Deskripsi Data

Dataset yang digunakan adalah Wisconsin Breast Cancer Dataset yang berisi 569 observasi dengan 30 fitur numerik hasil pengukuran sel tumor payudara. Variabel dependen yang digunakan adalah radius_mean (rata-rata radius tumor), sedangkan variabel independen meliputi texture_mean, smoothness_mean, compactness_mean, dan concavity_mean.

# Load library
library(readxl)
library(dplyr)

# Import dataset
data_kanker <- read_excel("cancer_dataset.xlsx")

# Seleksi variabel yang digunakan
data_model <- data_kanker %>%
  select(radius_mean, texture_mean, smoothness_mean, compactness_mean, concavity_mean)

# Tampilkan ringkasan statistik deskriptif
summary(data_model)
##   radius_mean      texture_mean   smoothness_mean   compactness_mean 
##  Min.   : 6.981   Min.   : 9.71   Min.   :0.05263   Min.   :0.01938  
##  1st Qu.:11.700   1st Qu.:16.17   1st Qu.:0.08637   1st Qu.:0.06492  
##  Median :13.370   Median :18.84   Median :0.09587   Median :0.09263  
##  Mean   :14.127   Mean   :19.29   Mean   :0.09636   Mean   :0.10434  
##  3rd Qu.:15.780   3rd Qu.:21.80   3rd Qu.:0.10530   3rd Qu.:0.13040  
##  Max.   :28.110   Max.   :39.28   Max.   :0.16340   Max.   :0.34540  
##  concavity_mean   
##  Min.   :0.00000  
##  1st Qu.:0.02956  
##  Median :0.06154  
##  Mean   :0.08880  
##  3rd Qu.:0.13070  
##  Max.   :0.42680

Jumlah observasi dalam dataset: 569 data.

  • Rata-rata radius_mean adalah 14.1273
  • Rata-rata texture_mean adalah 19.2896
  • Rata-rata smoothness_mean adalah 0.0964
  • Rata-rata compactness_mean adalah 0.1043
  • Rata-rata concavity_mean adalah 0.0888

Model Regresi

Bentuk umum persamaan regresi linier berganda: \[ Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \beta_4 X_4 + \epsilon \]

Keterangan:

  • \(Y\) = radius_mean (Rata-rata Radius Tumor)
  • \(X_1\) = texture_mean (Rata-rata Tekstur)
  • \(X_2\) = smoothness_mean (Rata-rata Kehalusan)
  • \(X_3\) = compactness_mean (Rata-rata Kekompakan)
  • \(X_4\) = concavity_mean (Rata-rata Cekung)
  • \(\epsilon\) = Error / Galat

Estimasi Parameter

model <- lm(radius_mean ~ texture_mean + smoothness_mean + compactness_mean + concavity_mean,
            data = data_model)
summary(model)
## 
## Call:
## lm(formula = radius_mean ~ texture_mean + smoothness_mean + compactness_mean + 
##     concavity_mean, data = data_model)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.4052  -1.3145  -0.0654   1.5331   6.7888 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       14.52674    1.01773  14.274  < 2e-16 ***
## texture_mean       0.07457    0.02572   2.900 0.003878 ** 
## smoothness_mean  -39.35931   10.09227  -3.900 0.000108 ***
## compactness_mean -17.47816    4.77437  -3.661 0.000275 ***
## concavity_mean    42.55000    2.82666  15.053  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.446 on 564 degrees of freedom
## Multiple R-squared:  0.5215, Adjusted R-squared:  0.5181 
## F-statistic: 153.7 on 4 and 564 DF,  p-value: < 2.2e-16

Model Akhir: \[ \widehat{radius} = 14.5267 + 0.0746 \cdot texture + -39.3593 \cdot smoothness + -17.4782 \cdot compactness + 42.55 \cdot concavity \]

Nilai R-Squared model: 0.5215, artinya variabel independen mampu menjelaskan 52.15% variasi pada radius_mean.

Pengujian Asumsi Klasik

Uji Normalitas Residual

Hipotesis:

  • \(H_0\): Residual berdistribusi normal
  • \(H_1\): Residual tidak berdistribusi normal
error <- model$residuals
ks.test(error, "pnorm", mean(error), sqrt(var(error)))
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  error
## D = 0.04953, p-value = 0.1226
## alternative hypothesis: two-sided

Uji Autokorelasi (Durbin-Watson)

Hipotesis:

  • \(H_0\): Tidak terdapat autokorelasi antar residual
  • \(H_1\): Terdapat autokorelasi antar residual
library(lmtest)
dwtest(model)
## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.7576, p-value = 0.001761
## alternative hypothesis: true autocorrelation is greater than 0

Uji Heteroskedastisitas (Breusch-Pagan)

Hipotesis:

  • \(H_0\): Ragam residual bersifat homoskedastis (konstan)
  • \(H_1\): Ragam residual bersifat heteroskedastis
bptest(model)
## 
##  studentized Breusch-Pagan test
## 
## data:  model
## BP = 107.18, df = 4, p-value < 2.2e-16

Uji Multikolinearitas (VIF)

Nilai VIF > 10 mengindikasikan adanya multikolinearitas yang serius antar variabel independen.

library(car)
vif(model)
##     texture_mean  smoothness_mean compactness_mean   concavity_mean 
##         1.161145         1.912218         6.034533         4.819628

Pengujian Hipotesis Model

Uji Simultan (Uji F)

Hipotesis:

  • \(H_0\): \(\beta_1 = \beta_2 = \beta_3 = \beta_4 = 0\) (tidak ada pengaruh simultan)
  • \(H_1\): Minimal satu \(\beta_i \neq 0\) (ada pengaruh simultan)
# F-statistic dan p-value dari summary model
fstat <- summary(model)$fstatistic
pf(fstat[1], fstat[2], fstat[3], lower.tail = FALSE)
##       value 
## 7.78587e-89

Nilai F-statistik: 153.685 dengan p-value: 0

Uji Parsial (Uji t)

# Koefisien, standard error, t-value, dan p-value
coef(summary(model))
##                      Estimate  Std. Error   t value     Pr(>|t|)
## (Intercept)       14.52674299  1.01773274 14.273632 1.103920e-39
## texture_mean       0.07457375  0.02571598  2.899899 3.878263e-03
## smoothness_mean  -39.35931445 10.09226981 -3.899947 1.078051e-04
## compactness_mean -17.47816100  4.77436839 -3.660832 2.750293e-04
## concavity_mean    42.54999565  2.82665920 15.053104 2.710719e-43

Plot Model Regresi

Scatterplot Variabel Independen vs Dependen

Scatterplot Variabel Prediktor vs Radius Mean

Scatterplot Variabel Prediktor vs Radius Mean

Diagnostic Plot Residual

Diagnostic Plot Model Regresi

Diagnostic Plot Model Regresi

Plot Nilai Aktual vs Nilai Prediksi

Nilai Aktual vs Nilai Prediksi

Nilai Aktual vs Nilai Prediksi