rm(list = ls())
# 로지스틱 회귀분석
# 1. 패키지 설치 및 로드
#install.packages("mlbench")
library(mlbench)
library(caret)
## Loading required package: ggplot2
## Loading required package: lattice
# 2. 데이터 불러오기
data(Sonar)
str(Sonar)
## 'data.frame': 208 obs. of 61 variables:
## $ V1 : num 0.02 0.0453 0.0262 0.01 0.0762 0.0286 0.0317 0.0519 0.0223 0.0164 ...
## $ V2 : num 0.0371 0.0523 0.0582 0.0171 0.0666 0.0453 0.0956 0.0548 0.0375 0.0173 ...
## $ V3 : num 0.0428 0.0843 0.1099 0.0623 0.0481 ...
## $ V4 : num 0.0207 0.0689 0.1083 0.0205 0.0394 ...
## $ V5 : num 0.0954 0.1183 0.0974 0.0205 0.059 ...
## $ V6 : num 0.0986 0.2583 0.228 0.0368 0.0649 ...
## $ V7 : num 0.154 0.216 0.243 0.11 0.121 ...
## $ V8 : num 0.16 0.348 0.377 0.128 0.247 ...
## $ V9 : num 0.3109 0.3337 0.5598 0.0598 0.3564 ...
## $ V10 : num 0.211 0.287 0.619 0.126 0.446 ...
## $ V11 : num 0.1609 0.4918 0.6333 0.0881 0.4152 ...
## $ V12 : num 0.158 0.655 0.706 0.199 0.395 ...
## $ V13 : num 0.2238 0.6919 0.5544 0.0184 0.4256 ...
## $ V14 : num 0.0645 0.7797 0.532 0.2261 0.4135 ...
## $ V15 : num 0.066 0.746 0.648 0.173 0.453 ...
## $ V16 : num 0.227 0.944 0.693 0.213 0.533 ...
## $ V17 : num 0.31 1 0.6759 0.0693 0.7306 ...
## $ V18 : num 0.3 0.887 0.755 0.228 0.619 ...
## $ V19 : num 0.508 0.802 0.893 0.406 0.203 ...
## $ V20 : num 0.48 0.782 0.862 0.397 0.464 ...
## $ V21 : num 0.578 0.521 0.797 0.274 0.415 ...
## $ V22 : num 0.507 0.405 0.674 0.369 0.429 ...
## $ V23 : num 0.433 0.396 0.429 0.556 0.573 ...
## $ V24 : num 0.555 0.391 0.365 0.485 0.54 ...
## $ V25 : num 0.671 0.325 0.533 0.314 0.316 ...
## $ V26 : num 0.641 0.32 0.241 0.533 0.229 ...
## $ V27 : num 0.71 0.327 0.507 0.526 0.7 ...
## $ V28 : num 0.808 0.277 0.853 0.252 1 ...
## $ V29 : num 0.679 0.442 0.604 0.209 0.726 ...
## $ V30 : num 0.386 0.203 0.851 0.356 0.472 ...
## $ V31 : num 0.131 0.379 0.851 0.626 0.51 ...
## $ V32 : num 0.26 0.295 0.504 0.734 0.546 ...
## $ V33 : num 0.512 0.198 0.186 0.612 0.288 ...
## $ V34 : num 0.7547 0.2341 0.2709 0.3497 0.0981 ...
## $ V35 : num 0.854 0.131 0.423 0.395 0.195 ...
## $ V36 : num 0.851 0.418 0.304 0.301 0.418 ...
## $ V37 : num 0.669 0.384 0.612 0.541 0.46 ...
## $ V38 : num 0.61 0.106 0.676 0.881 0.322 ...
## $ V39 : num 0.494 0.184 0.537 0.986 0.283 ...
## $ V40 : num 0.274 0.197 0.472 0.917 0.243 ...
## $ V41 : num 0.051 0.167 0.465 0.612 0.198 ...
## $ V42 : num 0.2834 0.0583 0.2587 0.5006 0.2444 ...
## $ V43 : num 0.282 0.14 0.213 0.321 0.185 ...
## $ V44 : num 0.4256 0.1628 0.2222 0.3202 0.0841 ...
## $ V45 : num 0.2641 0.0621 0.2111 0.4295 0.0692 ...
## $ V46 : num 0.1386 0.0203 0.0176 0.3654 0.0528 ...
## $ V47 : num 0.1051 0.053 0.1348 0.2655 0.0357 ...
## $ V48 : num 0.1343 0.0742 0.0744 0.1576 0.0085 ...
## $ V49 : num 0.0383 0.0409 0.013 0.0681 0.023 0.0264 0.0507 0.0285 0.0777 0.0092 ...
## $ V50 : num 0.0324 0.0061 0.0106 0.0294 0.0046 0.0081 0.0159 0.0178 0.0439 0.0198 ...
## $ V51 : num 0.0232 0.0125 0.0033 0.0241 0.0156 0.0104 0.0195 0.0052 0.0061 0.0118 ...
## $ V52 : num 0.0027 0.0084 0.0232 0.0121 0.0031 0.0045 0.0201 0.0081 0.0145 0.009 ...
## $ V53 : num 0.0065 0.0089 0.0166 0.0036 0.0054 0.0014 0.0248 0.012 0.0128 0.0223 ...
## $ V54 : num 0.0159 0.0048 0.0095 0.015 0.0105 0.0038 0.0131 0.0045 0.0145 0.0179 ...
## $ V55 : num 0.0072 0.0094 0.018 0.0085 0.011 0.0013 0.007 0.0121 0.0058 0.0084 ...
## $ V56 : num 0.0167 0.0191 0.0244 0.0073 0.0015 0.0089 0.0138 0.0097 0.0049 0.0068 ...
## $ V57 : num 0.018 0.014 0.0316 0.005 0.0072 0.0057 0.0092 0.0085 0.0065 0.0032 ...
## $ V58 : num 0.0084 0.0049 0.0164 0.0044 0.0048 0.0027 0.0143 0.0047 0.0093 0.0035 ...
## $ V59 : num 0.009 0.0052 0.0095 0.004 0.0107 0.0051 0.0036 0.0048 0.0059 0.0056 ...
## $ V60 : num 0.0032 0.0044 0.0078 0.0117 0.0094 0.0062 0.0103 0.0053 0.0022 0.004 ...
## $ Class: Factor w/ 2 levels "M","R": 2 2 2 2 2 2 2 2 2 2 ...
# 3. 종속변수 확인
table(Sonar$Class)
##
## M R
## 111 97
# 4. 데이터 분할 (Train/Test)
set.seed(123)
index <- createDataPartition(Sonar$Class, p = 0.7, list = FALSE)
train <- Sonar[index, ]
test <- Sonar[-index, ]
# 5. 로지스틱 회귀모형 적합
model <- glm(Class ~ ., data = train, family = binomial())
## Warning: glm.fit: algorithm did not converge
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
# 6. 예측 확률 및 분류
prob <- predict(model, newdata = test, type = "response")
round(prob, 2)
## 2 10 15 18 22 28 33 38 41 45 47 48 49 53 57 58
## 1.00 0.00 1.00 0.00 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00
## 59 63 65 69 72 73 75 78 84 89 90 92 93 98 99 100
## 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00 0.00 1.00
## 107 108 109 116 117 121 125 126 132 134 137 141 142 145 146 149
## 0.00 0.00 1.00 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00
## 151 153 155 158 159 161 163 168 172 182 186 199 202 206
## 1.00 0.00 0.00 1.00 1.00 0.97 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00
pred <- ifelse(prob > 0.5, "M", "R")
pred <- factor(pred, levels = levels(test$Class))
# 7. 혼동행렬로 성능 평가
confusionMatrix(pred, test$Class)
## Confusion Matrix and Statistics
##
## Reference
## Prediction M R
## M 8 19
## R 25 10
##
## Accuracy : 0.2903
## 95% CI : (0.182, 0.4195)
## No Information Rate : 0.5323
## P-Value [Acc > NIR] : 1.000
##
## Kappa : -0.4076
##
## Mcnemar's Test P-Value : 0.451
##
## Sensitivity : 0.2424
## Specificity : 0.3448
## Pos Pred Value : 0.2963
## Neg Pred Value : 0.2857
## Prevalence : 0.5323
## Detection Rate : 0.1290
## Detection Prevalence : 0.4355
## Balanced Accuracy : 0.2936
##
## 'Positive' Class : M
##
# 8. ROC AUC 평가
library(pROC)
## Type 'citation("pROC")' for a citation.
##
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
##
## cov, smooth, var
roc_obj <- roc(response = test$Class, predictor = prob,
levels = c("R", "M"))
## Setting direction: controls > cases
# 즉, roc() 함수는
# "정답 클래스와 예측 확률을 비교하여 ROC 곡선과 AUC를 계산"합니다.
# 모델이 지뢰(Mine) 클래스("M")를
# 얼마나 정확하게 잘 예측했는지 평가하겠다는 뜻입니다.
plot(roc_obj, main = "ROC Curve")
auc(roc_obj)
## Area under the curve: 0.7189
data(mtcars)
head
## function (x, ...)
## UseMethod("head")
## <bytecode: 0x0000021c3c199a00>
## <environment: namespace:utils>
# 로지스틱 회귀모형 : 수동변속기 여부(am) ~ 마력(hp) + 무게(wt)
model <- glm(am ~ hp + wt, data = mtcars, family = binomial)
summary(model)
##
## Call:
## glm(formula = am ~ hp + wt, family = binomial, data = mtcars)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 18.86630 7.44356 2.535 0.01126 *
## hp 0.03626 0.01773 2.044 0.04091 *
## wt -8.08348 3.06868 -2.634 0.00843 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 43.230 on 31 degrees of freedom
## Residual deviance: 10.059 on 29 degrees of freedom
## AIC: 16.059
##
## Number of Fisher Scoring iterations: 8
# 오즈(odds) 관점 해석에서 hp 해석 방법
# hp 로지스틱 회귀계수 : 0.03626
# 해석
exp(0.03626)
## [1] 1.036925
# hp가 1 증가할 때 -> 수동변속기(종속변수)
# 오즈가 약 1.037배 증가한다.
# 마력이 높아질수록 수동 변속기일 확률이
# 약간 더 커진다.