title: “Analisis Regresi Logistik Biner” author: “Tanti Putri Ramadani” date: “2026-03-09” output: html_document —
Import Data
data <- read.csv("C:/Users/Ashilah/Downloads/Titanic_data.csv")
head(data)## X PassengerId Survived Sex Age Fare Pclass_1 Pclass_2 Pclass_3
## 1 791 792 0 1 0.2000 0.05074862 0 1 0
## 2 792 793 0 0 0.3500 0.13575256 0 0 1
## 3 793 794 0 1 0.3500 0.05991421 1 0 0
## 4 794 795 0 1 0.3125 0.01541158 0 0 1
## 5 795 796 0 1 0.4875 0.02537431 0 1 0
## 6 796 797 1 0 0.6125 0.05061043 1 0 0
## Family_size Title_1 Title_2 Title_3 Title_4 Emb_1 Emb_2 Emb_3
## 1 0 1 0 0 0 0 0 1
## 2 1 0 0 0 1 0 0 1
## 3 0 1 0 0 0 1 0 0
## 4 0 1 0 0 0 0 0 1
## 5 0 1 0 0 0 0 0 1
## 6 0 0 1 0 0 0 0 1Nama Variabel dalam Dataset
names(data)## [1] "X" "PassengerId" "Survived" "Sex" "Age"
## [6] "Fare" "Pclass_1" "Pclass_2" "Pclass_3" "Family_size"
## [11] "Title_1" "Title_2" "Title_3" "Title_4" "Emb_1"
## [16] "Emb_2" "Emb_3"Struktur Data
str(data)## 'data.frame': 100 obs. of 17 variables:
## $ X : int 791 792 793 794 795 796 797 798 799 800 ...
## $ PassengerId: int 792 793 794 795 796 797 798 799 800 801 ...
## $ Survived : int 0 0 0 0 0 1 1 0 0 0 ...
## $ Sex : int 1 0 1 1 1 0 0 1 0 1 ...
## $ Age : num 0.2 0.35 0.35 0.312 0.487 ...
## $ Fare : num 0.0507 0.1358 0.0599 0.0154 0.0254 ...
## $ Pclass_1 : int 0 0 1 0 0 1 0 0 0 0 ...
## $ Pclass_2 : int 1 0 0 0 1 0 0 0 0 1 ...
## $ Pclass_3 : int 0 1 0 1 0 0 1 1 1 0 ...
## $ Family_size: num 0 1 0 0 0 0 0 0 0.2 0 ...
## $ Title_1 : int 1 0 1 1 1 0 1 1 1 1 ...
## $ Title_2 : int 0 0 0 0 0 1 0 0 0 0 ...
## $ Title_3 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ Title_4 : int 0 1 0 0 0 0 0 0 0 0 ...
## $ Emb_1 : int 0 0 1 0 0 0 0 1 0 0 ...
## $ Emb_2 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ Emb_3 : int 1 1 0 1 1 1 1 0 1 1 ...summary(data)## X PassengerId Survived Sex
## Min. :791.0 Min. :792.0 Min. :0.00 Min. :0.00
## 1st Qu.:815.8 1st Qu.:816.8 1st Qu.:0.00 1st Qu.:0.00
## Median :840.5 Median :841.5 Median :0.00 Median :1.00
## Mean :840.5 Mean :841.5 Mean :0.36 Mean :0.65
## 3rd Qu.:865.2 3rd Qu.:866.2 3rd Qu.:1.00 3rd Qu.:1.00
## Max. :890.0 Max. :891.0 Max. :1.00 Max. :1.00
## Age Fare Pclass_1 Pclass_2
## Min. :0.00525 Min. :0.00000 Min. :0.00 Min. :0.0
## 1st Qu.:0.27187 1st Qu.:0.01541 1st Qu.:0.00 1st Qu.:0.0
## Median :0.35000 Median :0.02537 Median :0.00 Median :0.0
## Mean :0.35566 Mean :0.04833 Mean :0.23 Mean :0.2
## 3rd Qu.:0.42656 3rd Qu.:0.05856 3rd Qu.:0.00 3rd Qu.:0.0
## Max. :0.92500 Max. :0.32180 Max. :1.00 Max. :1.0
## Pclass_3 Family_size Title_1 Title_2 Title_3
## Min. :0.00 Min. :0.000 Min. :0.00 Min. :0.00 Min. :0.00
## 1st Qu.:0.00 1st Qu.:0.000 1st Qu.:1.00 1st Qu.:0.00 1st Qu.:0.00
## Median :1.00 Median :0.000 Median :1.00 Median :0.00 Median :0.00
## Mean :0.57 Mean :0.104 Mean :0.77 Mean :0.01 Mean :0.08
## 3rd Qu.:1.00 3rd Qu.:0.100 3rd Qu.:1.00 3rd Qu.:0.00 3rd Qu.:0.00
## Max. :1.00 Max. :1.000 Max. :1.00 Max. :1.00 Max. :1.00
## Title_4 Emb_1 Emb_2 Emb_3
## Min. :0.00 Min. :0.00 Min. :0.00 Min. :0.00
## 1st Qu.:0.00 1st Qu.:0.00 1st Qu.:0.00 1st Qu.:0.00
## Median :0.00 Median :0.00 Median :0.00 Median :1.00
## Mean :0.14 Mean :0.21 Mean :0.04 Mean :0.74
## 3rd Qu.:0.00 3rd Qu.:0.00 3rd Qu.:0.00 3rd Qu.:1.00
## Max. :1.00 Max. :1.00 Max. :1.00 Max. :1.00Cek Missing Value
colSums(is.na(data))## X PassengerId Survived Sex Age Fare
## 0 0 0 0 0 0
## Pclass_1 Pclass_2 Pclass_3 Family_size Title_1 Title_2
## 0 0 0 0 0 0
## Title_3 Title_4 Emb_1 Emb_2 Emb_3
## 0 0 0 0 0Membersihkan data dari missing value
data <- na.omit(data)Korelasi Variabel Numerik
num_data <- data[sapply(data, is.numeric)]
if(ncol(num_data) > 1){
corr_matrix <- cor(num_data, use="complete.obs")
corrplot(corr_matrix,
method="color",
type="upper",
tl.cex=0.8)
}
Model Regresi Logistik
Model logistik:
\[ \ln\left(\frac{p}{1-p}\right)= \beta_0 + \beta_1X_1 + \beta_2X_2 + ... + \beta_kX_k \]
Model akan menggunakan semua variabel numerik sebagai prediktor.
predictors <- names(num_data)
predictors <- predictors[predictors != "Survived"]
formula_model <- as.formula(
paste("Survived ~", paste(predictors, collapse = "+"))
)
model_logit <- glm(formula_model,
data = data,
family = binomial)
summary(model_logit)##
## Call:
## glm(formula = formula_model, family = binomial, data = data)
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.629e+00 2.400e+03 0.002 0.99846
## X 4.563e-03 1.308e-02 0.349 0.72712
## PassengerId NA NA NA NA
## Sex -6.381e+00 1.483e+00 -4.301 1.7e-05 ***
## Age -2.168e+00 4.467e+00 -0.485 0.62735
## Fare 2.836e+01 1.405e+01 2.019 0.04352 *
## Pclass_1 1.555e+00 1.086e+00 1.432 0.15225
## Pclass_2 -5.604e-02 1.057e+00 -0.053 0.95772
## Pclass_3 NA NA NA NA
## Family_size -1.741e+01 5.660e+00 -3.077 0.00209 **
## Title_1 3.852e+00 1.502e+00 2.564 0.01034 *
## Title_2 1.567e+01 2.400e+03 0.007 0.99479
## Title_3 1.179e+01 3.644e+00 3.234 0.00122 **
## Title_4 NA NA NA NA
## Emb_1 -7.170e+00 2.400e+03 -0.003 0.99762
## Emb_2 -6.453e+00 2.400e+03 -0.003 0.99785
## Emb_3 -9.029e+00 2.400e+03 -0.004 0.99700
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 130.684 on 99 degrees of freedom
## Residual deviance: 51.135 on 86 degrees of freedom
## AIC: 79.135
##
## Number of Fisher Scoring iterations: 15Odds Ratio
odds_ratio <- data.frame(
Variabel = names(coef(model_logit)),
Odds_Ratio = exp(coef(model_logit))
)
odds_ratio## Variabel Odds_Ratio
## (Intercept) (Intercept) 1.023736e+02
## X X 1.004573e+00
## PassengerId PassengerId NA
## Sex Sex 1.694074e-03
## Age Age 1.143600e-01
## Fare Fare 2.063109e+12
## Pclass_1 Pclass_1 4.737205e+00
## Pclass_2 Pclass_2 9.454967e-01
## Pclass_3 Pclass_3 NA
## Family_size Family_size 2.739101e-08
## Title_1 Title_1 4.709295e+01
## Title_2 Title_2 6.400800e+06
## Title_3 Title_3 1.315294e+05
## Title_4 Title_4 NA
## Emb_1 Emb_1 7.692061e-04
## Emb_2 Emb_2 1.575650e-03
## Emb_3 Emb_3 1.198812e-04Prediksi Probabilitas
prob <- predict(model_logit, type="response")
prediksi <- ifelse(prob > 0.5, 1, 0)
hasil_prediksi <- data.frame(
Observasi = 1:nrow(data),
Probabilitas = round(prob,4),
Prediksi = prediksi
)
head(hasil_prediksi)## Observasi Probabilitas Prediksi
## 1 1 0.0855 0
## 2 2 0.0000 0
## 3 3 0.7396 1
## 4 4 0.0280 0
## 5 5 0.0242 0
## 6 6 1.0000 1Confusion Matrix
confusionMatrix(
as.factor(prediksi),
as.factor(data$Survived)
)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 60 6
## 1 4 30
##
## Accuracy : 0.9
## 95% CI : (0.8238, 0.951)
## No Information Rate : 0.64
## P-Value [Acc > NIR] : 2.814e-09
##
## Kappa : 0.7803
##
## Mcnemar's Test P-Value : 0.7518
##
## Sensitivity : 0.9375
## Specificity : 0.8333
## Pos Pred Value : 0.9091
## Neg Pred Value : 0.8824
## Prevalence : 0.6400
## Detection Rate : 0.6000
## Detection Prevalence : 0.6600
## Balanced Accuracy : 0.8854
##
## 'Positive' Class : 0
## ROC Curve
roc_curve <- roc(data$Survived, prob)## Setting levels: control = 0, case = 1## Setting direction: controls < casesplot(roc_curve,
col="blue",
main="ROC Curve Model Logistik")
auc(roc_curve)## Area under the curve: 0.9431Kesimpulan
Analisis ini menggunakan Regresi Logistik Biner untuk memodelkan probabilitas kejadian pada variabel dependen.
Tahapan analisis:
- Import data CSV
- Eksplorasi data
- Analisis korelasi variabel numerik
- Estimasi model regresi logistik
- Interpretasi menggunakan Odds Ratio
- Evaluasi model menggunakan Confusion Matrix dan ROC Curve