personal.Loan ~., # Personal.Loan은 Target으로 제외
UB.trd)[,-1] # [,-1] : 절편 제거
train.x Age Experience Income ZIP.Code Family2 Family3
2 -0.05431273 -0.12175295 -0.858672972 -1.75250883 0 1
3 -0.57446728 -0.46882565 -1.356496863 0.88354520 0 0
4 -0.92123699 -0.98943471 0.569865150 0.53745994 0 0
5 -0.92123699 -1.07620288 -0.620583285 -1.04610783 0 0
7 0.63922667 0.57239246 -0.036181326 -0.82923532 1 0
8 0.37914940 0.31208793 -1.118407176 0.44126189 0 0
9 -0.92123699 -0.90266653 0.158619327 -1.75250883 0 1
10 -1.00792941 -0.98943471 2.301426510 -0.08241975 0 0
11 1.67953578 1.61361058 0.678087735 0.87785301 0 0
12 -1.44139154 -1.33650741 -0.620583285 -1.64549562 0 1
13 0.20576455 0.22531976 0.872888388 -0.03517456 1 0
14 1.15938123 1.00623334 -0.728805870 0.99738903 0 0
15 1.85292063 1.78714693 0.829599354 -0.81215874 0 0
17 -0.66115971 -0.55559383 1.219200660 1.04861876 0 0
18 -0.31439001 -0.20852112 0.158619327 0.64731924 0 0
19 0.03237970 0.05178341 2.582805231 -0.89014177 1 0
22 0.98599638 0.57239246 -0.230981979 -1.74909351 0 1
23 -1.44139154 -1.33650741 -0.252626496 -1.64549562 0 0
24 -0.14100516 -0.20852112 -0.663872319 -1.05180002 1 0
25 -0.83454456 -0.81589836 1.695380034 1.33948976 1 0
26 -0.22769758 -0.12175295 -0.966895557 0.64731924 0 1
27 -0.48777486 -0.38205747 0.201908361 1.07935660 0 0
28 0.03237970 -0.03498477 1.825247136 -1.76673931 0 0
30 -0.66115971 -0.64236200 0.981110973 0.53290618 0 0
31 1.15938123 1.26653787 -0.837028455 -0.03517456 0 0
32 -0.48777486 -0.38205747 -0.966895557 0.54030603 0 0
33 0.63922667 0.65916064 -0.707161353 0.92965195 1 0
34 -1.35469911 -1.24973924 -1.204985244 -1.04610783 0 1
36 0.20576455 0.31208793 0.158619327 -0.29644616 0 1
37 1.15938123 1.26653787 1.024400007 0.88354520 0 0
38 0.46584182 0.39885611 -0.057825843 1.50627098 0 0
39 -0.31439001 -0.20852112 1.457290347 0.53859837 0 1
42 -1.00792941 -0.98943471 -0.295915530 0.54315213 0 1
43 -1.18131426 -1.16297106 1.262489694 -1.79235417 0 0
44 -0.57446728 -0.46882565 -0.620583285 1.39356558 0 0
45 0.03237970 -0.03498477 0.656443218 0.51070664 0 0
46 0.98599638 0.91946517 -0.469071666 0.88354520 0 0
48 -0.74785214 -0.72913018 2.604449748 -1.01764687 0 0
49 0.89930395 0.48562429 0.158619327 1.46813330 1 0
50 -0.48777486 -0.38205747 -0.534005217 -0.45241222 0 0
51 -1.18131426 -1.07620288 -1.421430414 -0.61179359 0 0
53 -1.35469911 -1.24973924 -0.036181326 0.47655348 0 0
54 0.37914940 0.48562429 2.517871680 -1.66371064 0 1
55 -1.44139154 -1.33650741 -0.642227802 1.50911708 0 0
56 -0.40108243 -0.29528930 1.414001313 0.48623021 1 0
58 0.89930395 0.91946517 1.240845177 1.39356558 1 0
59 -1.52808397 -1.59681194 0.418353531 0.51070664 1 0
60 -1.26800669 -1.33650741 2.474582646 -1.05180002 1 0
61 0.29245697 0.31208793 -0.750450387 -1.57320479 0 1
63 -0.31439001 -0.20852112 -1.118407176 -1.75250883 0 0
65 0.11907212 0.22531976 0.678087735 -1.78950808 1 0
66 1.15938123 1.26653787 1.240845177 -1.02903125 0 0
67 1.41945851 1.35330605 0.678087735 1.42430342 1 0
69 0.11907212 0.05178341 -0.295915530 0.13616041 0 1
71 -0.31439001 -0.20852112 0.894532905 -1.04326173 0 0
73 -0.14100516 -0.03498477 1.219200660 -0.66074644 0 0
74 -0.40108243 -0.38205747 0.245197395 0.81865421 0 0
75 -1.52808397 -1.51004376 1.327423245 0.82150031 1 0
77 1.07268880 1.00623334 -1.334852346 -1.05180002 0 1
78 0.03237970 -0.03498477 -0.966895557 -0.53950275 0 1
80 0.37914940 0.48562429 -1.183340727 0.88354520 1 0
81 1.24607365 1.35330605 -0.707161353 1.11920194 0 0
83 -0.40108243 -0.38205747 0.180263844 -0.37613685 0 0
84 -1.09462184 -0.98943471 -0.512360700 0.64731924 0 0
85 0.03237970 0.13855158 -1.204985244 -0.81842015 0 0
87 -0.48777486 -0.38205747 -0.685516836 0.75888620 0 0
89 1.67953578 1.78714693 -0.490716183 0.54030603 1 0
90 -1.78816124 -1.85711647 0.851243871 0.64618080 0 0
91 0.81261153 0.83269699 0.959466456 -1.64549562 0 0
93 -0.22769758 -0.12175295 -0.858672972 0.64731924 0 1
95 1.67953578 1.61361058 1.024400007 -0.31636884 0 0
97 -0.40108243 -0.46882565 0.136974810 1.05089564 0 0
98 0.72591910 0.65916064 1.890180687 -0.59585545 0 0
100 1.76622821 1.78714693 -1.269918795 -0.82923532 0 1
101 0.20576455 0.22531976 0.007107708 0.51924492 0 0
103 0.63922667 0.22531976 -0.642227802 0.22040485 0 1
106 -1.87485367 -1.77034829 -0.837028455 0.87443769 0 1
107 -0.22769758 -0.29528930 -0.101114877 -0.25660082 0 0
108 -0.31439001 -0.20852112 -0.663872319 -0.64366986 0 0
109 -1.09462184 -1.16297106 -0.901962006 1.12034038 0 0
110 -0.22769758 -0.29528930 -0.534005217 0.78222418 0 0
111 -0.40108243 -0.55559383 -1.399785897 -1.04610783 0 1
112 1.41945851 1.52684240 -0.620583285 0.55510573 0 0
113 -0.48777486 -0.46882565 0.180263844 -0.79280529 0 1
114 1.07268880 1.17976970 0.396709014 -0.26456989 1 0
115 -0.57446728 -0.55559383 -0.750450387 -0.46322738 0 1
117 0.72591910 0.74592882 -0.837028455 -0.19170983 0 0
118 1.07268880 1.09300152 -0.274271013 -0.19057140 1 0
122 0.55253425 0.48562429 -0.772094904 -0.82923532 0 1
125 -0.57446728 -0.46882565 0.093685776 -0.59585545 0 0
126 1.24607365 1.26653787 0.136974810 -1.06261518 0 1
127 -1.26800669 -1.33650741 0.894532905 -0.61008593 1 0
128 -1.00792941 -1.07620288 0.180263844 -0.29701538 0 0
129 -0.66115971 -0.55559383 0.007107708 -0.56113308 1 0
130 -0.40108243 -0.38205747 -0.079470360 -0.59016326 0 1
132 1.07268880 1.17976970 1.630446483 0.31432602 0 0
133 -1.26800669 -1.68358012 -0.490716183 -1.32502522 1 0
134 -1.35469911 -1.42327559 -0.750450387 -1.66371064 0 1
136 1.07268880 1.09300152 -0.620583285 -0.08981960 0 0
137 1.15938123 1.00623334 -0.534005217 1.06284924 0 0
138 0.29245697 0.39885611 1.175911626 1.07366441 1 0
139 1.15938123 1.17976970 -0.685516836 1.00194279 0 1
140 1.15938123 1.26653787 -1.204985244 0.07810006 0 0
141 0.46584182 0.39885611 -0.923606523 -1.66371064 1 0
142 -0.92123699 -0.81589836 -0.339204564 1.51594771 0 1
144 -1.78816124 -1.68358012 -0.425782632 0.54030603 0 0
147 0.03237970 -0.12175295 0.223552878 0.53176774 0 0
148 0.37914940 0.39885611 0.201908361 0.78222418 0 0
151 0.03237970 0.13855158 0.959466456 0.53461384 1 0
152 -1.70146882 -1.77034829 1.262489694 -0.19000218 0 1
154 1.24607365 1.35330605 -1.118407176 0.78734716 1 0
155 0.72591910 0.74592882 -0.339204564 -0.31636884 0 0
156 -1.87485367 -1.77034829 -0.295915530 0.81296202 0 0
158 -0.40108243 -0.29528930 0.201908361 0.48793787 0 0
161 -1.44139154 -1.77034829 1.305778728 1.50911708 0 0
162 1.33276608 1.26653787 0.136974810 1.07309519 1 0
163 -0.66115971 -0.72913018 -0.469071666 -1.78267745 0 0
164 -1.52808397 -1.42327559 -0.079470360 -1.16279776 0 0
165 0.63922667 0.57239246 0.396709014 1.11123287 1 0
167 -1.78816124 -1.68358012 -1.140051693 1.51367083 0 1
168 -1.09462184 -0.98943471 -1.096762659 0.64731924 0 1
171 -1.61477639 -1.68358012 1.392356796 -1.66086454 1 0
173 -0.66115971 -0.64236200 2.106625857 -0.25660082 1 0
178 -1.44139154 -1.51004376 -0.187692945 0.54884432 0 0
179 0.63922667 0.74592882 -1.075118142 1.50854786 0 0
181 0.46584182 0.57239246 -0.772094904 -1.57491244 1 0
183 -1.87485367 -1.77034829 1.327423245 1.11863272 0 0
184 -1.44139154 -1.51004376 1.608801966 -0.56625606 0 1
187 0.20576455 0.22531976 -0.620583285 1.39356558 0 0
188 0.03237970 0.05178341 1.846891653 0.64731924 0 1
191 1.24607365 1.35330605 0.418353531 -0.36816778 0 0
192 0.46584182 0.39885611 -0.966895557 -1.57320479 0 0
194 0.20576455 0.31208793 -1.140051693 -0.02834393 0 0
196 -1.00792941 -0.90266653 -1.313207829 0.80214686 0 0
197 0.20576455 0.31208793 1.976758755 0.13616041 0 0
198 0.81261153 0.91946517 -1.399785897 -1.03756954 0 0
199 -1.61477639 -1.51004376 -0.317560047 0.54372135 0 0
203 -1.35469911 -1.51004376 -0.122759394 0.64788846 0 0
204 1.07268880 1.17976970 -0.187692945 1.46813330 0 0
206 -0.66115971 -0.72913018 0.375064497 1.39356558 0 0
207 0.29245697 0.39885611 -0.923606523 -1.03187735 0 0
209 -0.48777486 -0.38205747 -0.014536809 0.53632150 0 0
210 1.59284336 1.61361058 2.128270374 0.87614535 0 0
211 0.46584182 0.48562429 -1.161696210 -0.59016326 1 0
212 -0.14100516 -0.20852112 -0.404138115 0.88354520 0 0
213 0.03237970 0.13855158 -0.101114877 -0.89014177 1 0
214 0.98599638 1.09300152 1.760313585 -1.04838470 0 0
215 0.72591910 0.65916064 0.439998048 -1.63752655 0 0
216 -0.66115971 -0.55559383 0.396709014 1.50854786 1 0
220 0.89930395 0.83269699 -0.274271013 0.87614535 0 0
222 -0.05431273 -0.12175295 0.201908361 1.07195675 1 0
223 -1.70146882 -1.59681194 0.656443218 0.64788846 0 1
224 0.81261153 0.39885611 -0.707161353 1.05089564 0 1
226 -0.57446728 -0.64236200 0.418353531 0.88354520 0 0
227 -1.87485367 -1.85711647 -0.750450387 0.52209102 1 0
228 0.11907212 0.22531976 1.608801966 0.78734716 1 0
229 0.11907212 0.13855158 -0.447427149 -0.27936959 0 0
230 0.20576455 0.31208793 -0.057825843 -0.02891315 1 0
232 -0.92123699 -0.90266653 -0.274271013 0.64675002 0 0
233 0.03237970 -0.12175295 -0.772094904 0.54315213 0 1
234 1.41945851 1.44007422 -0.339204564 -1.05180002 0 0
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1785 0.72591910 0.74592882 0.981110973 -1.03187735 0 1
1786 -1.44139154 -1.51004376 2.517871680 0.51924492 1 0
1788 -1.18131426 -1.24973924 -0.642227802 0.81979265 0 0
1789 -0.66115971 -0.64236200 -1.096762659 -1.16792073 0 0
1790 -0.14100516 -0.03498477 2.106625857 -1.04610783 0 0
1791 -0.14100516 -0.03498477 -0.663872319 -0.59414780 0 0
1792 0.20576455 0.13855158 1.414001313 0.64959612 0 0
1794 -0.92123699 -0.98943471 0.851243871 0.81296202 0 1
1798 -0.92123699 -0.90266653 1.500579381 -1.02618515 0 0
1799 -0.14100516 -0.03498477 2.409649095 0.52266024 0 1
1801 0.98599638 1.09300152 -0.620583285 0.51924492 0 1
1803 -1.44139154 -1.51004376 1.024400007 -0.20594031 1 0
1804 1.07268880 1.00623334 -0.317560047 0.78222418 0 0
1805 -0.48777486 -0.38205747 -0.209337462 -0.28847710 0 0
1806 0.46584182 0.48562429 -1.269918795 -0.45241222 1 0
1807 1.33276608 1.35330605 -1.378141380 -1.38194714 0 0
1808 0.03237970 -0.03498477 -0.274271013 -1.78267745 1 0
1809 0.81261153 0.91946517 -0.512360700 -0.08981960 0 0
1810 -0.92123699 -0.90266653 0.115330293 1.06854143 0 0
1812 -1.52808397 -1.51004376 -1.356496863 0.77767043 0 0
1814 1.33276608 1.35330605 -0.404138115 -1.78438510 0 1
1815 0.20576455 0.13855158 0.115330293 1.46813330 0 1
1817 -0.05431273 -0.12175295 0.375064497 -0.45241222 1 0
1818 -0.83454456 -0.81589836 -1.399785897 0.81751577 0 0
1819 -0.05431273 -0.03498477 -0.252626496 1.50854786 1 0
1820 1.24607365 1.17976970 -0.317560047 0.53632150 0 0
1821 0.11907212 0.13855158 -1.053473625 -1.57320479 0 0
1822 -1.18131426 -1.16297106 -0.425782632 1.61669950 0 0
1823 0.20576455 0.22531976 0.829599354 -0.08754272 0 0
1824 -1.09462184 -1.07620288 1.110978075 -1.05180002 0 0
1825 0.29245697 0.22531976 2.604449748 0.48623021 0 0
1826 0.89930395 1.00623334 1.890180687 0.88354520 0 0
1827 1.15938123 1.09300152 -0.837028455 -1.17418214 0 0
1828 0.89930395 0.83269699 0.851243871 -0.26400067 1 0
1829 -1.35469911 -1.42327559 -1.053473625 -0.59471701 1 0
1831 -0.66115971 -0.64236200 0.981110973 0.79873154 1 0
1833 0.72591910 0.74592882 0.115330293 -1.04610783 0 0
1834 -1.00792941 -0.98943471 2.258137476 0.64618080 0 0
1835 -0.40108243 -0.38205747 -1.096762659 0.55510573 1 0
1836 0.11907212 0.22531976 2.106625857 0.78450106 1 0
1837 -0.14100516 -0.12175295 0.007107708 -1.77983135 0 0
1839 -1.26800669 -1.16297106 0.548220633 0.88354520 0 0
1840 -1.52808397 -1.59681194 -0.663872319 1.39356558 0 0
1842 -0.31439001 -0.29528930 0.375064497 0.80556217 0 0
1844 -1.35469911 -1.24973924 1.738669068 -1.67224892 0 0
1845 1.67953578 1.70037875 -1.140051693 -0.25660082 0 1
1846 -0.22769758 -0.20852112 -0.187692945 -0.05851255 1 0
1847 0.89930395 1.00623334 -1.269918795 -1.75250883 0 0
1852 -1.00792941 -1.07620288 -0.295915530 0.48224568 0 0
1854 0.46584182 0.39885611 -0.295915530 -1.57491244 0 0
1855 0.55253425 0.39885611 -0.707161353 1.27232190 0 1
1856 1.67953578 1.61361058 -0.945251040 0.64675002 0 1
1857 0.46584182 0.31208793 -1.140051693 1.05089564 1 0
1858 -0.74785214 -0.64236200 0.678087735 0.51127585 0 0
1860 1.85292063 1.78714693 -1.161696210 -0.81215874 1 0
1861 -1.35469911 -1.24973924 2.279781993 -1.17532058 0 1
1862 1.41945851 1.52684240 1.890180687 -1.64720328 0 0
1863 -0.31439001 -0.29528930 0.180263844 1.39356558 0 0
1864 0.20576455 0.13855158 -0.663872319 0.80840827 0 0
1865 1.33276608 1.35330605 -0.274271013 -0.60610140 1 0
1866 -0.83454456 -1.24973924 0.353419980 -1.03927719 0 0
1867 0.20576455 0.31208793 0.353419980 0.77140902 0 0
1868 1.67953578 1.61361058 -1.140051693 0.78848560 1 0
1869 -1.78816124 -1.68358012 0.959466456 -0.19057140 0 0
1871 1.50615093 1.44007422 0.786310320 1.06114158 0 0
1872 -1.26800669 -1.33650741 0.548220633 0.51070664 0 0
1873 -0.22769758 -0.29528930 0.526576116 0.70253350 0 1
1876 -1.61477639 -1.51004376 0.829599354 -1.76560087 0 1
1877 1.41945851 1.52684240 1.067689041 -1.68363331 0 0
1878 0.46584182 0.31208793 0.093685776 -1.78210823 0 0
1880 0.89930395 0.83269699 0.093685776 -1.57491244 0 1
1882 0.03237970 -0.12175295 0.180263844 -1.02618515 0 1
1889 -0.83454456 -0.90266653 0.418353531 0.64731924 0 0
1890 0.89930395 0.83269699 0.807954837 -0.03517456 0 0
1891 0.55253425 0.57239246 2.388004578 -1.44456125 0 0
1892 -0.31439001 -0.20852112 -0.512360700 1.11464819 0 0
1893 0.81261153 0.83269699 -0.404138115 0.53632150 0 1
1894 0.29245697 0.31208793 -1.313207829 0.81979265 0 0
1897 -1.18131426 -1.16297106 0.201908361 0.64675002 0 0
1898 0.72591910 0.74592882 0.526576116 -0.05851255 0 0
1899 0.37914940 0.31208793 -0.663872319 1.40153465 0 0
1900 1.15938123 1.09300152 -0.858672972 0.53916759 0 0
1901 1.33276608 1.35330605 -1.378141380 -1.02618515 0 0
1902 -0.22769758 -0.12175295 2.755961367 0.64731924 1 0
1905 -0.66115971 -0.55559383 0.375064497 1.07707972 1 0
1907 -0.31439001 -0.29528930 0.526576116 -0.17178716 1 0
1909 0.37914940 0.48562429 -1.118407176 -0.64366986 0 0
1910 0.89930395 0.83269699 0.591509667 -1.77584682 0 1
1912 1.24607365 1.26653787 -0.469071666 0.87728379 0 1
1914 0.98599638 1.09300152 1.305778728 -0.60211686 0 0
1917 0.98599638 1.00623334 -0.209337462 1.12147882 0 1
1918 1.41945851 1.00623334 -0.447427149 1.61271497 0 0
1919 -0.57446728 -0.98943471 0.959466456 0.22040485 1 0
1920 -0.66115971 -0.64236200 -1.183340727 -0.62545485 1 0
1921 0.72591910 0.65916064 -0.923606523 -0.59073248 1 0
1922 -0.05431273 0.05178341 -0.230981979 1.39641168 0 0
1923 -0.57446728 -0.46882565 -1.053473625 -0.08241975 0 0
1925 1.41945851 1.52684240 0.093685776 -0.65960800 0 0
1926 -0.22769758 -0.12175295 0.158619327 -1.66371064 0 0
1927 -1.35469911 -1.24973924 -0.707161353 -1.74909351 0 0
1931 0.89930395 0.74592882 -0.490716183 0.51924492 0 1
1932 -1.52808397 -1.59681194 1.435645830 -0.59528623 1 0
1933 1.59284336 1.61361058 -0.014536809 -1.76161634 0 1
1934 1.50615093 1.61361058 -0.728805870 -1.05692299 0 0
1935 -0.14100516 -0.03498477 -0.101114877 1.50627098 0 0
1936 -1.00792941 -0.98943471 2.539516197 0.52266024 0 0
1937 0.37914940 0.31208793 0.180263844 -1.63752655 0 1
1938 0.46584182 0.39885611 2.323071027 1.07195675 0 0
1941 0.98599638 1.09300152 -0.404138115 -0.30612289 0 0
1942 -0.22769758 -0.12175295 -0.339204564 1.21767686 1 0
1943 1.33276608 1.35330605 -0.966895557 -1.68363331 1 0
1944 0.29245697 0.22531976 -0.750450387 1.33948976 0 0
1945 0.55253425 0.65916064 -0.750450387 -1.74909351 0 1
1946 0.98599638 1.09300152 -0.945251040 -0.03517456 0 1
1947 0.63922667 0.22531976 -0.339204564 0.88354520 0 0
1948 0.55253425 0.65916064 -0.252626496 0.53689072 0 0
1949 -0.57446728 -0.46882565 -0.252626496 0.44809253 0 0
1950 1.07268880 1.17976970 -1.183340727 -1.51628287 0 0
1951 -0.83454456 -0.72913018 -0.772094904 0.53575228 0 0
1952 -0.05431273 0.05178341 0.223552878 0.78677794 0 0
1953 -1.35469911 -1.33650741 0.093685776 -0.64366986 0 0
1954 0.29245697 0.39885611 -1.118407176 -1.77015462 0 0
1955 -0.14100516 -0.03498477 0.158619327 -1.66371064 0 0
1956 -0.22769758 -0.29528930 -0.901962006 -1.57491244 0 1
1957 -0.31439001 -0.20852112 0.331775463 0.78051653 0 0
1958 -1.44139154 -1.42327559 1.024400007 -1.78723120 1 0
1959 -1.52808397 -1.59681194 -0.685516836 1.47667159 0 0
1960 0.37914940 0.31208793 1.219200660 1.51708615 0 0
1961 -0.14100516 -0.12175295 -0.945251040 1.39356558 0 0
1962 0.55253425 0.48562429 0.872888388 0.64675002 0 0
1964 1.41945851 1.52684240 -0.512360700 0.78051653 1 0
1966 -0.05431273 -0.03498477 0.439998048 -1.74909351 0 1
1969 0.72591910 0.31208793 -0.534005217 -0.77800559 0 0
1972 -0.31439001 -0.29528930 -0.036181326 1.39356558 0 0
1973 -1.52808397 -1.59681194 0.872888388 0.81865421 0 0
1974 0.11907212 0.13855158 -1.356496863 -0.55544089 1 0
1976 -1.44139154 -1.51004376 0.851243871 0.54884432 1 0
1977 -0.57446728 -0.64236200 0.136974810 1.39356558 1 0
1979 -0.74785214 -0.81589836 -0.901962006 0.82206953 1 0
1983 1.07268880 1.09300152 -1.204985244 0.87273003 0 1
1985 -1.70146882 -1.68358012 -0.404138115 -0.30612289 0 0
1987 -0.31439001 -0.29528930 0.872888388 -1.76617009 1 0
1988 0.89930395 0.91946517 -0.469071666 0.54087525 0 1
1989 0.55253425 0.65916064 -1.204985244 -1.06261518 0 0
1992 0.03237970 0.13855158 -0.945251040 -1.37796261 0 1
1993 0.55253425 0.65916064 -0.772094904 0.64561158 1 0
1994 -1.35469911 -1.33650741 1.046044524 0.78393184 1 0
1995 -1.18131426 -1.07620288 2.366360061 0.51924492 0 0
1996 -0.92123699 -0.81589836 -0.707161353 0.88354520 0 0
1997 0.29245697 0.31208793 -0.772094904 0.64731924 0 0
1999 0.89930395 1.00623334 0.634798701 0.53689072 0 1
2000 0.20576455 0.13855158 0.136974810 0.43955424 1 0
2001 -1.52808397 -1.59681194 -1.118407176 1.42430342 0 0
2004 -0.14100516 -0.03498477 1.089333558 -1.64549562 0 0
2005 -1.35469911 -1.42327559 -0.642227802 -0.26400067 0 0
2007 1.59284336 1.61361058 0.028752225 0.88354520 0 0
2009 1.50615093 1.52684240 -0.923606523 -0.64366986 0 0
2010 -1.78816124 -1.77034829 0.548220633 -0.24635488 0 0
2014 -0.48777486 -0.46882565 -0.469071666 -0.27140052 0 1
2015 0.29245697 -0.12175295 2.063336823 1.07366441 0 1
2016 -1.35469911 -1.33650741 1.457290347 1.46813330 0 0
2017 -0.40108243 -0.29528930 0.418353531 -0.18943296 0 0
2019 1.50615093 1.61361058 1.868536170 -1.75250883 1 0
2021 1.15938123 1.17976970 -0.880317489 0.64618080 0 1
2026 0.11907212 -0.03498477 0.115330293 0.88354520 0 1
2029 -0.31439001 -0.29528930 -1.399785897 -0.82980454 1 0
2032 1.24607365 1.26653787 0.136974810 0.81979265 0 1
2033 1.41945851 1.44007422 -0.901962006 -1.65175703 0 1
2035 1.15938123 1.09300152 0.375064497 -0.19740203 0 0
2036 -0.83454456 -0.90266653 -0.966895557 -0.05851255 0 0
2037 0.03237970 -0.12175295 -1.183340727 0.64731924 0 1
2039 0.37914940 0.31208793 1.652091000 0.78734716 0 0
2042 -0.05431273 -0.03498477 2.301426510 1.27232190 0 1
2043 -0.40108243 -0.29528930 1.024400007 0.53176774 0 0
2044 0.98599638 1.00623334 -1.053473625 -1.77527760 1 0
2045 0.46584182 0.39885611 0.613154184 -0.27936959 0 0
2048 1.50615093 1.52684240 1.305778728 -1.43886906 0 1
2050 -0.22769758 -0.20852112 0.439998048 -0.25660082 0 0
2052 -1.00792941 -1.07620288 -0.772094904 -1.79292339 0 0
2054 1.07268880 1.00623334 0.245197395 -0.60211686 1 0
2056 0.29245697 0.22531976 -1.053473625 -1.64720328 0 0
2058 -0.74785214 -0.72913018 1.110978075 -0.80475889 1 0
2059 -1.09462184 -1.16297106 -1.204985244 -0.61179359 0 0
2060 -1.52808397 -1.51004376 2.149914891 -0.59585545 1 0
2061 0.72591910 0.74592882 -0.858672972 -0.61179359 0 0
2062 1.50615093 1.52684240 1.846891653 0.44524643 0 0
2063 0.98599638 0.91946517 -0.404138115 -0.36816778 0 1
2064 0.89930395 0.83269699 -0.901962006 0.51924492 1 0
2065 0.72591910 0.74592882 -0.187692945 0.78393184 0 0
2066 -1.44139154 -1.33650741 0.201908361 -0.46322738 0 1
2067 -0.40108243 -0.38205747 -0.945251040 1.50627098 1 0
2068 1.07268880 1.00623334 2.301426510 -0.79565139 0 0
2069 1.33276608 1.44007422 -1.313207829 -1.78950808 1 0
2071 1.41945851 1.44007422 0.461642565 -1.17304370 0 1
2072 0.55253425 0.65916064 0.201908361 0.87500691 0 0
2075 0.55253425 0.57239246 0.158619327 -0.69774569 0 0
2077 0.29245697 0.22531976 0.981110973 -1.21687358 0 0
2078 -1.00792941 -0.98943471 1.868536170 0.53518306 0 0
2079 -0.92123699 -0.81589836 -1.140051693 1.50627098 1 0
2080 -1.70146882 -1.59681194 -0.728805870 0.54884432 0 0
2081 1.67953578 1.70037875 -0.101114877 -0.83208141 0 0
2082 0.55253425 0.57239246 -0.620583285 1.04634188 0 0
2083 -1.18131426 -1.16297106 -0.404138115 -1.06261518 0 0
2084 -1.26800669 -1.16297106 -0.772094904 0.48793787 0 0
2087 -0.83454456 -0.72913018 0.223552878 -1.63752655 0 0
2088 0.46584182 0.57239246 2.474582646 0.64731924 1 0
2091 0.37914940 0.39885611 0.115330293 1.05601861 0 0
2092 -1.26800669 -1.42327559 -0.707161353 -1.02903125 0 0
2093 0.63922667 0.22531976 -1.183340727 -0.28164646 0 0
2094 0.20576455 0.22531976 0.028752225 0.53689072 0 0
2095 0.98599638 0.91946517 -0.209337462 -1.78950808 0 1
2096 0.11907212 0.05178341 2.171559408 0.48793787 0 0
2098 -0.74785214 -0.81589836 -1.291563312 -1.38194714 0 1
2099 1.15938123 1.26653787 0.439998048 -1.75250883 0 0
2103 -1.78816124 -1.85711647 0.158619327 -0.29644616 1 0
2104 -0.74785214 -0.64236200 1.717024551 -1.44456125 1 0
2105 -0.48777486 -0.55559383 -0.339204564 -1.66371064 0 0
2108 -0.40108243 -0.29528930 0.245197395 -1.63752655 0 0
2110 0.11907212 0.22531976 2.258137476 -0.08754272 0 0
2112 1.24607365 1.17976970 -0.728805870 0.53347540 0 0
2113 -1.61477639 -1.59681194 0.634798701 -0.02891315 0 0
2114 0.98599638 1.09300152 -1.053473625 -0.62830095 1 0
2116 0.98599638 0.91946517 -0.945251040 1.08277191 0 1
2117 -0.14100516 -0.29528930 -0.079470360 0.99738903 0 1
2118 -1.26800669 -1.16297106 -1.269918795 -1.01764687 0 1
2119 -1.26800669 -1.33650741 1.110978075 -1.05180002 1 0
2120 -0.57446728 -0.64236200 -0.512360700 0.99909669 0 1
2121 -0.40108243 -0.29528930 -0.642227802 -0.03517456 0 0
2122 -0.40108243 -0.29528930 -0.772094904 -0.56113308 0 0
2123 0.81261153 0.74592882 -0.209337462 0.15323699 0 1
2124 -1.52808397 -1.59681194 -1.399785897 1.05089564 0 0
2125 -0.92123699 -0.98943471 -0.642227802 -0.63399314 0 1
2127 -0.14100516 -0.12175295 0.201908361 -0.59585545 0 0
2129 1.67953578 1.70037875 -0.728805870 0.53290618 0 0
2130 -0.92123699 -0.90266653 -0.339204564 -0.80475889 0 0
2131 0.81261153 0.91946517 0.007107708 0.81922343 0 1
2132 0.81261153 0.91946517 -1.269918795 1.46813330 0 0
2133 1.15938123 1.26653787 -1.356496863 1.01389639 1 0
2134 -0.57446728 -0.46882565 -0.707161353 1.06284924 0 0
2136 -0.05431273 -0.46882565 -0.988540074 1.06512612 0 0
2141 0.63922667 0.57239246 0.331775463 -0.59073248 0 0
2143 0.81261153 0.91946517 -0.252626496 0.44126189 0 0
2145 -1.09462184 -1.24973924 2.041692306 0.88354520 0 1
2146 0.98599638 1.00623334 -0.728805870 0.88354520 0 1
2147 -1.61477639 -1.51004376 -0.945251040 -0.03403612 0 0
2149 0.72591910 0.83269699 -0.339204564 -0.66074644 1 0
2151 1.41945851 1.52684240 -0.425782632 -1.05180002 0 0
2152 -0.40108243 -0.38205747 -1.183340727 -0.81842015 1 0
2154 -0.48777486 -0.55559383 1.067689041 -1.77983135 0 0
2156 1.41945851 1.52684240 1.738669068 0.64731924 0 0
2157 -0.92123699 -0.81589836 0.418353531 -1.37796261 1 0
2159 0.37914940 0.39885611 0.201908361 0.88354520 0 0
2160 1.33276608 1.26653787 0.548220633 0.52209102 0 0
2162 0.55253425 0.65916064 -0.772094904 0.54827510 0 0
2163 -0.57446728 -0.64236200 0.007107708 1.04748032 0 1
2165 -1.61477639 -1.51004376 0.656443218 -0.66074644 1 0
2166 -1.61477639 -1.77034829 -0.772094904 1.57173119 0 0
2167 -1.18131426 -1.07620288 -1.053473625 0.20275906 0 1
2169 0.81261153 0.74592882 -0.209337462 -0.05965098 0 0
2170 0.55253425 0.57239246 -0.945251040 0.64731924 1 0
2171 -0.57446728 -0.64236200 -0.469071666 1.06512612 0 1
2172 -0.92123699 -0.81589836 -0.685516836 -0.03403612 0 0
2173 -0.57446728 -0.46882565 0.115330293 -0.64879284 1 0
2175 -1.35469911 -1.33650741 1.067689041 1.38730417 1 0
2176 -0.74785214 -0.72913018 1.868536170 0.64731924 1 0
2177 -0.40108243 -0.55559383 -0.490716183 -1.05180002 0 1
2180 0.29245697 0.22531976 -0.122759394 -1.78950808 0 0
2181 1.07268880 1.09300152 -0.685516836 -1.01764687 1 0
2182 -0.05431273 -0.46882565 -0.901962006 0.55510573 0 0
2183 -0.48777486 -0.55559383 -1.118407176 0.79588544 1 0
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1964 0 -0.47544561 0 0 -0.5664192
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1969 0 -0.30725480 0 1 -0.5664192
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1973 1 0.08519042 0 1 -0.5664192
1974 0 -1.09214524 0 0 0.2022118
1976 0 -0.98001804 0 0 -0.5664192
1977 0 -0.08300039 0 0 -0.5664192
1979 0 -0.30725480 0 1 -0.5664192
1983 0 -1.03608164 1 0 0.5175476
1985 1 -0.13906399 1 0 1.1580734
1987 0 -0.86789083 0 0 -0.5664192
1988 0 0.02912682 1 0 -0.5664192
1989 0 -0.92395443 0 0 0.6160900
1992 0 -0.81182723 0 0 -0.5664192
1993 0 -0.64363642 0 0 -0.5664192
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1995 0 2.27167094 0 0 -0.5664192
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1997 0 -0.30725480 0 1 -0.5664192
1999 0 1.15039888 0 1 -0.5664192
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1872 0 0 0 0
1873 0 0 0 0
1876 1 0 1 0
1877 0 0 0 0
1878 0 0 1 0
1880 0 0 0 0
1882 0 0 0 0
1889 0 0 1 0
1890 1 1 1 0
1891 0 0 0 0
1892 0 0 0 0
1893 0 0 0 1
1894 1 0 0 0
1897 1 0 0 1
1898 0 0 0 0
1899 0 0 1 0
1900 0 0 1 0
1901 0 0 1 0
1902 1 0 1 0
1905 0 0 1 0
1907 0 0 1 0
1909 0 0 1 0
1910 0 0 0 1
1912 0 0 0 0
1914 0 0 1 0
1917 0 0 1 0
1918 0 0 0 0
1919 0 1 1 1
1920 0 0 0 1
1921 0 0 0 0
1922 0 0 1 1
1923 0 0 0 0
1925 0 0 0 0
1926 0 0 1 0
1927 0 0 1 0
1931 0 0 1 0
1932 0 0 1 0
1933 0 0 0 0
1934 0 0 1 0
1935 0 0 1 1
1936 0 1 1 1
1937 0 0 1 0
1938 1 1 1 0
1941 0 0 1 0
1942 0 0 1 0
1943 0 0 1 0
1944 0 0 0 0
1945 0 1 1 1
1946 1 0 1 0
1947 0 0 1 1
1948 0 0 1 0
1949 0 0 0 0
1950 0 0 0 0
1951 0 0 0 0
1952 0 0 1 1
1953 0 0 1 0
1954 0 0 1 0
1955 0 0 1 0
1956 0 0 1 0
1957 0 0 0 0
1958 0 0 1 0
1959 0 0 1 1
1960 0 0 0 0
1961 0 0 1 0
1962 0 0 0 0
1964 0 0 0 1
1966 0 0 1 0
1969 0 0 1 0
1972 0 0 0 1
1973 0 0 1 0
1974 0 0 0 0
1976 0 0 1 1
1977 0 0 1 0
1979 1 0 1 0
1983 0 0 1 0
1985 0 0 1 0
1987 0 0 0 0
1988 1 1 1 1
1989 0 0 1 0
1992 0 0 0 0
1993 0 0 0 1
1994 0 0 0 0
1995 0 0 0 0
1996 0 0 0 0
1997 0 0 0 0
1999 0 0 0 0
2000 0 0 1 0
2001 0 0 1 0
2004 0 0 1 1
2005 0 0 0 0
2007 0 1 1 1
2009 0 0 1 0
2010 0 0 0 0
2014 0 0 1 0
2015 0 1 0 1
2016 0 0 1 0
2017 0 0 0 0
2019 0 0 1 1
2021 1 0 0 0
2026 1 0 0 0
2029 0 0 0 0
2032 0 0 1 0
2033 1 0 0 1
2035 0 0 0 0
2036 0 0 1 1
2037 0 0 1 0
2039 0 0 1 1
2042 0 0 0 0
2043 0 0 1 0
2044 0 0 1 1
2045 0 0 1 0
2048 0 0 0 1
2050 0 0 1 0
2052 0 0 0 0
2054 1 1 1 1
2056 0 0 1 0
2058 0 0 1 1
2059 0 0 0 0
2060 0 0 1 0
2061 0 0 1 1
2062 0 0 0 0
2063 0 1 1 1
2064 0 0 1 0
2065 0 0 0 1
2066 0 0 1 1
2067 0 0 0 1
2068 0 0 0 1
2069 0 0 1 0
2071 0 0 0 0
2072 0 0 1 0
2075 0 0 0 1
2077 0 0 0 0
2078 0 0 0 1
2079 0 0 0 0
2080 0 0 1 0
2081 0 0 1 0
2082 0 0 0 0
2083 0 0 1 0
2084 0 0 1 0
2087 0 0 1 1
2088 0 0 1 0
2091 0 0 0 1
2092 1 0 1 0
2093 0 0 1 0
2094 0 0 1 1
2095 0 0 0 1
2096 0 0 0 0
2098 0 0 1 0
2099 0 0 0 0
2103 0 0 1 1
2104 0 0 1 1
2105 0 0 1 0
2108 0 0 0 0
2110 0 0 0 0
2112 0 0 1 0
2113 0 0 1 0
2114 0 0 1 0
2116 0 0 0 0
2117 0 0 0 0
2118 0 0 1 0
2119 0 0 1 1
2120 0 0 0 0
2121 0 0 1 0
2122 0 0 0 1
2123 0 0 0 1
2124 0 0 1 0
2125 0 0 0 0
2127 0 0 0 0
2129 0 0 0 0
2130 0 0 0 0
2131 0 0 0 1
2132 0 0 0 0
2133 0 0 0 1
2134 0 0 1 0
2136 1 0 0 0
2141 1 0 1 0
2143 0 0 1 0
2145 1 1 1 0
2146 0 0 1 1
2147 0 0 0 0
2149 0 0 0 0
2151 1 0 0 1
2152 0 0 0 0
2154 0 0 1 0
2156 0 0 1 0
2157 0 0 1 1
2159 0 0 0 1
2160 0 0 0 1
2162 0 0 1 1
2163 0 0 1 0
2165 1 0 1 0
2166 0 0 1 0
2167 0 0 1 1
2169 0 0 1 0
2170 0 0 1 1
2171 1 0 0 1
2172 0 0 1 0
2173 0 0 0 0
2175 0 0 1 0
2176 0 0 0 0
2177 0 0 1 0
2180 0 0 0 0
2181 0 0 1 0
2182 0 0 1 0
2183 0 0 0 0
2184 0 0 1 1
2186 0 0 1 1
2187 0 0 1 0
2188 0 0 0 0
2189 0 0 1 1
2190 0 0 1 1
2191 1 0 0 1
2192 0 0 1 0
2193 0 0 0 1
2194 0 0 1 0
2197 0 0 1 0
2199 0 0 1 0
2202 0 0 0 0
2203 0 0 1 0
2205 0 0 0 0
2206 0 0 0 0
2207 0 0 0 0
2208 0 0 1 0
2209 1 0 1 0
2210 0 0 0 0
2211 0 0 0 0
2212 0 0 1 1
2214 0 0 0 0
2215 0 0 1 1
2216 0 0 1 0
2217 0 0 0 0
2218 0 1 1 0
2219 0 0 0 0
2220 0 0 1 0
2223 0 0 1 0
2224 1 0 0 0
2225 0 0 1 0
2226 0 0 0 0
2227 0 0 1 0
2228 0 0 1 1
2230 0 0 1 1
2232 1 0 1 0
2233 0 0 1 0
2234 0 0 1 0
2235 0 0 1 0
2236 0 0 1 1
2237 0 0 1 0
2238 0 0 1 1
2239 0 0 1 0
2240 1 0 0 0
2241 1 0 0 0
2243 1 0 1 0
2244 0 0 1 1
2245 0 0 0 0
2246 0 0 0 1
2247 0 0 0 0
2248 0 0 0 0
2249 0 0 1 0
2250 0 0 1 0
2251 0 0 1 0
2252 0 0 0 0
2253 0 0 1 0
2254 0 0 1 0
2255 0 0 0 0
2256 0 0 1 0
2257 0 1 1 1
2259 0 0 0 0
2262 0 0 1 0
2263 0 0 0 1
2265 0 0 1 0
2266 0 0 0 0
2270 0 0 1 0
2271 0 0 1 0
2272 0 0 1 1
2273 0 0 1 0
2274 0 0 1 1
2276 0 0 1 0
2278 0 0 0 0
2280 0 1 1 1
2281 0 0 0 0
2282 0 0 1 1
2283 0 0 1 1
2284 0 0 0 0
2285 0 0 1 1
2287 0 0 1 0
2288 0 0 1 0
2289 0 0 1 0
2290 0 0 0 0
2292 0 0 0 0
2294 0 0 1 0
2296 0 0 1 0
2297 0 0 0 1
2298 0 0 1 1
2300 0 0 0 0
2301 0 0 0 0
2303 0 0 0 1
2304 0 0 1 1
2307 0 0 0 0
2309 0 0 1 0
2310 0 0 1 0
2311 0 0 0 0
2312 0 0 1 1
2313 0 0 1 0
2315 1 0 1 0
2316 0 0 1 0
2317 0 0 1 0
2321 0 0 1 0
2323 0 0 1 0
2325 0 0 1 0
2326 0 0 0 0
2327 0 0 0 0
2328 1 0 1 0
2329 0 0 1 0
2330 0 0 1 0
2331 0 0 1 1
2332 0 0 0 0
2333 0 0 1 1
2335 0 0 0 0
2336 0 0 0 0
2337 0 0 0 0
2339 0 0 0 1
2341 0 0 0 0
2342 0 0 1 0
2343 0 0 1 0
2344 0 0 1 1
2348 0 0 0 1
2349 0 0 1 1
2350 1 1 1 0
2351 0 0 1 1
2352 0 0 1 1
2353 0 0 0 0
2355 0 0 1 0
2356 0 0 1 1
2357 0 1 1 1
2358 0 0 0 0
2359 1 0 1 0
2360 0 1 1 1
2362 1 1 1 0
2363 0 0 1 0
2365 0 0 0 1
2366 0 0 0 0
2367 1 0 1 0
2368 0 0 1 1
2369 0 0 1 1
2370 0 0 1 0
2372 0 0 0 0
2373 0 0 1 1
2374 0 0 0 0
2376 1 1 1 1
2377 0 0 0 0
2378 0 0 0 0
2379 1 1 1 0
2380 0 0 1 0
2381 0 0 0 0
2384 0 0 1 1
2385 0 0 1 0
2386 0 0 0 0
2387 0 0 1 0
2388 0 0 0 1
2389 1 0 0 0
2390 0 0 0 1
2391 0 0 1 0
2392 0 0 1 0
2393 0 0 0 1
2395 0 0 0 0
2396 0 0 0 1
2397 0 0 0 1
2398 0 0 1 0
2399 1 0 0 1
2402 0 0 1 0
2403 0 0 0 0
2404 0 0 0 0
2405 0 0 1 0
2406 1 0 1 0
2407 0 0 1 0
2408 0 0 1 0
2409 0 0 1 0
2410 0 0 1 0
2412 0 0 1 0
2414 0 0 0 0
2415 0 0 0 0
2417 0 0 1 0
2418 0 0 1 1
2420 0 0 1 0
2421 0 0 0 1
2422 0 0 1 0
2423 0 0 0 0
2424 0 0 1 0
2425 0 0 0 0
2426 0 0 1 1
2428 0 0 1 0
2429 0 0 0 1
2431 0 0 1 0
2432 0 0 1 0
2433 0 0 0 1
2434 1 1 1 0
2436 0 0 1 0
2438 0 0 0 1
2440 0 0 0 1
2442 0 0 1 1
2443 0 0 0 0
2444 0 1 1 1
2445 0 0 1 1
2446 0 0 1 0
2449 0 0 1 1
2451 0 0 0 0
2452 0 0 1 1
2453 0 0 1 0
2454 0 0 1 0
2455 0 0 0 0
2456 0 0 1 0
2458 0 0 1 1
2460 0 0 1 1
2461 0 0 1 0
2462 0 0 1 0
2463 0 0 1 0
2464 0 0 1 0
2465 0 0 1 0
2466 0 0 1 0
2468 1 0 1 0
2472 0 0 1 0
2476 0 0 0 0
2477 0 0 1 0
2481 0 0 0 0
2482 0 0 0 0
2483 0 0 0 1
2484 1 0 0 0
2487 0 0 0 0
2489 0 0 1 0
2490 0 0 1 0
2493 0 0 1 0
2494 0 0 0 0
2495 0 0 1 0
2496 0 0 0 1test.x <- model.matrix(Personal.Loan ~., # Personal.Loan은 Target으로 제외
UB.ted)[,-1] # [,-1] : 절편 제거
test.x Age Experience Income ZIP.Code Family2
1 -1.78816124 -1.68358012 -0.534005217 -1.17304370 0
6 -0.74785214 -0.64236200 -0.966895557 -0.59585545 0
16 1.24607365 0.83269699 -1.118407176 1.07366441 0
20 0.81261153 0.65916064 -1.140051693 0.88354520 0
21 0.89930395 0.91946517 -1.053473625 0.48224568 0
29 0.89930395 0.83269699 -0.555649734 0.78051653 0
35 -1.26800669 -1.33650741 -0.512360700 0.49363006 0
40 -0.66115971 -0.64236200 0.136974810 0.53916759 0
41 0.98599638 1.00623334 0.223552878 -0.28221568 0
47 -0.57446728 -0.55559383 -0.663872319 1.05089564 0
52 1.33276608 1.44007422 1.240845177 0.88354520 0
57 0.81261153 0.83269699 -0.966895557 0.47655348 0
62 0.11907212 0.05178341 1.110978075 0.13616041 0
64 -0.31439001 -0.29528930 -0.901962006 0.77140902 0
68 0.63922667 0.22531976 -0.620583285 1.11294053 0
70 0.63922667 0.74592882 -1.161696210 -1.77755447 0
72 0.63922667 0.74592882 -0.101114877 0.42077000 0
76 -1.26800669 -1.16297106 1.327423245 0.98657387 0
79 0.72591910 0.83269699 1.284134211 0.07810006 1
82 0.11907212 0.13855158 -0.728805870 0.82206953 0
86 -1.61477639 -1.59681194 0.764665803 0.47655348 0
88 0.20576455 0.13855158 0.093685776 0.64731924 0
92 -0.92123699 -0.90266653 -0.966895557 0.53347540 0
94 1.24607365 1.17976970 -0.209337462 0.78677794 1
96 -0.66115971 -0.72913018 -0.555649734 1.39413480 0
99 0.29245697 0.22531976 0.439998048 -0.45184300 0
102 1.33276608 1.35330605 -0.945251040 0.81979265 0
104 -0.22769758 -0.20852112 -1.118407176 1.42430342 1
105 0.89930395 1.00623334 -0.772094904 0.08151537 0
116 1.67953578 1.70037875 0.158619327 -0.65106971 0
119 -0.40108243 -0.38205747 -0.014536809 -0.29644616 0
120 -1.18131426 -1.16297106 0.829599354 0.64675002 0
121 0.72591910 0.74592882 -1.334852346 -1.77072384 1
123 1.07268880 1.00623334 -0.014536809 0.77140902 1
124 -0.74785214 -0.64236200 0.223552878 -0.59073248 0
131 -1.52808397 -1.42327559 0.158619327 0.92965195 0
135 0.63922667 0.74592882 0.526576116 1.06284924 0
143 -1.09462184 -0.98943471 -0.555649734 -0.79565139 0
145 0.29245697 0.22531976 -0.079470360 -0.61179359 1
146 1.15938123 1.26653787 1.089333558 -1.79918480 0
149 0.55253425 0.65916064 1.933469721 -0.99317044 1
150 0.20576455 0.13855158 -0.685516836 0.44809253 0
153 0.98599638 1.00623334 -1.075118142 -0.02891315 0
157 -1.70146882 -1.77034829 -1.269918795 -0.59016326 0
159 -1.18131426 -1.24973924 0.115330293 0.88354520 1
160 1.33276608 1.26653787 -0.707161353 0.78393184 0
166 -1.61477639 -1.68358012 -0.663872319 0.87557613 0
169 0.37914940 0.48562429 -1.313207829 -1.05180002 0
170 -1.61477639 -1.68358012 0.829599354 -1.51685209 0
172 0.55253425 0.65916064 -1.356496863 1.50797864 0
174 1.07268880 1.17976970 -0.685516836 -1.74909351 0
175 -0.31439001 -0.29528930 2.041692306 1.32924382 1
176 -0.05431273 -0.03498477 0.245197395 -0.82923532 0
177 0.55253425 0.39885611 -0.642227802 -0.03232846 0
180 1.41945851 1.44007422 -1.356496863 -0.69774569 0
182 -0.83454456 -0.72913018 -1.378141380 0.20275906 0
185 0.55253425 0.48562429 -0.230981979 -0.25660082 1
186 -0.57446728 -0.55559383 0.894532905 -1.05180002 0
189 1.59284336 1.70037875 2.063336823 -1.05180002 1
190 0.81261153 0.74592882 0.829599354 0.49818381 1
193 0.37914940 0.22531976 0.245197395 -0.59528623 0
195 0.63922667 0.74592882 1.522223898 -0.26798520 1
200 -0.83454456 -0.81589836 1.825247136 -0.57820966 0
201 -1.18131426 -1.24973924 -0.966895557 -1.03187735 0
202 -0.92123699 -0.98943471 -1.161696210 0.82036187 1
205 0.89930395 0.91946517 -0.274271013 1.69752863 1
208 -1.00792941 -0.90266653 -0.057825843 0.53916759 0
217 -1.61477639 -1.51004376 1.110978075 1.33948976 1
218 -0.57446728 -0.55559383 0.007107708 0.64731924 0
219 -0.14100516 -0.03498477 -0.036181326 -0.20537109 0
221 -1.18131426 -1.24973924 -1.053473625 -0.59073248 1
225 0.55253425 0.57239246 -0.339204564 0.64731924 0
231 0.11907212 0.13855158 0.396709014 0.88354520 0
235 -1.70146882 -1.68358012 0.136974810 1.39356558 0
240 -1.52808397 -1.51004376 -0.469071666 0.53745994 0
243 -0.40108243 -0.38205747 0.028752225 0.47655348 0
249 0.81261153 0.74592882 0.548220633 -0.59585545 1
251 -1.35469911 -1.24973924 -0.966895557 0.64731924 0
252 0.72591910 0.65916064 2.084981340 -0.56113308 1
255 1.67953578 1.78714693 1.305778728 -0.69774569 0
260 0.89930395 0.83269699 -0.404138115 0.53461384 0
262 -0.31439001 -0.38205747 0.807954837 -0.03517456 1
267 1.50615093 1.52684240 -0.274271013 0.88354520 1
271 1.24607365 1.35330605 -0.230981979 0.50956820 0
272 -0.48777486 -0.55559383 -0.079470360 0.99909669 0
275 -1.35469911 -1.33650741 0.007107708 1.39356558 0
285 -0.14100516 -0.12175295 -0.101114877 -0.20594031 0
286 -0.48777486 -0.64236200 -0.101114877 0.64731924 0
288 -0.74785214 -0.72913018 -0.252626496 -0.60211686 0
291 0.46584182 0.39885611 0.136974810 -0.45241222 0
293 -1.35469911 -1.33650741 -0.772094904 0.78222418 0
296 1.24607365 1.17976970 -0.209337462 0.64675002 1
297 -1.00792941 -0.98943471 1.046044524 -1.44854579 0
303 -0.05431273 0.05178341 1.695380034 0.78677794 1
309 -1.18131426 -1.07620288 1.175911626 0.88354520 1
311 0.98599638 1.00623334 -0.750450387 -1.64549562 0
312 0.55253425 0.48562429 1.024400007 0.78677794 0
313 -0.83454456 -1.24973924 -1.140051693 -0.81215874 0
322 -0.14100516 -0.03498477 0.591509667 -0.25660082 0
328 1.07268880 1.00623334 0.872888388 -1.04610783 1
332 -1.18131426 -1.24973924 -0.988540074 0.53916759 0
339 -1.44139154 -1.51004376 1.717024551 0.27846521 1
340 -0.57446728 -0.64236200 0.331775463 -0.60211686 0
347 -0.14100516 -0.12175295 -0.512360700 -1.37910105 0
355 -0.14100516 -0.03498477 2.149914891 -1.64549562 1
356 -0.22769758 -0.12175295 -0.057825843 -0.60723984 0
359 -1.35469911 -1.24973924 1.457290347 0.78051653 1
360 -1.18131426 -1.24973924 -0.901962006 -0.03517456 0
366 0.98599638 1.00623334 2.171559408 -1.75250883 0
368 -1.18131426 -1.07620288 0.526576116 1.07366441 1
373 0.89930395 0.83269699 -0.642227802 -0.03574378 0
374 0.29245697 0.39885611 -1.161696210 -1.63752655 0
375 -1.35469911 -1.33650741 0.526576116 -0.69831491 1
376 -1.09462184 -1.16297106 0.353419980 -0.46778114 0
378 -1.35469911 -1.33650741 -0.728805870 0.70253350 0
379 0.11907212 0.22531976 -0.772094904 0.82548484 1
381 1.50615093 1.09300152 -0.858672972 0.64731924 0
382 0.81261153 0.74592882 -0.014536809 1.39356558 1
383 1.67953578 1.78714693 1.284134211 0.98828153 0
385 0.46584182 0.39885611 -1.140051693 -47.73517271 0
386 -0.92123699 -0.98943471 -0.728805870 0.44126189 0
392 1.07268880 1.00623334 -1.399785897 0.51924492 0
398 -1.70146882 -1.59681194 -0.555649734 -1.51685209 0
400 -1.52808397 -1.51004376 0.223552878 -1.78950808 0
407 -0.05431273 -0.12175295 1.110978075 -0.46322738 0
408 1.59284336 1.70037875 -0.339204564 0.15323699 0
409 1.24607365 1.35330605 0.331775463 -0.80988187 1
413 -0.05431273 -0.03498477 0.331775463 0.08151537 0
415 0.55253425 0.65916064 -0.707161353 0.64959612 0
424 -0.22769758 -0.12175295 1.890180687 1.39356558 1
427 -0.31439001 -0.20852112 0.028752225 -0.56113308 0
429 1.41945851 1.52684240 -1.075118142 0.88354520 1
435 -1.35469911 -1.24973924 -0.620583285 1.50911708 0
436 0.55253425 0.48562429 0.136974810 0.87728379 0
441 1.59284336 1.61361058 -0.317560047 -0.30839977 1
447 0.11907212 0.22531976 -1.118407176 -0.03403612 0
448 0.29245697 0.22531976 -0.057825843 1.11920194 0
465 -0.22769758 -0.12175295 0.201908361 0.64731924 0
469 -1.00792941 -0.90266653 -1.140051693 -0.30384601 0
471 -1.18131426 -1.24973924 0.223552878 -1.23053484 0
479 -0.14100516 -0.03498477 1.652091000 1.07707972 1
483 0.89930395 1.00623334 2.149914891 0.48623021 0
488 -0.57446728 -0.64236200 0.310130946 0.54030603 0
490 0.63922667 0.65916064 -0.663872319 -1.01764687 1
492 -0.31439001 -0.20852112 -0.858672972 -0.59927077 0
494 0.37914940 0.31208793 2.149914891 0.88354520 0
499 -1.18131426 -1.07620288 -0.663872319 1.05601861 0
512 -1.26800669 -1.33650741 0.180263844 0.55510573 0
514 -1.35469911 -1.24973924 -0.555649734 0.81922343 0
515 -1.61477639 -1.68358012 0.007107708 -0.81842015 0
516 -0.40108243 -0.38205747 0.851243871 -0.22074001 0
518 0.72591910 0.57239246 -0.663872319 -0.19000218 0
519 -1.52808397 -1.42327559 -0.858672972 -0.27936959 0
522 0.20576455 0.31208793 0.028752225 -0.36987544 0
532 -1.18131426 -1.24973924 -0.512360700 -1.57491244 0
534 -1.61477639 -1.59681194 0.591509667 -0.20537109 0
535 0.63922667 0.65916064 -0.707161353 -0.02891315 1
536 0.46584182 0.39885611 1.262489694 0.55510573 0
539 -1.26800669 -1.33650741 -1.356496863 0.77767043 0
540 0.98599638 1.00623334 -1.140051693 0.88354520 0
541 -1.78816124 -1.85711647 0.764665803 0.47939958 0
542 -1.35469911 -1.24973924 1.457290347 1.05089564 1
545 -0.92123699 -0.90266653 1.955114238 -0.88444958 1
547 -1.61477639 -1.59681194 -0.122759394 0.48793787 0
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1476 -0.14100516 -0.12175295 0.093685776 -0.62830095 1
1479 1.67953578 1.61361058 1.868536170 0.93079039 0
1482 -0.92123699 -0.98943471 2.279781993 -1.16279776 1
1483 1.24607365 1.26653787 -1.421430414 0.55510573 0
1487 -0.92123699 -0.98943471 1.457290347 -0.08298897 1
1489 -0.66115971 -0.72913018 -0.750450387 1.51253239 1
1490 1.41945851 1.52684240 0.548220633 -0.89014177 0
1495 1.15938123 1.26653787 -0.295915530 -1.75250883 0
1497 -0.83454456 -0.72913018 -1.204985244 -1.04610783 0
1503 1.67953578 1.61361058 0.851243871 -1.78267745 0
1507 0.55253425 0.57239246 -1.053473625 1.12147882 1
1511 0.98599638 1.00623334 -0.880317489 1.46813330 1
1516 0.72591910 0.65916064 -0.988540074 0.64731924 0
1517 -0.40108243 -0.29528930 -0.534005217 -0.59073248 0
1520 1.50615093 1.52684240 -1.118407176 -0.59927077 0
1528 0.98599638 1.09300152 -0.620583285 0.54030603 0
1532 -0.57446728 -0.64236200 -1.053473625 -1.63012670 0
1533 -0.05431273 -0.03498477 -0.404138115 0.80840827 0
1534 1.41945851 1.44007422 1.760313585 0.44126189 0
1539 0.81261153 0.83269699 -0.858672972 1.50968630 0
1547 -1.09462184 -0.98943471 0.678087735 1.12034038 0
1548 0.11907212 0.05178341 -0.469071666 0.88354520 0
1551 -0.48777486 -0.55559383 -0.750450387 -0.02891315 0
1552 0.37914940 0.39885611 2.561160714 0.53916759 1
1565 1.59284336 1.70037875 -0.230981979 0.87557613 0
1572 -0.74785214 -0.64236200 -0.014536809 1.47439471 0
1573 1.59284336 1.70037875 -0.230981979 -0.82923532 0
1574 -0.14100516 -0.03498477 -0.101114877 -0.64879284 0
1575 1.41945851 1.44007422 -0.685516836 -0.60439374 0
1580 -1.44139154 -1.33650741 1.046044524 0.64731924 0
1584 1.33276608 1.35330605 2.388004578 -0.64879284 0
1585 0.03237970 -0.03498477 -1.053473625 0.13274510 0
1586 0.98599638 0.91946517 1.240845177 -1.51742131 1
1587 1.15938123 1.09300152 -0.512360700 0.54315213 1
1592 -0.57446728 -0.64236200 -0.036181326 1.50797864 1
1603 -0.48777486 -0.55559383 0.007107708 -1.66371064 0
1604 -0.83454456 -1.24973924 1.392356796 -0.57820966 0
1608 0.81261153 0.74592882 -1.140051693 -0.64879284 0
1610 1.76622821 1.78714693 0.678087735 -0.08241975 0
1616 1.41945851 1.35330605 -0.230981979 -0.03346690 0
1618 1.33276608 1.35330605 -0.642227802 -1.06204596 0
1620 -0.05431273 0.05178341 -0.966895557 -1.80032324 0
1622 -1.26800669 -1.24973924 -0.447427149 -0.61179359 0
1625 -1.52808397 -1.59681194 -0.923606523 -1.78950808 1
1627 -1.26800669 -1.24973924 2.301426510 -0.03403612 1
1628 0.03237970 -0.03498477 0.180263844 -1.22484265 0
1629 -0.31439001 -0.20852112 0.353419980 1.07935660 0
1630 0.63922667 0.74592882 1.738669068 0.13616041 0
1633 -1.26800669 -1.33650741 0.418353531 1.06114158 1
1636 0.29245697 0.31208793 -0.079470360 -1.04610783 0
1644 -0.40108243 -0.38205747 -1.313207829 -1.16279776 1
1645 1.15938123 1.26653787 -0.880317489 -1.03187735 0
1655 1.24607365 1.17976970 0.613154184 0.64731924 1
1661 -0.74785214 -0.81589836 -0.858672972 1.46813330 0
1666 -0.74785214 -0.72913018 0.569865150 -0.24635488 0
1668 -0.14100516 -0.03498477 -1.118407176 -1.78950808 0
1671 -0.66115971 -0.55559383 -1.053473625 1.11977116 0
1677 0.03237970 -0.03498477 0.007107708 -0.19740203 0
1678 -1.00792941 -0.90266653 -0.685516836 -0.56625606 0
1687 1.41945851 1.52684240 -0.750450387 1.61385341 0
1688 1.50615093 1.61361058 0.201908361 -1.78893886 0
1689 1.24607365 1.17976970 0.743021286 -0.57820966 1
1692 0.89930395 1.00623334 -0.555649734 0.54030603 0
1696 -1.35469911 -1.24973924 2.388004578 -0.71539148 0
1698 1.59284336 1.52684240 -0.901962006 -1.76617009 0
1701 -0.22769758 -0.38205747 -0.057825843 -1.75250883 0
1706 0.20576455 0.31208793 0.115330293 -1.66371064 0
1709 0.03237970 -0.03498477 -1.334852346 -1.66086454 0
1711 -1.26800669 -1.33650741 -0.966895557 1.27346034 1
1714 -0.14100516 -0.03498477 -1.269918795 -1.57263557 0
1719 -0.48777486 -0.38205747 -1.183340727 -0.64879284 0
1728 0.55253425 0.48562429 -0.425782632 -1.77527760 1
1731 -0.40108243 -0.29528930 -0.490716183 0.70253350 1
1733 -1.78816124 -1.77034829 0.310130946 0.79588544 1
1734 -0.48777486 -0.38205747 1.110978075 1.11407897 1
1736 1.24607365 1.35330605 -0.923606523 1.07195675 0
1738 -0.14100516 -0.12175295 -0.079470360 -0.43761252 0
1751 1.24607365 1.17976970 -0.274271013 1.33948976 0
1752 0.81261153 0.91946517 -1.053473625 0.88354520 1
1754 0.63922667 0.74592882 -1.053473625 -0.66017722 1
1764 0.20576455 0.31208793 1.305778728 0.53347540 0
1766 -1.70146882 -1.77034829 1.630446483 1.07195675 1
1776 0.03237970 0.13855158 -0.014536809 -1.02903125 0
1777 0.37914940 0.48562429 -0.685516836 0.51924492 0
1779 -1.61477639 -1.51004376 -0.901962006 0.87785301 0
1783 -0.74785214 -0.81589836 -0.295915530 1.51253239 1
1787 -0.92123699 -0.81589836 -0.858672972 -0.02891315 0
1793 0.03237970 -0.03498477 0.959466456 -0.09038882 0
1795 0.89930395 1.00623334 0.526576116 -1.03187735 0
1796 0.29245697 0.31208793 -0.079470360 -1.78950808 0
1797 0.98599638 1.00623334 -0.685516836 -0.19170983 1
1800 -0.66115971 -0.55559383 -0.988540074 1.51025552 0
1802 -0.92123699 -0.90266653 0.093685776 -0.59585545 0
1811 1.24607365 1.17976970 -0.837028455 -1.78893886 0
1813 -0.22769758 -0.12175295 1.175911626 1.07366441 0
1816 1.67953578 1.61361058 -1.204985244 0.99909669 1
1830 1.15938123 0.74592882 -0.620583285 1.40153465 0
1832 0.11907212 0.13855158 -0.945251040 0.54087525 0
1838 -0.22769758 -0.20852112 0.634798701 -1.75250883 0
1841 0.81261153 0.39885611 -1.096762659 -0.03517456 0
1843 0.63922667 0.74592882 0.418353531 1.07195675 0
1848 -1.78816124 -1.77034829 -0.469071666 1.11464819 0
1849 -0.92123699 -0.90266653 -0.945251040 1.06114158 0
1850 0.37914940 0.48562429 -0.685516836 -1.44456125 0
1851 -0.83454456 -0.90266653 -1.161696210 -1.78438510 0
1853 -1.18131426 -1.24973924 -0.425782632 0.81296202 0
1859 -0.92123699 -0.81589836 -0.187692945 -1.37796261 0
1870 0.81261153 0.83269699 -0.642227802 0.48793787 1
1874 -1.52808397 -1.42327559 -0.101114877 0.77994731 0
1875 -0.74785214 -0.81589836 0.180263844 1.50911708 0
1879 0.89930395 0.83269699 -0.317560047 1.51708615 0
1881 -0.14100516 -0.12175295 -0.534005217 0.88354520 0
1883 0.89930395 1.00623334 1.110978075 -1.04610783 0
1884 0.89930395 0.83269699 2.409649095 -0.82923532 0
1885 0.98599638 1.09300152 1.933469721 0.54884432 0
1886 -1.26800669 -1.24973924 -1.183340727 1.61271497 0
1887 1.67953578 1.78714693 0.894532905 0.53347540 0
1888 -1.26800669 -1.16297106 0.158619327 1.04634188 1
1895 0.46584182 0.39885611 -0.966895557 0.64618080 0
1896 -1.70146882 -1.59681194 -0.036181326 1.04463423 0
1903 -0.57446728 -0.55559383 0.245197395 0.47655348 0
1904 0.89930395 0.48562429 -0.512360700 -1.74909351 0
1906 -1.78816124 -1.85711647 0.829599354 -0.37613685 1
1908 -0.31439001 -0.20852112 0.894532905 0.30920304 0
1911 -0.22769758 -0.20852112 0.201908361 1.39356558 1
1913 -0.31439001 -0.38205747 2.539516197 0.64675002 0
1915 0.20576455 0.31208793 -0.425782632 1.39356558 0
1916 -0.74785214 -0.81589836 -0.101114877 -0.71539148 0
1924 -0.05431273 -0.12175295 -1.118407176 -1.43943828 0
1928 -0.92123699 -0.90266653 -0.252626496 -0.03517456 0
1929 1.07268880 1.17976970 -0.837028455 0.54315213 0
1930 -0.14100516 -0.12175295 -0.945251040 0.75888620 0
1939 -1.35469911 -1.42327559 -0.772094904 -1.66371064 0
1940 0.81261153 0.91946517 -1.096762659 0.54315213 1
1963 -1.52808397 -1.42327559 1.760313585 -1.79235417 0
1965 -1.00792941 -0.90266653 -0.858672972 1.07707972 0
1967 0.55253425 0.48562429 0.872888388 -1.04610783 1
1968 -0.22769758 -0.20852112 0.331775463 0.64618080 0
1970 1.59284336 1.52684240 0.894532905 0.53347540 0
1971 -1.61477639 -1.51004376 1.608801966 -0.22074001 0
1975 -0.57446728 -0.64236200 -0.230981979 -1.74909351 0
1978 -0.40108243 -0.46882565 -0.425782632 0.64618080 0
1980 -0.40108243 -0.29528930 -1.356496863 -1.04610783 0
1981 -0.05431273 -0.12175295 1.457290347 0.87557613 0
1982 0.55253425 0.48562429 0.223552878 -0.79678982 0
1984 -1.26800669 -1.33650741 -1.161696210 0.88354520 1
1986 -1.26800669 -1.16297106 -0.923606523 0.99738903 0
1990 1.15938123 1.26653787 -0.404138115 -1.64720328 0
1991 -1.18131426 -1.07620288 -0.966895557 -0.20537109 0
1998 0.72591910 0.83269699 -0.274271013 -0.61179359 0
2002 -0.14100516 -0.29528930 1.175911626 1.00194279 1
2003 -1.35469911 -1.42327559 1.478934864 -0.59300936 0
2006 0.11907212 0.22531976 2.084981340 -1.65858766 1
2008 0.20576455 0.05178341 0.093685776 0.47939958 0
2011 1.33276608 1.35330605 -0.707161353 1.61271497 1
2012 0.03237970 0.05178341 -0.750450387 -0.37613685 0
2013 0.98599638 0.91946517 -0.490716183 0.44126189 0
2018 -0.31439001 -0.46882565 -1.291563312 -0.62830095 0
2020 -0.22769758 -0.29528930 -0.642227802 0.82150031 0
2022 0.03237970 -0.03498477 0.634798701 -1.01764687 0
2023 -1.09462184 -1.51004376 -0.057825843 0.22382017 0
2024 0.81261153 0.74592882 -0.404138115 0.88354520 0
2025 -0.83454456 -0.72913018 0.851243871 0.64731924 0
2027 1.15938123 1.09300152 0.136974810 0.42077000 1
2028 -0.66115971 -0.72913018 2.279781993 0.81296202 1
2030 -1.35469911 -1.51004376 -0.274271013 -0.57820966 0
2031 1.50615093 1.52684240 0.807954837 1.50627098 1
2034 0.29245697 0.22531976 0.201908361 -0.59300936 0
2038 -0.92123699 -1.07620288 -0.469071666 1.39356558 1
2040 0.46584182 0.39885611 -0.901962006 -0.88957255 1
2041 -0.40108243 -0.38205747 0.375064497 0.88354520 0
2046 0.55253425 0.65916064 -0.642227802 1.07195675 0
2047 -0.22769758 -0.38205747 1.890180687 1.11920194 0
2049 -1.52808397 -1.42327559 -0.663872319 0.93079039 0
2051 -0.40108243 -0.46882565 -0.966895557 0.48736865 1
2053 -1.52808397 -1.51004376 1.002755490 0.51924492 0
2055 -0.57446728 -0.46882565 0.331775463 -0.59300936 1
2057 -1.09462184 -1.07620288 -1.161696210 -0.27140052 0
2070 -1.35469911 -1.42327559 -0.837028455 -1.76958540 0
2073 -1.44139154 -1.51004376 -0.750450387 1.51594771 0
2074 0.03237970 -0.03498477 -0.425782632 -1.17304370 0
2076 -0.48777486 -0.38205747 -0.447427149 0.54372135 0
2085 -0.83454456 -0.98943471 -0.642227802 0.42077000 0
2086 0.37914940 0.31208793 -0.620583285 0.53347540 0
2089 -0.57446728 -0.98943471 -0.966895557 0.87273003 0
2090 0.63922667 0.74592882 0.461642565 0.64675002 0
2097 0.81261153 0.74592882 -0.425782632 1.07195675 1
2100 0.63922667 0.74592882 -1.378141380 -1.74909351 1
2101 -1.26800669 -1.24973924 1.543868415 0.43955424 0
2102 -0.92123699 -1.33650741 2.799250401 1.06114158 0
2106 -1.26800669 -1.33650741 -0.534005217 0.53859837 0
2107 1.41945851 1.52684240 1.262489694 -1.68363331 0
2109 0.89930395 1.00623334 0.245197395 0.54884432 0
2111 -1.52808397 -1.42327559 0.656443218 0.64504236 0
2115 1.41945851 1.35330605 -0.101114877 1.06512612 1
2126 -0.14100516 -0.03498477 0.418353531 -0.71596070 0
2128 -0.48777486 -0.55559383 2.279781993 0.88354520 1
2135 0.37914940 0.31208793 -0.122759394 1.51025552 0
2137 0.37914940 0.48562429 0.894532905 1.04748032 0
2138 1.67953578 1.70037875 0.201908361 -0.46322738 0
2139 -0.83454456 -0.81589836 -0.728805870 0.25228113 1
2140 0.98599638 1.00623334 0.851243871 -0.79678982 0
2142 -1.52808397 -1.42327559 -0.772094904 -0.60268608 0
2144 0.89930395 0.91946517 -0.187692945 -0.61179359 0
2148 -1.61477639 -1.51004376 -1.161696210 -0.66074644 0
2150 0.20576455 0.13855158 1.652091000 1.06512612 0
2153 1.41945851 1.52684240 -0.945251040 0.64675002 0
2155 -1.18131426 -1.07620288 -0.620583285 0.79133169 0
2158 -1.78816124 -1.77034829 -0.057825843 0.31831055 0
2161 -0.22769758 -0.29528930 -0.404138115 0.43556970 0
2164 -1.09462184 -1.51004376 -0.101114877 -0.57308669 0
2168 1.67953578 1.70037875 1.911825204 0.81296202 0
2174 -1.00792941 -0.90266653 -0.858672972 0.13616041 0
2178 -1.26800669 -1.16297106 0.743021286 0.76230151 0
2179 -0.74785214 -0.64236200 1.825247136 0.44126189 1
2185 1.41945851 1.35330605 2.366360061 -1.74909351 1
2195 -1.00792941 -0.98943471 1.067689041 0.78848560 0
2196 0.46584182 0.57239246 -0.880317489 -0.64366986 0
2198 1.24607365 1.26653787 -0.858672972 0.53176774 0
2200 0.29245697 0.31208793 -0.490716183 -1.22484265 0
2201 0.37914940 0.39885611 -0.966895557 -1.74909351 1
2204 0.37914940 0.39885611 1.219200660 -1.05180002 0
2213 0.03237970 0.13855158 0.201908361 1.07707972 0
2221 1.67953578 1.70037875 0.136974810 0.53347540 0
2222 1.15938123 1.09300152 -0.014536809 -0.63285470 1
2229 0.20576455 0.22531976 -0.663872319 -1.65858766 0
2231 -0.83454456 -0.81589836 2.366360061 0.87443769 0
2242 -1.70146882 -1.77034829 -1.291563312 0.64504236 0
2258 0.11907212 0.22531976 1.219200660 -0.79963592 1
2260 -1.87485367 -1.77034829 0.180263844 -1.57491244 0
2261 -0.57446728 -0.55559383 -1.269918795 0.22382017 1
2264 0.11907212 0.05178341 -0.988540074 -0.17064872 0
2267 -0.66115971 -0.64236200 1.500579381 0.78677794 0
2268 -0.66115971 -0.64236200 2.041692306 -0.29644616 1
2269 -1.61477639 -1.51004376 0.678087735 0.64675002 0
2275 -0.48777486 -0.46882565 -1.140051693 -1.78381588 1
2277 -1.44139154 -1.51004376 2.128270374 -0.61179359 0
2279 -1.35469911 -1.42327559 2.820894918 -1.17304370 1
2286 0.20576455 0.13855158 0.872888388 -0.66074644 0
2291 -0.66115971 -0.64236200 0.093685776 -0.69774569 0
2293 0.98599638 1.09300152 2.084981340 1.07195675 1
2295 -0.57446728 -0.46882565 1.197556143 -1.78324666 1
2299 0.20576455 0.31208793 -1.399785897 -0.30612289 0
2302 -0.66115971 -0.64236200 0.223552878 0.13388354 0
2305 -1.61477639 -1.59681194 2.084981340 1.50854786 0
2306 -1.18131426 -1.16297106 2.409649095 -0.65960800 1
2308 0.89930395 0.91946517 -0.295915530 -0.65960800 0
2314 1.07268880 1.00623334 -0.425782632 0.49363006 0
2318 -1.26800669 -1.33650741 1.197556143 1.50627098 0
2319 1.24607365 1.17976970 -1.096762659 0.93079039 0
2320 -1.00792941 -0.98943471 2.691027816 1.50911708 1
2322 -0.40108243 -0.46882565 -0.750450387 -1.01764687 0
2324 -1.26800669 -1.16297106 0.851243871 0.78222418 1
2334 -0.05431273 0.05178341 -0.274271013 1.50513254 0
2338 -0.22769758 -0.38205747 2.755961367 1.07366441 0
2340 0.89930395 0.91946517 -0.036181326 -1.74909351 0
2345 1.67953578 1.70037875 -1.161696210 0.81979265 0
2346 1.67953578 1.70037875 0.331775463 -1.63752655 0
2347 0.55253425 0.48562429 -0.317560047 -0.28904631 1
2354 1.33276608 1.35330605 -1.334852346 -0.08241975 0
2361 -1.61477639 -1.68358012 0.245197395 0.07639240 1
2364 -0.57446728 -0.64236200 -0.274271013 -1.74909351 1
2371 -1.09462184 -1.16297106 -0.490716183 0.49647616 0
2375 -1.18131426 -1.33650741 -0.707161353 -0.66017722 1
2382 -1.09462184 -0.98943471 -0.534005217 1.00194279 0
2383 0.03237970 -0.03498477 2.409649095 0.54827510 0
2394 0.63922667 0.65916064 -1.291563312 0.47655348 0
2400 1.41945851 1.35330605 -0.707161353 -1.66371064 1
2401 1.33276608 1.35330605 2.063336823 -1.01764687 1
2411 -1.44139154 -1.42327559 1.219200660 -0.30612289 1
2413 1.33276608 1.35330605 -0.317560047 -0.02834393 0
2416 -0.05431273 0.05178341 -1.356496863 0.55510573 0
2419 -0.40108243 -0.29528930 -0.988540074 1.39356558 0
2427 1.33276608 1.35330605 -0.404138115 0.54884432 0
2430 -1.09462184 -1.16297106 -0.339204564 1.39356558 0
2435 -0.66115971 -0.72913018 0.418353531 1.39356558 0
2437 0.63922667 0.74592882 -0.750450387 -0.30839977 0
2439 1.41945851 1.44007422 -0.966895557 -1.21687358 0
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2457 0.72591910 0.83269699 -0.750450387 1.16303182 1
2459 0.03237970 -0.03498477 -0.036181326 -0.03403612 1
2467 -1.87485367 -1.94388465 0.136974810 0.53347540 1
2469 0.29245697 0.22531976 1.284134211 0.64675002 0
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2471 -1.09462184 -1.16297106 0.158619327 -0.59528623 1
2473 1.41945851 1.35330605 0.981110973 0.88354520 1
2474 0.98599638 1.00623334 -0.750450387 -0.56113308 0
2475 1.59284336 1.52684240 -0.728805870 -0.59528623 1
2478 -0.48777486 -0.55559383 2.279781993 -1.78893886 0
2479 -1.35469911 -1.33650741 2.258137476 0.50956820 1
2480 0.81261153 0.83269699 0.180263844 0.88354520 0
2485 0.03237970 0.05178341 -0.945251040 -0.26798520 0
2486 1.33276608 1.35330605 -0.555649734 0.48793787 0
2488 -0.05431273 -0.03498477 -0.728805870 -0.16040278 0
2491 0.55253425 0.65916064 2.041692306 -1.57320479 0
2492 -0.66115971 -0.55559383 0.136974810 -0.17064872 1
2497 1.50615093 1.44007422 -0.901962006 -0.02891315 0
2498 -1.09462184 -0.98943471 -1.291563312 1.11863272 0
2499 -0.66115971 -0.55559383 0.807954837 -0.64879284 1
2500 0.63922667 0.57239246 -0.772094904 0.53347540 0
Family3 Family4 CCAvg Education2 Education3 Mortgage
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1930 0 0 1 0
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1986 0 0 0 0
1990 1 0 0 0
1991 0 0 1 1
1998 0 0 1 0
2002 0 0 0 1
2003 0 0 0 0
2006 0 1 1 1
2008 0 0 1 1
2011 0 0 0 0
2012 0 0 1 0
2013 0 0 1 1
2018 1 0 0 0
2020 1 1 1 0
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2499 0 0 0 0
2500 1 0 1 06. 모형 훈련
Package "glmnet"에서 제공하는 함수 glmnet()을 이용하여 Ridge Regression을 수행할 수 있다. 함수 glmnet()는 Target이 2개의 클래스를 가질 때 “두 번째 클래스”에 속할 확률을 모델링하며, “두 번째 클래스”란 “Factor” 변환하였을 때 두 번째 수준(Level)을 의미한다. 예를 들어, “a”와 “b” 2개의 클래스를 가진 Target을 “Factor” 변환하였을 때 수준이 “a” “b”라면, 첫 번째 클래스는 “a”, 두 번째 클래스는 “b”가 된다. 함수 glmnet()에 대한 자세한 옵션은 여기를 참고한다.
glmnet(x, y, family, alpha, lambda, ...)x: 예측 변수를 포함하는 행렬y: Target을 포함하는 변수family: Target의 분포"gaussian": 수치형인 Target"binomial": 2개의 클래스를 가지는 Target"multinomial": 3개 이상 클래스를 가지는 Target"poisson": Count Data인 Target
alpha: Elasticnet Mixing Parameter0: Ridge Regression1: Lasso Regression0 < alpha < 1: Elastic Net Regression
lambda: Regularization Parameter- 직접 값을 지정하면 해당 값에 대한 결과만 보여준다.
- 값을 지정하지 않으면 100개의
lambda값에 대한 결과를 보여준다.
6-1. 람다 값 직접 지정
ridge.fit <- glmnet(x = train.x, # 예측 변수를 포함하는 행렬
y = UB.trd$Personal.Loan, # Target
family = "binomial", # Binary Classification
alpha = 0, # 0 : Ridge / 1 : Lasso / 0 < alpha < 1 : Elastic Net
lambda = 1)
round(coef(ridge.fit), 3) # 회귀계수 추정치16 x 1 sparse Matrix of class "dgCMatrix"
s0
(Intercept) -2.265
Age -0.004
Experience -0.004
Income 0.138
ZIP.Code 0.002
Family2 -0.040
Family3 0.046
Family4 0.030
CCAvg 0.093
Education2 0.058
Education3 0.058
Mortgage 0.038
Securities.Account1 0.019
CD.Account1 0.380
Online1 0.016
CreditCard1 -0.014Result! 데이터 “UB.trd”의 Target “Personal.Loan”은 “no”와 “yes” 2개의 클래스를 가지며, “Factor” 변환하면 알파벳순으로 수준을 부여하기 때문에 “yes”가 두 번째 클래스가 된다. 즉, “yes”에 속할 확률(= 개인 대출 제의를 수락할 확률)을 \(p\)라고 할 때, 추정된 회귀계수를 이용하여 다음과 같은 모형식을 얻을 수 있다.
\[
\begin{align*}
\log{\frac{p}{1-p}} = &-2.265 -0.004 Z_{\text{Age}} -0.004 Z_{\text{Experience}} + 0.138 Z_{\text{Income}} \\
&+0.002 Z_{\text{ZIP.Code}} -0.040 X_{\text{Family2}} + 0.046 X_{\text{Family3}} + 0.030 X_{\text{Family4}} \\
&+ 0.093 Z_{\text{CCAvg}} + 0.058 X_{\text{Education2}} + 0.058 X_{\text{Education3}} + 0.038 Z_{\text{Mortgage}} \\
&+ 0.019 X_{\text{Securities.Account1}} + 0.380 X_{\text{CD.Account1}} + 0.016 X_{\text{Online1}} -0.014 X_{\text{CreditCard1}}
\end{align*}
\]
여기서, \(Z_{\text{예측 변수}}\)는 표준화한 예측 변수, \(X_{\text{예측 변수}}\)는 더미 변수를 의미한다.
6-2. 교차 검증을 통한 최적의 람다 값
# 100개의 람다 값에 따른 결과
ridge.fit <- glmnet(x = train.x, # 예측 변수를 포함하는 행렬
y = UB.trd$Personal.Loan, # Target
family = "binomial", # Binary Classification
alpha = 0) # 0 : Ridge / 1 : Lasso / 0 < alpha < 1 : Elastic Net
plot(ridge.fit, xvar = "lambda") # 람다 값에 따른 회귀계수 추정치 확인
Result! 100개의 \(\lambda\) 값에 대한 회귀계수 추정치의 변화를 보여준다. 해당 그림을 통해 \(\lambda\) 값이 클수록 회귀계수 추정치는 작아진다는 것을 알 수 있다.
ridge.fit$lambda # 100개의 람다 값 [1] 159.18530945 145.04372529 132.15844050 120.41784889 109.72025908
[6] 99.97301366 91.09168667 82.99935228 75.62591858 68.90752041
[11] 62.78596621 57.20823402 52.12601218 47.49528092 43.27593107
[16] 39.43141663 35.92843825 32.73665482 29.82842063 27.17854595
[21] 24.76407884 22.56410633 20.55957331 18.73311748 17.06891896
[26] 15.55256324 14.17091639 12.91201123 11.76494374 10.71977856
[31] 9.76746298 8.89974849 8.10911936 7.38872755 6.73233336
[36] 6.13425142 5.58930143 5.09276329 4.64033624 4.22810156
[41] 3.85248867 3.51024419 3.19840377 2.91426640 2.65537100
[46] 2.41947516 2.20453566 2.00869078 1.83024423 1.66765038
[51] 1.51950091 1.38451264 1.26151635 1.14944672 1.04733304
[56] 0.95429086 0.86951429 0.79226904 0.72188604 0.65775567
[61] 0.59932247 0.54608031 0.49756804 0.45336547 0.41308973
[66] 0.37639198 0.34295435 0.31248723 0.28472673 0.25943239
[71] 0.23638513 0.21538533 0.19625109 0.17881668 0.16293110
[76] 0.14845675 0.13526826 0.12325140 0.11230209 0.10232548
[81] 0.09323517 0.08495241 0.07740547 0.07052898 0.06426338
[86] 0.05855440 0.05335259 0.04861289 0.04429426 0.04035928
[91] 0.03677387 0.03350698 0.03053031 0.02781808 0.02534680
[96] 0.02309506 0.02104336 0.01917393 0.01747057 0.01591853coef(ridge.fit) # 100개의 람다 값에 따른 회귀계수 추정치16 x 100 sparse Matrix of class "dgCMatrix"
(Intercept) -2.166511e+00 -2.167074e+00 -2.167129e+00
Age -6.393465e-39 -4.351962e-05 -4.775977e-05
Experience -5.888500e-39 -4.008018e-05 -4.398229e-05
Income 1.608392e-37 1.096704e-03 1.203557e-03
ZIP.Code 1.228136e-39 8.412200e-06 9.234586e-06
Family2 -4.313568e-38 -2.943123e-04 -3.230029e-04
Family3 4.743758e-38 3.237809e-04 3.553374e-04
Family4 2.892734e-38 1.975239e-04 2.167871e-04
CCAvg 1.131406e-37 7.712529e-04 8.463497e-04
Education2 5.765293e-38 3.935973e-04 4.319701e-04
Education3 5.749138e-38 3.925216e-04 4.308034e-04
Mortgage 4.739507e-38 3.230502e-04 3.545050e-04
Securities.Account1 3.247497e-38 2.209800e-04 2.425057e-04
CD.Account1 4.479005e-37 3.054235e-03 3.351708e-03
Online1 2.257208e-38 1.537655e-04 1.687253e-04
CreditCard1 -9.577375e-39 -6.558972e-05 -7.200808e-05
(Intercept) -2.167189e+00 -2.167256e+00 -2.167328e+00
Age -5.240201e-05 -5.749395e-05 -6.307884e-05
Experience -4.825679e-05 -5.294525e-05 -5.808746e-05
Income 1.320764e-03 1.449370e-03 1.590482e-03
ZIP.Code 1.013865e-05 1.113161e-05 1.222230e-05
Family2 -3.544817e-04 -3.890268e-04 -4.269368e-04
Family3 3.899804e-04 4.280007e-04 4.697274e-04
Family4 2.379334e-04 2.611435e-04 2.866190e-04
CCAvg 9.287407e-04 1.019139e-03 1.118319e-03
Education2 4.740964e-04 5.203320e-04 5.710779e-04
Education3 4.728206e-04 5.189373e-04 5.695539e-04
Mortgage 3.890119e-04 4.268715e-04 4.684084e-04
Securities.Account1 2.660679e-04 2.919107e-04 3.202529e-04
CD.Account1 3.678119e-03 4.036277e-03 4.429262e-03
Online1 1.851370e-04 2.031410e-04 2.228907e-04
CreditCard1 -7.905702e-05 -8.679901e-05 -9.530279e-05
(Intercept) -2.167408e+00 -2.167496e+00 -2.167593e+00
Age -6.920404e-05 -7.592135e-05 -8.328748e-05
Experience -6.372698e-05 -6.991147e-05 -7.669307e-05
Income 1.745311e-03 1.915186e-03 2.101564e-03
ZIP.Code 1.342043e-05 1.473669e-05 1.618289e-05
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Family3 0.124429553 0.134888801 0.146067049
Family4 0.090288417 0.098977919 0.108384866
CCAvg 0.193455751 0.203359207 0.213244646
Education2 0.167142707 0.182447862 0.198950789
Education3 0.164061615 0.178755850 0.194573386
Mortgage 0.074138169 0.077227288 0.080206654
Securities.Account1 0.006641728 0.002437146 -0.002491852
CD.Account1 0.825908116 0.872183773 0.919117803
Online1 0.026219159 0.026357459 0.026287034
CreditCard1 -0.055723337 -0.062512090 -0.069981836
(Intercept) -2.551271325 -2.583116886 -2.616647898
Age -0.008336316 -0.008437370 -0.008486311
Experience -0.007838837 -0.007963443 -0.008043826
Income 0.380590460 0.403697847 0.427617253
ZIP.Code 0.009799820 0.010924464 0.012149683
Family2 -0.127694715 -0.136723974 -0.146113661
Family3 0.157992775 0.170693008 0.184192747
Family4 0.118542047 0.129479645 0.141224584
CCAvg 0.223062393 0.232763753 0.242301335
Education2 0.216707493 0.235771404 0.256192731
Education3 0.211570578 0.229802840 0.249324101
Mortgage 0.083056882 0.085760470 0.088301849
Securities.Account1 -0.008181460 -0.014662578 -0.021959914
CD.Account1 0.966598511 1.014526761 1.062816257
Online1 0.025987416 0.025439307 0.024624714
CreditCard1 -0.078165448 -0.087092106 -0.096786787
(Intercept) -2.651868557 -2.688783200 -2.727396031
Age -0.008476817 -0.008402345 -0.008256814
Experience -0.008074020 -0.008048449 -0.007961892
Income 0.452342382 0.477868424 0.504188940
ZIP.Code 0.013478664 0.014913738 0.016456331
Family2 -0.155841638 -0.165880423 -0.176197956
Family3 0.198514861 0.213679096 0.229701964
Family4 0.153800527 0.167226754 0.181518152
CCAvg 0.251631163 0.260711567 0.269504749
Education2 0.278017835 0.301288689 0.326042264
Education3 0.270185829 0.292436779 0.316122032
Mortgage 0.090667700 0.092846681 0.094829554
Securities.Account1 -0.030095325 -0.039083473 -0.048934857
CD.Account1 1.111398354 1.160216913 1.209230809
Online1 0.023527431 0.022132850 0.020428319
CreditCard1 -0.107269841 -0.118556589 -0.130657014
(Intercept) -2.767711673 -2.809735291 -2.853472526
Age -0.008034621 -0.007730784 -0.007341042
Experience -0.007809690 -0.007587896 -0.007293401
Income 0.531296246 0.559181137 0.587832616
ZIP.Code 0.018106851 0.019864610 0.021727747
Family2 -0.186757634 -0.197518638 -0.208436392
Family3 0.246596310 0.264371033 0.283030912
Family4 0.196684771 0.212731547 0.229658119
CCAvg 0.277977045 0.286099328 0.293847308
Education2 0.352310033 0.380117541 0.409484064
Education3 0.341282389 0.367953762 0.396166635
Mortgage 0.096609103 0.098180080 0.099539135
Securities.Account1 -0.059655423 -0.071246818 -0.083706647
CD.Account1 1.258412283 1.307745649 1.357225788
Online1 0.018403235 0.016049160 0.013359930
CreditCard1 -0.143575530 -0.157310821 -0.171855783
(Intercept) -2.898929236 -2.946111096 -2.995023086
Age -0.006861938 -0.006290872 -0.005626107
Experience -0.006924038 -0.006478648 -0.005957116
Income 0.617237652 0.647380994 0.678245031
ZIP.Code 0.023693184 0.025756589 0.027912377
Family2 -0.219463144 -0.230548661 -0.241641005
Family3 0.302576532 0.323004322 0.344306691
Family4 0.247458750 0.266122364 0.285632689
CCAvg 0.301201739 0.308148512 0.314678649
Education2 0.440422358 0.472938535 0.507032031
Education3 0.425945617 0.457309098 0.490269017
Mortgage 0.100684751 0.101617181 0.102338375
Securities.Account1 -0.097028718 -0.111203284 -0.126217285
CD.Account1 1.406856529 1.456648994 1.506619974
Online1 0.010331733 0.006963160 0.003255223
CreditCard1 -0.187197556 -0.203317675 -0.220192317
(Intercept) -3.0456688846 -3.098050226 -3.152166232
Age -0.0048667606 -0.004012751 -0.003064726
Experience -0.0053603726 -0.004690352 -0.003949931
Income 0.7098097298 0.742052633 0.774948938
ZIP.Code 0.0301537174 0.032472583 0.034859811
Family2 -0.2526873773 -0.263634977 -0.274431869
Family3 0.3664722467 0.389486101 0.413330213
Family4 0.3059685338 0.327104154 0.349009722
CCAvg 0.3207881823 0.326477933 0.331753197
Education2 0.5426956973 0.579915970 0.618673131
Education3 0.5248307479 0.560993086 0.598748342
Mortgage 0.1028519086 0.103162903 0.103277935
Securities.Account1 -0.1420545978 -0.158696293 -0.176120906
CD.Account1 1.5567903781 1.607183803 1.657825230
Online1 -0.0007886813 -0.005162853 -0.009859421
CreditCard1 -0.2377926555 -0.256085316 -0.275032906
(Intercept) -3.207986085 -3.2655477885 -3.3248194930
Age -0.002032185 -0.0009033606 0.0003136534
Experience -0.003141005 -0.0022702074 -0.0013416653
Income 0.808446392 0.8425572898 0.8772335620
ZIP.Code 0.037305092 0.0397974956 0.0423250094
Family2 -0.285021567 -0.2953678593 -0.3054210387
Family3 0.437986031 0.4634276144 0.4896310229
Family4 0.371651198 0.3949939282 0.4189985493
CCAvg 0.336620278 0.3411000584 0.3452050752
Education2 0.658930830 0.7006767072 0.7438668142
Education3 0.638076193 0.6789672070 0.7213911836
Mortgage 0.103203896 0.1029522982 0.1025323157
Securities.Account1 -0.194325256 -0.2132517842 -0.2328868297
CD.Account1 1.708740257 1.7599584777 1.8115004017
Online1 -0.014869887 -0.0201801292 -0.0257781781
CreditCard1 -0.294593612 -0.3147264617 -0.3353848343
(Intercept) -3.3857841922 -3.4484199013 -3.51269915
Age 0.0016163872 0.0030021947 0.00446836
Experience -0.0003608313 0.0006664885 0.00173424
Income 0.9124431341 0.9481529097 0.98432894
ZIP.Code 0.0448750560 0.0474345783 0.04999021
Family2 -0.3151402044 -0.3244886278 -0.33343401
Family3 0.5165694697 0.5442148346 0.57253783
Family4 0.4436246587 0.4688307046 0.49457444
CCAvg 0.3489540978 0.3523679541 0.35546889
Education2 0.7884604546 0.8344126767 0.88167449
Education3 0.7653170036 0.8107085481 0.85752498
Mortgage 0.1019551529 0.1012328053 0.10037787
Securities.Account1 -0.2532016511 -0.2741662804 -0.29574964
CD.Account1 1.8633869194 1.9156362487 1.96826324
Online1 -0.0316497199 -0.0377794927 -0.04415156
CreditCard1 -0.3565217833 -0.3780896142 -0.40004042
(Intercept) -3.578588702 -3.646049402 -3.715035981
Age 0.006012173 0.007630983 0.009322242
Experience 0.002836221 0.003966163 0.005117786
Income 1.020936651 1.057940996 1.095306588
ZIP.Code 0.052528450 0.055035860 0.057499236
Family2 -0.341948664 -0.350009577 -0.357598381
Family3 0.601508147 0.631094523 0.661264747
Family4 0.520813354 0.547504982 0.574607166
CCAvg 0.358280050 0.360824995 0.363127285
Education2 0.930193114 0.979912179 1.030771876
Education3 0.905721016 0.955247192 1.006050019
Mortgage 0.099403355 0.098322536 0.097148757
Securities.Account1 -0.317919711 -0.340643588 -0.363887590
CD.Account1 2.021278999 2.074690565 2.128500666
Online1 -0.050749545 -0.057556825 -0.064556681
CreditCard1 -0.422326604 -0.444901302 -0.467718754
(Intercept) -3.785451536 -3.857329584 -3.930564281
Age 0.011055876 0.012880715 0.014771270
Experience 0.006303689 0.007484735 0.008669392
Income 1.132936143 1.170909339 1.209137392
ZIP.Code 0.059905651 0.062243316 0.064500626
Family2 -0.364696974 -0.371306242 -0.377415594
Family3 0.692001164 0.723243513 0.754967742
Family4 0.602080646 0.629881309 0.657969672
CCAvg 0.365229466 0.367123315 0.368843564
Education2 1.082694467 1.135646049 1.189542311
Education3 1.058060703 1.111242334 1.165519173
Mortgage 0.095898360 0.094579489 0.093206878
Securities.Account1 -0.387696476 -0.411896015 -0.436512559
CD.Account1 2.182768343 2.237387195 2.292389453
Online1 -0.071735072 -0.079070669 -0.086549112
CreditCard1 -0.490747131 -0.513924794 -0.537218761
(Intercept) -4.005085203 -4.08081605 -4.15767389 -4.23556904
Age 0.016725651 0.01874211 0.02081900 0.02295478
Experience 0.009851477 0.01102482 0.01218323 0.01332046
Income 1.247583693 1.28621140 1.32498290 1.36385965
ZIP.Code 0.066667068 0.06873319 0.07069071 0.07253261
Family2 -0.383023418 -0.38813172 -0.39274571 -0.39687351
Family3 0.787136617 0.81971139 0.85265142 0.88591401
Family4 0.686305308 0.71484818 0.74355832 0.77239564
CCAvg 0.370410630 0.37184384 0.37316120 0.37437932
Education2 1.244310796 1.29987628 1.35616043 1.41308180
Education3 1.220822710 1.27708083 1.33421747 1.39215257
Mortgage 0.091792707 0.09034861 0.08888558 0.08741389
Securities.Account1 -0.461509095 -0.48684754 -0.51248865 -0.53839191
CD.Account1 2.347758347 2.40347204 2.45950307 2.51581815
Online1 -0.094153965 -0.10186883 -0.10967734 -0.11756306
CreditCard1 -0.560589664 -0.58399993 -0.60741360 -0.63079614coef(ridge.fit)[,100] # 100번째 람다 값에 대한 회귀계수 추정치 (Intercept) Age Experience
-4.23556904 0.02295478 0.01332046
Income ZIP.Code Family2
1.36385965 0.07253261 -0.39687351
Family3 Family4 CCAvg
0.88591401 0.77239564 0.37437932
Education2 Education3 Mortgage
1.41308180 1.39215257 0.08741389
Securities.Account1 CD.Account1 Online1
-0.53839191 2.51581815 -0.11756306
CreditCard1
-0.63079614 Caution! \(\lambda\)는 모형이 Training Dataset에 과적합 되는 것을 방지하기 위해 사용하는 모수이며, 교차 검증(Cross Validation)을 통해 최적의 값을 찾을 수 있다. 이러한 방법은 package "glmnet"에서 제공하는 함수 cv.glmnet()을 통해 수행할 수 있으며, 함수에 대한 자세한 옵션은 여기를 참고한다.
set.seed(200) # Seed 고정 -> 동일한 결과를 출력하기 위해
cv.ridge.fit <- cv.glmnet(x = train.x, # 예측 변수를 포함하는 행렬
y = UB.trd$Personal.Loan, # Target
family = "binomial", # Binary Classification
alpha = 0, # 0 : Ridge / 1 : Lasso / 0 < alpha < 1 : Elastic Net
nfolds = 5, # 5-Fold Cross Validation
type.measure = "auc") # AUC에 기반하여 최적의 람다 값 찾기
plot(cv.ridge.fit) # Plot
Result! 100개의 \(\lambda\) 값에 대한 AUC의 변화를 보여준다.
Caution! 만약 \(\lambda\) 값에 대해 직접 후보 값을 지정하고 싶으면 함수 cv.glmnet()의 옵션 lambda = 후보 값을 이용하면 된다.
cv.ridge.fit$lambda.min # 최적의 람다 값[1] 0.01917393max(cv.ridge.fit$cvm) # 최적의 람다 값에 대한 AUC[1] 0.960008516 x 1 sparse Matrix of class "dgCMatrix"
s1
(Intercept) -4.081
Age 0.019
Experience 0.011
Income 1.286
ZIP.Code 0.069
Family2 -0.388
Family3 0.820
Family4 0.715
CCAvg 0.372
Education2 1.300
Education3 1.277
Mortgage 0.090
Securities.Account1 -0.487
CD.Account1 2.403
Online1 -0.102
CreditCard1 -0.584Result! 최적의 \(\lambda\) 값에 대해 추정된 회귀계수를 이용하여 다음과 같은 모형식을 얻을 수 있다.
\[
\begin{align*}
\log{\frac{p}{1-p}} = &-4.081 + 0.019 Z_{\text{Age}} + 0.011 Z_{\text{Experience}} + 1.286 Z_{\text{Income}} \\
&+0.069 Z_{\text{ZIP.Code}}-0.388 X_{\text{Family2}} + 0.820 X_{\text{Family3}} + 0.715 X_{\text{Family4}} \\
&+ 0.372 Z_{\text{CCAvg}} + 1.300 X_{\text{Education2}} + 1.277 X_{\text{Education3}} + 0.090 Z_{\text{Mortgage}} \\
&-0.487 X_{\text{Securities.Account1}} + 2.403 X_{\text{CD.Account1}} -0.102 X_{\text{Online1}} -0.584 X_{\text{CreditCard1}}
\end{align*}
\]
7. 모형 평가
Caution! 모형 평가를 위해 Test Dataset에 대한 예측 class/확률 이 필요하며, 함수 predict()를 이용하여 생성한다.
# 예측 class 생성
test.ridge.class <- predict(cv.ridge.fit,
newx = test.x, # Test Dataset including Only 예측 변수
s = "lambda.min", # 최적의 람다 값 기반
type = "class") # 예측 class 생성
test.ridge.class %>%
as_tibble# A tibble: 749 × 1
lambda.min
<chr>
1 no
2 no
3 no
4 no
5 no
6 no
7 no
8 no
9 no
10 no
# ℹ 739 more rows7-1. ConfusionMatrix
CM <- caret::confusionMatrix(as.factor(test.ridge.class), UB.ted$Personal.Loan,
positive = "yes") # confusionMatrix(예측 class, 실제 class, positive = "관심 class")
CMConfusion Matrix and Statistics
Reference
Prediction no yes
no 669 39
yes 4 37
Accuracy : 0.9426
95% CI : (0.9234, 0.9581)
No Information Rate : 0.8985
P-Value [Acc > NIR] : 1.196e-05
Kappa : 0.6043
Mcnemar's Test P-Value : 2.161e-07
Sensitivity : 0.48684
Specificity : 0.99406
Pos Pred Value : 0.90244
Neg Pred Value : 0.94492
Prevalence : 0.10147
Detection Rate : 0.04940
Detection Prevalence : 0.05474
Balanced Accuracy : 0.74045
'Positive' Class : yes
7-2. ROC 곡선
# 예측 확률 생성
test.ridge.prob <- predict(cv.ridge.fit,
newx = test.x, # Test Dataset including Only 예측 변수
s = "lambda.min", # 최적의 람다 값 기반
type = "response") # 예측 확률 생성
test.ridge.prob %>% # "Personal.Loan = yes"에 대한 예측 확률
as_tibble# A tibble: 749 × 1
lambda.min
<dbl>
1 0.00819
2 0.0239
3 0.00692
4 0.00373
5 0.0257
6 0.0159
7 0.0504
8 0.114
9 0.0914
10 0.0458
# ℹ 739 more rowsac <- UB.ted$Personal.Loan # Test Dataset의 실제 class
pp <- as.numeric(test.ridge.prob) # 예측 확률을 수치형으로 변환1) Package “pROC”
pacman::p_load("pROC")
ridge.roc <- roc(ac, pp, plot = T, col = "gray") # roc(실제 class, 예측 확률)
auc <- round(auc(ridge.roc), 3)
legend("bottomright", legend = auc, bty = "n")
Caution! Package "pROC"를 통해 출력한 ROC 곡선은 다양한 함수를 이용해서 그래프를 수정할 수 있다.
# 함수 plot.roc() 이용
plot.roc(ridge.roc,
col="gray", # Line Color
print.auc = TRUE, # AUC 출력 여부
print.auc.col = "red", # AUC 글씨 색깔
print.thres = TRUE, # Cutoff Value 출력 여부
print.thres.pch = 19, # Cutoff Value를 표시하는 도형 모양
print.thres.col = "red", # Cutoff Value를 표시하는 도형의 색깔
auc.polygon = TRUE, # 곡선 아래 면적에 대한 여부
auc.polygon.col = "gray90") # 곡선 아래 면적의 색깔
# 함수 ggroc() 이용
ggroc(ridge.roc) +
annotate(geom = "text", x = 0.9, y = 1.0,
label = paste("AUC = ", auc),
size = 5,
color="red") +
theme_bw()
2) Package “Epi”
pacman::p_load("Epi")
# install_version("etm", version = "1.1", repos = "http://cran.us.r-project.org")
ROC(pp, ac, plot = "ROC") # ROC(예측 확률, 실제 class) 
3) Package “ROCR”
pacman::p_load("ROCR")
ridge.pred <- prediction(pp, ac) # prediction(예측 확률, 실제 class)
ridge.perf <- performance(ridge.pred, "tpr", "fpr") # performance(, "민감도", "1-특이도")
plot(ridge.perf, col = "gray") # ROC Curve
perf.auc <- performance(ridge.pred, "auc") # AUC
auc <- attributes(perf.auc)$y.values
legend("bottomright", legend = auc, bty = "n")
7-3. 향상 차트
1) Package “ROCR”
ridge.perf <- performance(ridge.pred, "lift", "rpp") # Lift Chart
plot(ridge.perf, main = "lift curve",
colorize = T, # Coloring according to cutoff
lwd = 2) 