Pre-Processing Data
Carolin
2023-09-04
1 Eksplorasi Data
df <- read.csv("D:/Kuliah/Mat/TSA Kominfo/Praktikum/2.ChurnDetection.csv", header = TRUE, sep = ",")
# Melihat struktur data
cat("STRUKTUR :", "\n\n")## STRUKTUR :str(df) ## 'data.frame': 667 obs. of 20 variables:
## $ State : chr "LA" "IN" "NY" "SC" ...
## $ Account.length : int 117 65 161 111 49 36 65 119 10 68 ...
## $ Area.code : int 408 415 415 415 510 408 415 415 408 415 ...
## $ International.plan : chr "No" "No" "No" "No" ...
## $ Voice.mail.plan : chr "No" "No" "No" "No" ...
## $ Number.vmail.messages : int 0 0 0 0 0 30 0 0 0 0 ...
## $ Total.day.minutes : num 184 129 333 110 119 ...
## $ Total.day.calls : int 97 137 67 103 117 128 120 114 112 70 ...
## $ Total.day.charge : num 31.4 21.9 56.6 18.8 20.3 ...
## $ Total.eve.minutes : num 352 228 318 137 215 ...
## $ Total.eve.calls : int 80 83 97 102 109 80 122 117 66 164 ...
## $ Total.eve.charge : num 29.9 19.4 27 11.7 18.3 ...
## $ Total.night.minutes : num 216 209 161 190 179 ...
## $ Total.night.calls : int 90 111 128 105 90 109 118 91 57 103 ...
## $ Total.night.charge : num 9.71 9.4 7.23 8.53 8.04 ...
## $ Total.intl.minutes : num 8.7 12.7 5.4 7.7 11.1 14.5 13.2 8.8 11.4 12.1 ...
## $ Total.intl.calls : int 4 6 9 6 1 6 5 3 6 3 ...
## $ Total.intl.charge : num 2.35 3.43 1.46 2.08 3 3.92 3.56 2.38 3.08 3.27 ...
## $ Customer.service.calls: int 1 4 4 2 1 0 3 5 2 3 ...
## $ Churn : chr "False" "True" "True" "False" ...# Melihat ringkasan data
cat("\n\n", "SUMMMARY :", "\n\n")##
##
## SUMMMARY :summary(df)## State Account.length Area.code International.plan
## Length:667 Min. : 1.0 Min. :408.0 Length:667
## Class :character 1st Qu.: 76.0 1st Qu.:408.0 Class :character
## Mode :character Median :102.0 Median :415.0 Mode :character
## Mean :102.8 Mean :436.2
## 3rd Qu.:128.0 3rd Qu.:415.0
## Max. :232.0 Max. :510.0
## Voice.mail.plan Number.vmail.messages Total.day.minutes Total.day.calls
## Length:667 Min. : 0.000 Min. : 25.9 Min. : 30.0
## Class :character 1st Qu.: 0.000 1st Qu.:146.2 1st Qu.: 87.5
## Mode :character Median : 0.000 Median :178.3 Median :101.0
## Mean : 8.408 Mean :180.9 Mean :100.9
## 3rd Qu.:20.000 3rd Qu.:220.7 3rd Qu.:115.0
## Max. :51.000 Max. :334.3 Max. :165.0
## Total.day.charge Total.eve.minutes Total.eve.calls Total.eve.charge
## Min. : 4.40 Min. : 48.1 Min. : 37.0 Min. : 4.09
## 1st Qu.:24.86 1st Qu.:171.1 1st Qu.: 88.0 1st Qu.:14.54
## Median :30.31 Median :203.7 Median :101.0 Median :17.31
## Mean :30.76 Mean :203.4 Mean :100.5 Mean :17.29
## 3rd Qu.:37.52 3rd Qu.:236.4 3rd Qu.:113.0 3rd Qu.:20.09
## Max. :56.83 Max. :361.8 Max. :168.0 Max. :30.75
## Total.night.minutes Total.night.calls Total.night.charge Total.intl.minutes
## Min. : 23.2 Min. : 42.0 Min. : 1.040 Min. : 0.00
## 1st Qu.:167.9 1st Qu.: 86.0 1st Qu.: 7.560 1st Qu.: 8.60
## Median :201.6 Median :100.0 Median : 9.070 Median :10.50
## Mean :199.7 Mean :100.1 Mean : 8.986 Mean :10.24
## 3rd Qu.:231.5 3rd Qu.:113.5 3rd Qu.:10.420 3rd Qu.:12.05
## Max. :367.7 Max. :175.0 Max. :16.550 Max. :18.30
## Total.intl.calls Total.intl.charge Customer.service.calls Churn
## Min. : 0.000 Min. :0.000 Min. :0.000 Length:667
## 1st Qu.: 3.000 1st Qu.:2.320 1st Qu.:1.000 Class :character
## Median : 4.000 Median :2.840 Median :1.000 Mode :character
## Mean : 4.528 Mean :2.765 Mean :1.564
## 3rd Qu.: 6.000 3rd Qu.:3.255 3rd Qu.:2.000
## Max. :18.000 Max. :4.940 Max. :8.000summary(df$Total.day.calls)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 30.0 87.5 101.0 100.9 115.0 165.01.1 Histogram
histogram <- hist(df$Total.day.calls, main="HISTOGRAM Total Calls (Day) ", xlab = "Days")
cat("Breaks :", histogram$breaks, "\n")## Breaks : 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170cat("Counts :", histogram$counts, "\n")## Counts : 3 1 11 30 56 99 125 127 96 75 24 18 0 2cat("Mids :", histogram$mids, "\n")## Mids : 35 45 55 65 75 85 95 105 115 125 135 145 155 165hist(df$Total.day.calls, freq = FALSE, main="HISTOGRAM Total Calls", xlab = "Days")
histo.2 <- hist(df$Total.day.calls, freq = FALSE, breaks = 30,
main="HISTOGRAM Total Calls", xlab = "Days")
cat("BREAKS :", histo.2$breaks, "\n\n")## BREAKS : 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165n <- length(df$Total.day.calls) # banyaknya amatan
k1 <- sqrt(n) # akar kuadrat banyaknya amatan
histo.3 <- hist(df$Total.day.calls, freq = FALSE, breaks = k1,
main="HISTOGRAM Total Calls", xlab = "Days")
cat("BREAKS :", histo.3$breaks, "\n\n")## BREAKS : 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165length(histo.3$breaks)## [1] 28k2 <- log2(n)+1 # Formula yang diusulkan H.A. Sturges
histo.4 <- hist(df$Total.day.calls, freq = FALSE, breaks = k2,
main="HISTOGRAM Total Calls", xlab = "Days")
cat("BREAKS :", histo.4$breaks, "\n\n")## BREAKS : 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170k3 <- 2*n^(1/3) # Formula yang diusulkan Rice University
histo.5 <- hist(df$Total.day.calls, freq = FALSE, breaks = k3,
main="HISTOGRAM Total Calls", xlab = "Days")
cat("BREAKS :", histo.5$breaks, "\n\n")## BREAKS : 30 40 50 60 70 80 90 100 110 120 130 140 150 160 1701.1.1 Histogram dengan kurva
# visualisasi histogram dengan kurva
hist(df$Total.day.calls, freq = FALSE, main = "Distribusi Total Panggilan",
xlab = "Total Panggilan", col = "lightgreen",
xlim = c(20,180), ylim = c(0,0.02))
# Menambahkan kurva Normal
curve(dnorm(x, mean = mean(df$Total.day.calls), sd = sd(df$Total.day.calls)),
add = TRUE, col = "darkblue", lwd = 2)
1.1.2 Histogram (perbandingan sebaran)
par(mfrow = c(1,2))
hist(df[df$Total.day.calls < 100,]$Total.day.calls, main = "",
col = "green", xlab = "Total Panggilan dibawah 100")
hist(df[df$Total.day.calls >= 100,]$Total.day.calls, main = "",
col = "blue", xlab = "Total Panggilan diatas 100")
plot(density(df$Total.day.calls), main = "Perbandingan", ylim = c(0, 0.022))
lines(density(df$Total.eve.calls), col = "green")
lines(density(df$Total.night.calls), col = "red")
legend("topleft", c("Day Calls", "Evenening Calls", "Night Calls"),
col =c("black","green","red"), lty=1)
hist(df$Total.intl.calls, freq = FALSE, breaks=20, main = "Distribusi Total Panggilan Int",
xlab = "Total Panggilan", col = "lightgreen",)
hist(df$Total.intl.charge, freq = FALSE, breaks=20, main = "Distribusi Total Panggilan Int",
xlab = "Total Panggilan", col = "lightgreen",)
1.2 Boxplot
1.2.1 Visualisasi boxplot (vertical)
boxplot(df$Total.day.calls, main = "Distribusi Total Panggilan",
ylab = "Total Panggilan", horizontal = TRUE)
1.2.2 Visualisasi boxplot
boxplot(df$Total.day.calls, horizontal = TRUE,
main = "Distribusi Total Panggilan", ylab = "Total Panggilan")
1.2.3 Statistik lima Serangkai
cat("Minimum :", min(df$Total.day.calls)) # atau ## Minimum : 30cat("Q1 (25%) :", quantile(df$Total.day.calls)[1], "\n")## Q1 (25%) : 30cat("Q1 (25%) :", quantile(df$Total.day.calls)[2], "\n")## Q1 (25%) : 87.5cat("Q2 (Med) :", quantile(df$Total.day.calls)[3], "\n")## Q2 (Med) : 101cat("Q3 (75%) :", quantile(df$Total.day.calls)[4], "\n")## Q3 (75%) : 115cat("Maximum :", max(df$Total.day.calls), "\n") ## Maximum : 165quantile(df$Total.day.calls)[5]## 100%
## 165quantile(df$Total.day.calls)## 0% 25% 50% 75% 100%
## 30.0 87.5 101.0 115.0 165.01.2.4 Alternatif Kuantil (dan persentil)
1.2.4.1 Q1, Median (Q2), Q3
Q1 <- quantile(df$Total.day.calls, probs=0.25, names=F)
Q2 <- quantile(df$Total.day.calls, probs=0.5, names=F)
Q3 <- quantile(df$Total.day.calls, probs=0.75, names=F)
cat("Kuartil 1:", Q1, "\n")## Kuartil 1: 87.5cat("Median:", Q2, "\n")## Median: 101cat("Kuartil 3:", Q3, "\n")## Kuartil 3: 1151.2.4.2 Persentil ke-5 dan ke-95
P5 <- quantile(df$Total.day.calls, probs=0.05, names=F)
P95 <- quantile(df$Total.day.calls, probs=0.95, names=F)
cat("Persentil-5:", P5, "\n")## Persentil-5: 68cat("Persentil-95:", P95, "\n")## Persentil-95: 1341.2.4.3 Deteksi Amatan Pencilan
Q1 <- quantile(df$Total.day.calls)[2]
Q3 <- quantile(df$Total.day.calls)[4]
BA <- Q3 + (3/2*(Q3-Q1)) #Batas Atas
BB <- Q1 - (3/2*(Q3-Q1)) #Batas Bawah
cat("Batas Bawah :", BB, "\n")## Batas Bawah : 46.25cat("Batas Atas :", BA, "\n")## Batas Atas : 156.25Amatan dengan nilai kurang dari Batas Bawah atau Lebih dari Batas atas merupakan amatan outlier. Mengecek amatan di bawah Batas Bawah dan di atas Batas Atas
df[df$Total.day.calls < BB,]$Total.day.calls## [1] 30 35 40df[df$Total.day.calls > BA,]$Total.day.calls## [1] 163 1651.2.5 Boxplot By Group
boxplot(Total.day.calls ~ Churn, data = df,
col = c("#FFE0B2", "#F57C00"), horizontal = TRUE)
boxplot(Total.intl.calls ~ Churn, data = df,
col = c("#FFE0B2", "#F57C00"), horizontal = TRUE)
boxplot(Customer.service.calls ~ Churn, data = df,
col = c("#FFE0B2", "#F57C00"), horizontal = TRUE)
1.2.6 Layout
Membuat Layout untuk Tampilan Histogram dan Boxplot
nf <- layout(mat = matrix(c(1,2), 2,1, byrow = TRUE), heights = c(3,1.5))
par(mar=c(3.1, 3.1, 2.1, 2.1))1.2.6.1 Histogram
hist(df$Total.day.calls, col = "lightblue", main = "Sebaran Total Panggilan") 
1.2.6.2 Boxplot
boxplot(df$Total.day.calls, horizontal = T, frame = F, col = "lightgreen")
props.1 <- table(df[,c("Churn", "International.plan")])
props.1## International.plan
## Churn No Yes
## False 538 34
## True 76 19prop.table(props.1)## International.plan
## Churn No Yes
## False 0.80659670 0.05097451
## True 0.11394303 0.02848576barplot(prop.table(props.1, 2),
col = c("orange", "lightgreen"),
legend = c("False", "True"))
barplot(prop.table(props.1, 2), col = c("orange", "lightgreen"))
cat("Mean :", mean(df$Total.day.calls), "\n")## Mean : 100.937cat("Median :", median(df$Total.day.calls), "\n")## Median : 101# Create the function 'Modus'
getmode <- function(v) {
uniqv <- unique(v)
uniqv[which.max(tabulate(match(v, uniqv)))]
}
cat("Mode :", getmode(df$Total.day.calls))## Mode : 102getmode.alt <- function(data) {
# Hitung frekuensi kemunculan setiap nilai dalam data
frek <- table(data)
# Temukan nilai dengan frekuensi tertinggi
mode <- names(frek)[which.max(frek)]
return(mode)
}
cat("Mode :", getmode.alt(df$Total.day.calls))## Mode : 1021.3 Penyebaran Data
Ukuran Penyebaran Data
ragam <- var(df$Total.day.calls)
sp.baku <- sd(df$Total.day.calls) # atau --> sqrt(var(df$Total.day.calls))
jangkauan <- range(df$Total.day.calls)
jak <- IQR(df$Total.day.calls)
cat("Ragam :", ragam, "\n")## Ragam : 416.0291cat("Sp. Baku :", sp.baku, "\n")## Sp. Baku : 20.39679cat("Jangkauan :", jangkauan, "\n")## Jangkauan : 30 165cat("JAK :", jak, "\n")## JAK : 27.51.3.1 Coef. of Variation
cv <- sd(df$Total.day.calls)/mean(df$Total.day.calls) * 100
cat("Coefficient of Variation :", cv, "\n")## Coefficient of Variation : 20.207441.3.2 Koefisien Gini
# install.packages("DescTools")
library("DescTools")
gini <- DescTools::Gini(df$Total.day.calls)
cat("\n'\", Gini Coef :", gini, "\n")##
## '", Gini Coef : 0.113967plot(ineq::Lc(df$Total.day.calls),col="darkred",lwd=2)## Registered S3 methods overwritten by 'ineq':
## method from
## plot.Lc DescTools
## lines.Lc DescTools
1.3.3 Bentuk Sebaran
moments::skewness(df$Total.day.calls) # Kemencengan## [1] -0.05265871moments::kurtosis(df$Total.day.calls) # Keruncingan## [1] 3.0617122 Pima Indians Diabetes
Akan dilakukan eksplorasi pada data Pima Indians Diabetes. Memuat Pustaka yang diperlukan.
library(ggplot2)
library(gridExtra)setwd("D:/Kuliah/Mat/TSA Kominfo/Praktikum")
diabetes <- read.csv('pima-indians-diabeter-database.csv', sep = ',')
head(diabetes)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 6 148 72 35 0 33.6
## 2 1 85 66 29 0 26.6
## 3 8 183 64 0 0 23.3
## 4 1 89 66 23 94 28.1
## 5 0 137 40 35 168 43.1
## 6 5 116 74 0 0 25.6
## DiabetesPedigreeFunction Age Outcome
## 1 0.627 50 1
## 2 0.351 31 0
## 3 0.672 32 1
## 4 0.167 21 0
## 5 2.288 33 1
## 6 0.201 30 02.1 Daftar variabel :
Pregnancies : Number of times pregnant
Glucose : Plasma glucose concentration a 2 hours in an oral glucose tolerance test
BloodPressure : Diastolic blood pressure (mm Hg)
SkinThickness : Triceps skin fold thickness (mm) Insulin : 2-Hour serum insulin (mu U/ml)
BMI : Body mass index (weight in kg/(height in m)^2)
DiabetesPedigreeFunction : Diabetes pedigree function
Age : Age (years)
Outcome : Class variable (0 or 1) 268 of 768 are 1, the others are 0
diabetes$Outcome <- as.factor(diabetes$Outcome)summary(diabetes)## Pregnancies Glucose BloodPressure SkinThickness
## Min. : 0.000 Min. : 0.0 Min. : 0.00 Min. : 0.00
## 1st Qu.: 1.000 1st Qu.: 99.0 1st Qu.: 62.00 1st Qu.: 0.00
## Median : 3.000 Median :117.0 Median : 72.00 Median :23.00
## Mean : 3.845 Mean :120.9 Mean : 69.11 Mean :20.54
## 3rd Qu.: 6.000 3rd Qu.:140.2 3rd Qu.: 80.00 3rd Qu.:32.00
## Max. :17.000 Max. :199.0 Max. :122.00 Max. :99.00
## Insulin BMI DiabetesPedigreeFunction Age
## Min. : 0.0 Min. : 0.00 Min. :0.0780 Min. :21.00
## 1st Qu.: 0.0 1st Qu.:27.30 1st Qu.:0.2437 1st Qu.:24.00
## Median : 30.5 Median :32.00 Median :0.3725 Median :29.00
## Mean : 79.8 Mean :31.99 Mean :0.4719 Mean :33.24
## 3rd Qu.:127.2 3rd Qu.:36.60 3rd Qu.:0.6262 3rd Qu.:41.00
## Max. :846.0 Max. :67.10 Max. :2.4200 Max. :81.00
## Outcome
## 0:500
## 1:268
##
##
##
## 2.2 Amatan
2.2.1 Amatan dengan missing value
print(colSums(is.na(diabetes)))## Pregnancies Glucose BloodPressure
## 0 0 0
## SkinThickness Insulin BMI
## 0 0 0
## DiabetesPedigreeFunction Age Outcome
## 0 0 02.2.2 Amatan dengan nilai 0
why ?
num.zero = colSums(diabetes==0)
print(data.frame(num.zero))## num.zero
## Pregnancies 111
## Glucose 5
## BloodPressure 35
## SkinThickness 227
## Insulin 374
## BMI 11
## DiabetesPedigreeFunction 0
## Age 0
## Outcome 5002.2.3 Persentase amatan dengan nilai 0
pct.zero = round(colSums(diabetes==0)/length(diabetes$Outcome), 4)*100
print(data.frame(pct.zero))## pct.zero
## Pregnancies 14.45
## Glucose 0.65
## BloodPressure 4.56
## SkinThickness 29.56
## Insulin 48.70
## BMI 1.43
## DiabetesPedigreeFunction 0.00
## Age 0.00
## Outcome 65.10plot1 <- ggplot(diabetes, aes(x = Pregnancies)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("Pregnancies")
plot2 <- ggplot(diabetes, aes(x = Glucose)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("Glucose")
plot3 <- ggplot(diabetes, aes(x = BloodPressure)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("BloodPressure")
plot4 <- ggplot(diabetes, aes(x = SkinThickness)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("SkinThickness")
plot5 <- ggplot(diabetes, aes(x = Insulin)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("Insulin")
plot6 <- ggplot(diabetes, aes(x = BMI)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("BMI")
plot7 <- ggplot(diabetes, aes(x = DiabetesPedigreeFunction)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("DiabetesPedigreeFunction")
plot8 <- ggplot(diabetes, aes(x = Age)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("Age")
plot9 <- ggplot(diabetes, aes(x = Outcome)) +
geom_bar(fill="darkred") +
ggtitle("Outcome")
# Mengatur grid 3x3
grid.arrange(
plot1, plot2, plot3,
plot4, plot5, plot6,
plot7, plot8, plot9,
ncol = 3
)
2.3 Kolom
2.3.1 Pregnancies
summary(diabetes$Pregnancies)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.000 3.000 3.845 6.000 17.000cat("Jumlah nilai 0:", num.zero[1], "\n")## Jumlah nilai 0: 111cat("Persentase nilai 0:", pct.zero[1])## Persentase nilai 0: 14.45plot1 <- ggplot(diabetes, aes(x = Pregnancies)) +
geom_histogram(bins = 10, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = Pregnancies)) +
geom_boxplot(fill = "darkgreen", alpha=0.7)
plot3 <- ggplot(diabetes, aes(x = Pregnancies, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(y = Pregnancies, x=Outcome)) +
geom_boxplot(aes(fill=Outcome))
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
2.3.2 Glucose
summary(diabetes$Glucose)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 99.0 117.0 120.9 140.2 199.0cat("Jumlah nilai 0:", num.zero[2], "\n")## Jumlah nilai 0: 5cat("Persentase nilai 0:", pct.zero[2])## Persentase nilai 0: 0.65plot1 <- ggplot(diabetes, aes(x = Glucose)) +
geom_histogram(bins = 20, fill = "red", alpha = 0.7 )
plot2 <- ggplot(diabetes, aes(x = Glucose)) +
geom_boxplot(fill = "darkgreen", alpha=0.7)
plot3 <- ggplot(diabetes, aes(x = Glucose, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(y = Glucose, x=Outcome)) +
geom_boxplot(aes(fill=Outcome))
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
2.3.3 Blood Pressure
summary(diabetes$BloodPressure)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 62.00 72.00 69.11 80.00 122.00cat("Jumlah nilai 0:", num.zero[3], "\n")## Jumlah nilai 0: 35cat("Persentase nilai 0:", pct.zero[3])## Persentase nilai 0: 4.56plot1 <- ggplot(diabetes, aes(x = BloodPressure)) +
geom_histogram(bins = 20, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = BloodPressure)) +
geom_boxplot(fill = "darkgreen", alpha=0.7)
plot3 <- ggplot(diabetes, aes(x = BloodPressure, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(y = BloodPressure, x=Outcome)) +
geom_boxplot(aes(fill=Outcome))
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
2.3.4 Skin Thickness
summary(diabetes$SkinThickness)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 23.00 20.54 32.00 99.00cat("Jumlah nilai 0:", num.zero[4], "\n")## Jumlah nilai 0: 227cat("Persentase nilai 0:", pct.zero[4])## Persentase nilai 0: 29.56plot1 <- ggplot(diabetes, aes(x = SkinThickness)) +
geom_histogram(bins = 20, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = SkinThickness)) +
geom_boxplot(fill = "darkgreen", alpha=0.7)
plot3 <- ggplot(diabetes, aes(x = SkinThickness, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(y = SkinThickness, x=Outcome)) +
geom_boxplot(aes(fill=Outcome))
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
2.3.5 Insulin
summary(diabetes$Insulin)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 0.0 30.5 79.8 127.2 846.0cat("Jumlah nilai 0:", num.zero[5], "\n")## Jumlah nilai 0: 374cat("Persentase nilai 0:", pct.zero[5])## Persentase nilai 0: 48.7plot1 <- ggplot(diabetes, aes(x = Insulin)) +
geom_histogram(bins = 20, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = Insulin)) +
geom_boxplot(fill = "darkgreen", alpha=0.7)
plot3 <- ggplot(diabetes, aes(x = Insulin, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(y = Insulin, x=Outcome)) +
geom_boxplot(aes(fill=Outcome))
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
2.3.6 Body Mass Index
summary(diabetes$BMI)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 27.30 32.00 31.99 36.60 67.10cat("Jumlah nilai 0:", num.zero[6], "\n")## Jumlah nilai 0: 11cat("Persentase nilai 0:", pct.zero[6])## Persentase nilai 0: 1.43plot1 <- ggplot(diabetes, aes(x = BMI)) +
geom_histogram(bins = 20, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = BMI)) +
geom_boxplot(fill = "darkgreen", alpha=0.7)
plot3 <- ggplot(diabetes, aes(x = BMI, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(y = BMI, x=Outcome)) +
geom_boxplot(aes(fill=Outcome))
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
2.3.7 Diabetes Pedigree Function
summary(diabetes$DiabetesPedigreeFunction)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0780 0.2437 0.3725 0.4719 0.6262 2.4200cat("Jumlah nilai 0:", num.zero[7], "\n")## Jumlah nilai 0: 0cat("Persentase nilai 0:", pct.zero[7])## Persentase nilai 0: 0plot1 <- ggplot(diabetes, aes(x = DiabetesPedigreeFunction)) +
geom_histogram(bins = 20, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = DiabetesPedigreeFunction)) +
geom_boxplot(fill = "darkgreen", alpha=0.7)
plot3 <- ggplot(diabetes, aes(x = DiabetesPedigreeFunction, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(y = DiabetesPedigreeFunction, x=Outcome)) +
geom_boxplot(aes(fill=Outcome))
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
2.3.8 Age
summary(diabetes$Age)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 21.00 24.00 29.00 33.24 41.00 81.00cat("Jumlah nilai 0:", num.zero[8], "\n")## Jumlah nilai 0: 0cat("Persentase nilai 0:", pct.zero[8])## Persentase nilai 0: 0plot1 <- ggplot(diabetes, aes(x = Age)) +
geom_histogram(bins = 20, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = Age)) +
geom_boxplot(fill = "darkgreen", alpha=0.7)
plot3 <- ggplot(diabetes, aes(x = Age, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(y = Age, x=Outcome)) +
geom_boxplot(aes(fill=Outcome))
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
3 Outlier Analysis
Data yang digunakan merupakan data “cars” yang tersedia di R.
head(cars)## speed dist
## 1 4 2
## 2 4 10
## 3 7 4
## 4 7 22
## 5 8 16
## 6 9 10summary(cars)## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00str(cars)## 'data.frame': 50 obs. of 2 variables:
## $ speed: num 4 4 7 7 8 9 10 10 10 11 ...
## $ dist : num 2 10 4 22 16 10 18 26 34 17 ...cars <- cars[1:30, ] # data awal diambil 30 baris pertama saja3.1 Plot data awal tanpa outlier.
plot(cars$speed, cars$dist, xlim=c(0, 28), ylim=c(0, 100),
main="Speed - Dist", xlab="speed", ylab="dist",
pch="*", col="red", cex=2)
abline(lm(dist ~ speed, data=cars), col="darkgreen", lwd=4, lty=2)
3.2 Penambahan outlier pada data
cars_outliers <- data.frame(speed=c(24,24,25,25,25),
dist=c(81, 80, 86, 88, 85)) # introduce outliers.
cars_mod1 <- rbind(cars, cars_outliers) # data dengan outlier.
cars_mod1## speed dist
## 1 4 2
## 2 4 10
## 3 7 4
## 4 7 22
## 5 8 16
## 6 9 10
## 7 10 18
## 8 10 26
## 9 10 34
## 10 11 17
## 11 11 28
## 12 12 14
## 13 12 20
## 14 12 24
## 15 12 28
## 16 13 26
## 17 13 34
## 18 13 34
## 19 13 46
## 20 14 26
## 21 14 36
## 22 14 60
## 23 14 80
## 24 15 20
## 25 15 26
## 26 15 54
## 27 16 32
## 28 16 40
## 29 17 32
## 30 17 40
## 31 24 81
## 32 24 80
## 33 25 86
## 34 25 88
## 35 25 853.3 Plot data dengan outlier.
par(mfrow=c(1, 2))
# Plot data awal tanpa outlier.
model_1 = lm(dist ~ speed, data=cars)
plot(cars$speed, cars$dist, xlim=c(0, 28), ylim=c(0, 100),
main="Speed - Dist", xlab="speed", ylab="dist",
pch="*", col="red", cex=2)
abline(model_1, col="darkgreen", lwd=4, lty=2)
model_2 = lm(dist ~ speed, data=cars_mod1) # lm = linear model
plot(cars_mod1$speed, cars_mod1$dist, xlim=c(0, 28), ylim=c(0, 230),
main="With Outliers", xlab="speed", ylab="dist",
pch="*", col="red", cex=2)
abline(model_2, col="blue", lwd=3, lty=2)
model_1##
## Call:
## lm(formula = dist ~ speed, data = cars)
##
## Coefficients:
## (Intercept) speed
## -6.845 2.973model_2##
## Call:
## lm(formula = dist ~ speed, data = cars_mod1)
##
## Coefficients:
## (Intercept) speed
## -17.129 3.905cars_outliers <- data.frame(speed=c(24,24,25,25,25), dist=c(81, 80, 86, 88, 85)) # introduce outliers.
# menambahkan data outlier pada data cars yang asli
cars_mod2 <- rbind(cars, cars_outliers) # data dengan amatan berpengaruh.
View(cars_mod2)
length(cars_mod2$speed)## [1] 35model_3 = lm(dist ~ speed, data=cars_mod2)
plot(cars_mod2$speed, cars_mod2$dist, xlim=c(0, 28), ylim=c(0, 100),
main="Speed - Dist", xlab="speed", ylab="dist",
pch="*", col="red", cex=2)
abline(model_3, col="darkgreen", lwd=4, lty=2)
summary(model_3)##
## Call:
## lm(formula = dist ~ speed, data = cars_mod2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.453 -8.425 0.358 4.993 42.453
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.1288 5.8048 -2.951 0.00579 **
## speed 3.9054 0.3928 9.943 1.87e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.63 on 33 degrees of freedom
## Multiple R-squared: 0.7498, Adjusted R-squared: 0.7422
## F-statistic: 98.87 on 1 and 33 DF, p-value: 1.866e-11influence.measures(model_3)## Influence measures of
## lm(formula = dist ~ speed, data = cars_mod2) :
##
## dfb.1_ dfb.sped dffit cov.r cook.d hat inf
## 1 0.10699 -0.094246 0.10793 1.203 5.99e-03 0.1203 *
## 2 0.35568 -0.313326 0.35881 1.141 6.45e-02 0.1203
## 3 -0.13469 0.109816 -0.14107 1.129 1.02e-02 0.0725
## 4 0.25846 -0.210730 0.27070 1.082 3.67e-02 0.0725
## 5 0.03571 -0.027935 0.03847 1.130 7.63e-04 0.0604
## 6 -0.13203 0.097683 -0.14860 1.091 1.12e-02 0.0503
## 7 -0.05451 0.037223 -0.06565 1.103 2.22e-03 0.0421
## 8 0.05658 -0.038642 0.06815 1.103 2.39e-03 0.0421
## 9 0.16988 -0.116012 0.20460 1.047 2.10e-02 0.0421
## 10 -0.10178 0.061347 -0.13621 1.069 9.42e-03 0.0358
## 11 0.02482 -0.014960 0.03321 1.101 5.68e-04 0.0358
## 12 -0.14615 0.070347 -0.23046 0.994 2.61e-02 0.0315
## 13 -0.08903 0.042856 -0.14040 1.058 9.97e-03 0.0315
## 14 -0.05213 0.025094 -0.08221 1.084 3.46e-03 0.0315
## 15 -0.01573 0.007573 -0.02481 1.097 3.17e-04 0.0315
## 16 -0.05162 0.014249 -0.10526 1.070 5.65e-03 0.0291
## 17 0.00241 -0.000664 0.00491 1.095 1.24e-05 0.0291
## 18 0.00241 -0.000664 0.00491 1.095 1.24e-05 0.0291
## 19 0.08427 -0.023262 0.17184 1.031 1.48e-02 0.0291
## 20 -0.05140 -0.007505 -0.15888 1.039 1.27e-02 0.0286
## 21 -0.00680 -0.000993 -0.02101 1.094 2.28e-04 0.0286
## 22 0.10389 0.015169 0.32110 0.890 4.79e-02 0.0286
## 23 0.23173 0.033835 0.71623 0.459 1.71e-01 0.0286 *
## 24 -0.04671 -0.070634 -0.31355 0.908 4.61e-02 0.0301
## 25 -0.03287 -0.049708 -0.22066 0.996 2.39e-02 0.0301
## 26 0.02647 0.040030 0.17770 1.030 1.58e-02 0.0301
## 27 0.00336 -0.076952 -0.20070 1.025 2.00e-02 0.0335
## 28 0.00133 -0.030406 -0.07930 1.088 3.22e-03 0.0335
## 29 0.04614 -0.146120 -0.28434 0.980 3.92e-02 0.0388
## 30 0.02422 -0.076717 -0.14928 1.069 1.13e-02 0.0388
## 31 -0.09257 0.125965 0.14257 1.212 1.04e-02 0.1303 *
## 32 -0.07146 0.097245 0.11006 1.217 6.23e-03 0.1303 *
## 33 -0.13321 0.177100 0.19668 1.236 1.98e-02 0.1510 *
## 34 -0.18225 0.242289 0.26907 1.221 3.69e-02 0.1510 *
## 35 -0.10884 0.144698 0.16069 1.241 1.33e-02 0.1510 *summary(model_1)##
## Call:
## lm(formula = dist ~ speed, data = cars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.751 -8.818 -1.993 2.885 45.222
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.8446 8.7420 -0.783 0.440223
## speed 2.9730 0.7046 4.219 0.000233 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.1 on 28 degrees of freedom
## Multiple R-squared: 0.3887, Adjusted R-squared: 0.3669
## F-statistic: 17.8 on 1 and 28 DF, p-value: 0.00023274 Outlier: Data BPR
setwd("D:/Kuliah/Mat/TSA Kominfo/Praktikum") # set working directory
bpr <- read.csv("2. eksplorasi01.csv")
head(bpr)## Kode.Bank Non.Performing.Loan Growth.Laba.Rugi.Berjalan Spread.Margin
## 1 1 10.49833 11.538745 11.611141
## 2 2 15.27000 -11.188068 11.691391
## 3 3 1.63000 9.325274 3.620513
## 4 4 27.65167 8.167480 12.871722
## 5 5 51.32000 26.825480 14.429154
## 6 6 9.03000 13.969876 3.836760
## Cash.Ratio Modal.inti.thdp.Aset BOPO Ratio.Kredit.thdp.DPK
## 1 21.76331 0.09385150 0.9067301 0.9671143
## 2 14.10585 0.09061287 1.4005322 1.4584551
## 3 18.23885 0.08618314 0.7979953 0.9339539
## 4 66.29771 0.05432665 1.6785487 1.2375042
## 5 29.92377 0.28228712 1.3184079 0.8857992
## 6 50.76537 0.14190734 0.8538458 1.5697280
## Rasio.biaya.tenaga.thd.pendapatan.operasional
## 1 0.3536502
## 2 0.7167977
## 3 0.3055795
## 4 0.2392941
## 5 0.5862838
## 6 0.2692363
## Rasio.Pendapatan.Operasional.thd.Aset.Produktif
## 1 0.2591038
## 2 0.1616119
## 3 0.1904516
## 4 0.2774885
## 5 0.3958143
## 6 0.2129047str(bpr)## 'data.frame': 147 obs. of 10 variables:
## $ Kode.Bank : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Non.Performing.Loan : num 10.5 15.27 1.63 27.65 51.32 ...
## $ Growth.Laba.Rugi.Berjalan : num 11.54 -11.19 9.33 8.17 26.83 ...
## $ Spread.Margin : num 11.61 11.69 3.62 12.87 14.43 ...
## $ Cash.Ratio : num 21.8 14.1 18.2 66.3 29.9 ...
## $ Modal.inti.thdp.Aset : num 0.0939 0.0906 0.0862 0.0543 0.2823 ...
## $ BOPO : num 0.907 1.401 0.798 1.679 1.318 ...
## $ Ratio.Kredit.thdp.DPK : num 0.967 1.458 0.934 1.238 0.886 ...
## $ Rasio.biaya.tenaga.thd.pendapatan.operasional : num 0.354 0.717 0.306 0.239 0.586 ...
## $ Rasio.Pendapatan.Operasional.thd.Aset.Produktif: num 0.259 0.162 0.19 0.277 0.396 ...summary(bpr)## Kode.Bank Non.Performing.Loan Growth.Laba.Rugi.Berjalan
## Min. : 1.0 Min. : 0.3433 Min. :-679.401
## 1st Qu.: 37.5 1st Qu.: 4.9733 1st Qu.: 9.668
## Median : 74.0 Median : 9.5683 Median : 13.085
## Mean : 74.0 Mean :14.1751 Mean : 90.354
## 3rd Qu.:110.5 3rd Qu.:19.4375 3rd Qu.: 20.382
## Max. :147.0 Max. :61.6100 Max. :8406.827
##
## Spread.Margin Cash.Ratio Modal.inti.thdp.Aset BOPO
## Min. :-47.267 Min. : 4.904 Min. :-0.40167 Min. :0.6342
## 1st Qu.: 8.627 1st Qu.: 18.125 1st Qu.: 0.09245 1st Qu.:0.8926
## Median : 11.219 Median : 25.903 Median : 0.12070 Median :0.9734
## Mean : 10.841 Mean : 37.481 Mean : 0.15401 Mean :1.0727
## 3rd Qu.: 13.804 3rd Qu.: 41.177 3rd Qu.: 0.19269 3rd Qu.:1.1209
## Max. : 50.109 Max. :458.130 Max. : 0.71460 Max. :2.4607
## NA's :15
## Ratio.Kredit.thdp.DPK Rasio.biaya.tenaga.thd.pendapatan.operasional
## Min. :0.5961 Min. :0.1562
## 1st Qu.:0.9678 1st Qu.:0.2773
## Median :1.1626 Median :0.3502
## Mean :1.3924 Mean :0.3882
## 3rd Qu.:1.5659 3rd Qu.:0.4707
## Max. :4.1955 Max. :1.1470
##
## Rasio.Pendapatan.Operasional.thd.Aset.Produktif
## Min. :0.1346
## 1st Qu.:0.1954
## Median :0.2200
## Mean :0.2292
## 3rd Qu.:0.2517
## Max. :0.4427
## par0 <- par(mfrow=c(3,3))
for (i in 2:10) boxplot(bpr[,i], main=colnames(bpr)[i], horizontal = TRUE)
par(par0)par0 <- par(mfrow=c(3,3))
for (i in 2:10) hist(bpr[,i], main=colnames(bpr)[i], freq = FALSE)
par(par0)# Non Performing Loan
boxplot(bpr$Non.Performing.Loan, main="Non Performing Loan", horizontal=T)
hist(bpr$Non.Performing.Loan, main="Non Performing Loan", breaks=20)
# Membuat QQ plot
qqnorm(bpr$Non.Performing.Loan)
qqline(bpr$Non.Performing.Loan)
4.1 Fungsi WInsorized
Fungsi WInsorized digunakan untuk mengganti nilai-nilai outlier dengan nilai “batas bawah” untuk sebelah kiri dan nilai “batas atas” untuk sebelah kanan
winval <- function (x, tr = 0.2)
{
y <- sort(x)
n <- length(x)
# menentukan indeks batas bawah
ibot <- floor(tr * n) + 1
# menentukan indeks batas atas
itop <- length(x) - ibot + 1
xbot <- y[ibot] # mengambil nilai pada indeks batas bawah
xtop <- y[itop] # mengambil nilai pada indeks batas atas
#(data dengan nilai kurang dari xbot akan diganti dengan data xbot)
winval <- ifelse(x <= xbot, xbot, x)
#(data dengan nilai lebih dari xtop akan diganti dengan xtop)
winval <- ifelse(winval >= xtop, xtop, winval)
winval
}
winmean <- function (x, tr = 0.2)
{
winmean <- mean(winval(x, tr))
winmean
}
winvar <- function (x, tr = 0.2)
{
winvar <- var(winval(x, tr))
winvar
}
winse <- function (x, tr = 0.2)
{
n = length(x)
h = n - 2 * floor(tr * n)
top = (n - 1) * sqrt(winvar(x, tr = tr))
bot = (h - 1) * sqrt(n)
se = top/bot
se
}x <- bpr$Non.Performing.Loan
x.bar <- mean(x) # rataan sample
x.med <- median(x) # median sample
x.bar.tr.50 <- mean(x,trim=.5) # rataan terpangkas 50% (median)
x.bar.tr.20 <- mean(x,trim=.2) # rataan terpangkas 20%
x.bar.tr.10 <- mean(x,trim=.1) # rataan terpangkas 10%
x.winmean <- winmean(x) # winsorized mean 20%
x.winmean.10 <- winmean(x, tr=0.1) # winsorized mean 10%
cat("Mean :", x.bar, "\n")## Mean : 14.17514cat("Median :", x.med, "\n\n")## Median : 9.568333cat("Tr. mean (50%) :", x.bar.tr.50, "\n")## Tr. mean (50%) : 9.568333cat("Tr. mean (20%) :", x.bar.tr.20, "\n")## Tr. mean (20%) : 10.71661cat("Tr. mean (10%) :", x.bar.tr.10, "\n")## Tr. mean (10%) : 11.88604cat("win. mean (20%) :", x.winmean, "\n")## win. mean (20%) : 11.86249cat("win. mean (10%) :", x.winmean.10, "\n\n")## win. mean (10%) : 13.00679cat("Quatile :", quantile(x))## Quatile : 0.3433333 4.973333 9.568333 19.4375 61.61IQR(x)## [1] 14.46417mad(x)## [1] 7.894845winvar(x) # winsorized variance .20## [1] 52.02483winvar(x, tr=0.1) # winsorized variance .10## [1] 91.665184.2 Selang Kepercayaan
trimse <- function (x, tr = 0.2)
{
trimse <- sqrt(winvar(x, tr))/((1 - 2 * tr) * sqrt(length(x)))
trimse
}
se.med <- sqrt((pi/2)*(mad(x)^2/length(x))) # s.e median# SK 95% Mean
ci.mean <- t.test(x)$conf.int
ci.level <- attr(t.test(x)$conf.int, "conf.level")
# SK 95% Trimmed Mean
ci.tr.mean <- c(mean(x,trim=.2)-qnorm(0.975)*trimse(x),mean(x,trim=.2)+qnorm(0.975)*trimse(x))
# SK 95% Median
ci.med <- c(median(x)-qnorm(0.975)*se.med,median(x)+qnorm(0.975)*se.med)
# SK 95% Winsorized Mean
ci.win.mean <- c(winmean(x)-qnorm(0.975)*winse(x),winmean(x)+qnorm(0.975)*winse(x))
cat("Selang Kepercayaan : ", ci.level, "\n\n")## Selang Kepercayaan : 0.95cat("Mean : ", ci.mean, "\n")## Mean : 12.0626 16.28767cat("Tr. Mean : ", ci.tr.mean, "\n")## Tr. Mean : 8.773294 12.65993cat("Median : ", ci.med, "\n")## Median : 7.968801 11.16787cat("Win. Mean : ", ci.win.mean, "\n utk 20% (default di fungsi kita)")## Win. Mean : 9.928011 13.79698
## utk 20% (default di fungsi kita)library(MASS)# M-ESTIMATOR
x <- bpr$Non.Performing.Loan
hub.1 <- hubers(x)
hub.1$mu## [1] 12.27906hub.1$s## [1] 9.795196hub.2 <- hubers(x, k=1.345)
hub.2$mu## [1] 11.98978hub.2$s## [1] 9.686614hub.3 <- hubers(x,mu=median(x))
hub.3$mu## [1] 9.568333hub.3$s## [1] 8.719008hub.4 <- hubers(x,s=1)
hub.4$mu## [1] 9.54636hub.4$s## [1] 15 Outlier: Data Handphone
data(phones)
str(phones)## List of 2
## $ year : num [1:24] 50 51 52 53 54 55 56 57 58 59 ...
## $ calls: num [1:24] 4.4 4.7 4.7 5.9 6.6 7.3 8.1 8.8 10.6 12 ...data.frame(phones)## year calls
## 1 50 4.4
## 2 51 4.7
## 3 52 4.7
## 4 53 5.9
## 5 54 6.6
## 6 55 7.3
## 7 56 8.1
## 8 57 8.8
## 9 58 10.6
## 10 59 12.0
## 11 60 13.5
## 12 61 14.9
## 13 62 16.1
## 14 63 21.2
## 15 64 119.0
## 16 65 124.0
## 17 66 142.0
## 18 67 159.0
## 19 68 182.0
## 20 69 212.0
## 21 70 43.0
## 22 71 24.0
## 23 72 27.0
## 24 73 29.0attach(phones)
plot(year,calls)
plot(phones$year,phones$calls, pch=19, cex=2, col="darkred")
fit.ols <- lm(calls~year, data=phones) # ols = ordinary linear square
# calls sebagai peubah y dan year sebgai peubah x
summary(fit.ols)##
## Call:
## lm(formula = calls ~ year, data = phones)
##
## Residuals:
## Min 1Q Median 3Q Max
## -78.97 -33.52 -12.04 23.38 124.20
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -260.059 102.607 -2.535 0.0189 *
## year 5.041 1.658 3.041 0.0060 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 56.22 on 22 degrees of freedom
## Multiple R-squared: 0.2959, Adjusted R-squared: 0.2639
## F-statistic: 9.247 on 1 and 22 DF, p-value: 0.005998par(mfrow=c(1,4))
plot(fit.ols,1:2)
plot(fit.ols,4)
abline(fit.ols$coef)
hmat.p <- hat(model.matrix(fit.ols))
h.phone <- hat(hmat.p)
cook.d <- cooks.distance(fit.ols)
plot(h.phone/(1-h.phone),cook.d,xlab="h/(1-h)",ylab="Cook distance")
fit.hub <- rlm(calls~year,maxit=50, data=phones)
summary(fit.hub,cor=F)##
## Call: rlm(formula = calls ~ year, data = phones, maxit = 50)
## Residuals:
## Min 1Q Median 3Q Max
## -18.314 -5.953 -1.681 26.460 173.769
##
## Coefficients:
## Value Std. Error t value
## (Intercept) -102.6222 26.6082 -3.8568
## year 2.0414 0.4299 4.7480
##
## Residual standard error: 9.032 on 22 degrees of freedompar(mfrow=c(1,3))
plot(fit.hub,1)
plot(fit.hub,2)
abline(fit.hub$coef)
fit.hub2 <- rlm(calls~year,scale.est="proposal 2", data=phones)
summary(fit.hub2,cor=F)##
## Call: rlm(formula = calls ~ year, data = phones, scale.est = "proposal 2")
## Residuals:
## Min 1Q Median 3Q Max
## -68.15 -29.46 -11.52 22.74 132.67
##
## Coefficients:
## Value Std. Error t value
## (Intercept) -227.9250 101.8740 -2.2373
## year 4.4530 1.6461 2.7052
##
## Residual standard error: 57.25 on 22 degrees of freedomfit.lms <- lqs(calls~year,method="lms", data=phones)
fit.lms## Call:
## lqs.formula(formula = calls ~ year, data = phones, method = "lms")
##
## Coefficients:
## (Intercept) year
## -55.947 1.155
##
## Scale estimates 0.9377 0.9095fit.lts <- lqs(calls~year,method="lts", data=phones)
fit.lts## Call:
## lqs.formula(formula = calls ~ year, data = phones, method = "lts")
##
## Coefficients:
## (Intercept) year
## -56.162 1.159
##
## Scale estimates 1.249 1.131par(mfrow=c(1,2))
plot(fit.lms$fit,fit.lms$res,main="lms")
plot(fit.lts$fit,fit.lts$res,main="lts")
par(mfrow=c(1,1))data.frame(diabetes)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 6 148 72 35 0 33.6
## 2 1 85 66 29 0 26.6
## 3 8 183 64 0 0 23.3
## 4 1 89 66 23 94 28.1
## 5 0 137 40 35 168 43.1
## 6 5 116 74 0 0 25.6
## 7 3 78 50 32 88 31.0
## 8 10 115 0 0 0 35.3
## 9 2 197 70 45 543 30.5
## 10 8 125 96 0 0 0.0
## 11 4 110 92 0 0 37.6
## 12 10 168 74 0 0 38.0
## 13 10 139 80 0 0 27.1
## 14 1 189 60 23 846 30.1
## 15 5 166 72 19 175 25.8
## 16 7 100 0 0 0 30.0
## 17 0 118 84 47 230 45.8
## 18 7 107 74 0 0 29.6
## 19 1 103 30 38 83 43.3
## 20 1 115 70 30 96 34.6
## 21 3 126 88 41 235 39.3
## 22 8 99 84 0 0 35.4
## 23 7 196 90 0 0 39.8
## 24 9 119 80 35 0 29.0
## 25 11 143 94 33 146 36.6
## 26 10 125 70 26 115 31.1
## 27 7 147 76 0 0 39.4
## 28 1 97 66 15 140 23.2
## 29 13 145 82 19 110 22.2
## 30 5 117 92 0 0 34.1
## 31 5 109 75 26 0 36.0
## 32 3 158 76 36 245 31.6
## 33 3 88 58 11 54 24.8
## 34 6 92 92 0 0 19.9
## 35 10 122 78 31 0 27.6
## 36 4 103 60 33 192 24.0
## 37 11 138 76 0 0 33.2
## 38 9 102 76 37 0 32.9
## 39 2 90 68 42 0 38.2
## 40 4 111 72 47 207 37.1
## 41 3 180 64 25 70 34.0
## 42 7 133 84 0 0 40.2
## 43 7 106 92 18 0 22.7
## 44 9 171 110 24 240 45.4
## 45 7 159 64 0 0 27.4
## 46 0 180 66 39 0 42.0
## 47 1 146 56 0 0 29.7
## 48 2 71 70 27 0 28.0
## 49 7 103 66 32 0 39.1
## 50 7 105 0 0 0 0.0
## 51 1 103 80 11 82 19.4
## 52 1 101 50 15 36 24.2
## 53 5 88 66 21 23 24.4
## 54 8 176 90 34 300 33.7
## 55 7 150 66 42 342 34.7
## 56 1 73 50 10 0 23.0
## 57 7 187 68 39 304 37.7
## 58 0 100 88 60 110 46.8
## 59 0 146 82 0 0 40.5
## 60 0 105 64 41 142 41.5
## 61 2 84 0 0 0 0.0
## 62 8 133 72 0 0 32.9
## 63 5 44 62 0 0 25.0
## 64 2 141 58 34 128 25.4
## 65 7 114 66 0 0 32.8
## 66 5 99 74 27 0 29.0
## 67 0 109 88 30 0 32.5
## 68 2 109 92 0 0 42.7
## 69 1 95 66 13 38 19.6
## 70 4 146 85 27 100 28.9
## 71 2 100 66 20 90 32.9
## 72 5 139 64 35 140 28.6
## 73 13 126 90 0 0 43.4
## 74 4 129 86 20 270 35.1
## 75 1 79 75 30 0 32.0
## 76 1 0 48 20 0 24.7
## 77 7 62 78 0 0 32.6
## 78 5 95 72 33 0 37.7
## 79 0 131 0 0 0 43.2
## 80 2 112 66 22 0 25.0
## 81 3 113 44 13 0 22.4
## 82 2 74 0 0 0 0.0
## 83 7 83 78 26 71 29.3
## 84 0 101 65 28 0 24.6
## 85 5 137 108 0 0 48.8
## 86 2 110 74 29 125 32.4
## 87 13 106 72 54 0 36.6
## 88 2 100 68 25 71 38.5
## 89 15 136 70 32 110 37.1
## 90 1 107 68 19 0 26.5
## 91 1 80 55 0 0 19.1
## 92 4 123 80 15 176 32.0
## 93 7 81 78 40 48 46.7
## 94 4 134 72 0 0 23.8
## 95 2 142 82 18 64 24.7
## 96 6 144 72 27 228 33.9
## 97 2 92 62 28 0 31.6
## 98 1 71 48 18 76 20.4
## 99 6 93 50 30 64 28.7
## 100 1 122 90 51 220 49.7
## 101 1 163 72 0 0 39.0
## 102 1 151 60 0 0 26.1
## 103 0 125 96 0 0 22.5
## 104 1 81 72 18 40 26.6
## 105 2 85 65 0 0 39.6
## 106 1 126 56 29 152 28.7
## 107 1 96 122 0 0 22.4
## 108 4 144 58 28 140 29.5
## 109 3 83 58 31 18 34.3
## 110 0 95 85 25 36 37.4
## 111 3 171 72 33 135 33.3
## 112 8 155 62 26 495 34.0
## 113 1 89 76 34 37 31.2
## 114 4 76 62 0 0 34.0
## 115 7 160 54 32 175 30.5
## 116 4 146 92 0 0 31.2
## 117 5 124 74 0 0 34.0
## 118 5 78 48 0 0 33.7
## 119 4 97 60 23 0 28.2
## 120 4 99 76 15 51 23.2
## 121 0 162 76 56 100 53.2
## 122 6 111 64 39 0 34.2
## 123 2 107 74 30 100 33.6
## 124 5 132 80 0 0 26.8
## 125 0 113 76 0 0 33.3
## 126 1 88 30 42 99 55.0
## 127 3 120 70 30 135 42.9
## 128 1 118 58 36 94 33.3
## 129 1 117 88 24 145 34.5
## 130 0 105 84 0 0 27.9
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## 132 9 122 56 0 0 33.3
## 133 3 170 64 37 225 34.5
## 134 8 84 74 31 0 38.3
## 135 2 96 68 13 49 21.1
## 136 2 125 60 20 140 33.8
## 137 0 100 70 26 50 30.8
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## 139 0 129 80 0 0 31.2
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## 141 3 128 78 0 0 21.1
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## 146 0 102 75 23 0 0.0
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## 150 2 90 70 17 0 27.3
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## 154 1 153 82 42 485 40.6
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## 160 17 163 72 41 114 40.9
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## 219 5 85 74 22 0 29.0
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## 644 4 90 0 0 0 28.0
## 645 3 103 72 30 152 27.6
## 646 2 157 74 35 440 39.4
## 647 1 167 74 17 144 23.4
## 648 0 179 50 36 159 37.8
## 649 11 136 84 35 130 28.3
## 650 0 107 60 25 0 26.4
## 651 1 91 54 25 100 25.2
## 652 1 117 60 23 106 33.8
## 653 5 123 74 40 77 34.1
## 654 2 120 54 0 0 26.8
## 655 1 106 70 28 135 34.2
## 656 2 155 52 27 540 38.7
## 657 2 101 58 35 90 21.8
## 658 1 120 80 48 200 38.9
## 659 11 127 106 0 0 39.0
## 660 3 80 82 31 70 34.2
## 661 10 162 84 0 0 27.7
## 662 1 199 76 43 0 42.9
## 663 8 167 106 46 231 37.6
## 664 9 145 80 46 130 37.9
## 665 6 115 60 39 0 33.7
## 666 1 112 80 45 132 34.8
## 667 4 145 82 18 0 32.5
## 668 10 111 70 27 0 27.5
## 669 6 98 58 33 190 34.0
## 670 9 154 78 30 100 30.9
## 671 6 165 68 26 168 33.6
## 672 1 99 58 10 0 25.4
## 673 10 68 106 23 49 35.5
## 674 3 123 100 35 240 57.3
## 675 8 91 82 0 0 35.6
## 676 6 195 70 0 0 30.9
## 677 9 156 86 0 0 24.8
## 678 0 93 60 0 0 35.3
## 679 3 121 52 0 0 36.0
## 680 2 101 58 17 265 24.2
## 681 2 56 56 28 45 24.2
## 682 0 162 76 36 0 49.6
## 683 0 95 64 39 105 44.6
## 684 4 125 80 0 0 32.3
## 685 5 136 82 0 0 0.0
## 686 2 129 74 26 205 33.2
## 687 3 130 64 0 0 23.1
## 688 1 107 50 19 0 28.3
## 689 1 140 74 26 180 24.1
## 690 1 144 82 46 180 46.1
## 691 8 107 80 0 0 24.6
## 692 13 158 114 0 0 42.3
## 693 2 121 70 32 95 39.1
## 694 7 129 68 49 125 38.5
## 695 2 90 60 0 0 23.5
## 696 7 142 90 24 480 30.4
## 697 3 169 74 19 125 29.9
## 698 0 99 0 0 0 25.0
## 699 4 127 88 11 155 34.5
## 700 4 118 70 0 0 44.5
## 701 2 122 76 27 200 35.9
## 702 6 125 78 31 0 27.6
## 703 1 168 88 29 0 35.0
## 704 2 129 0 0 0 38.5
## 705 4 110 76 20 100 28.4
## 706 6 80 80 36 0 39.8
## 707 10 115 0 0 0 0.0
## 708 2 127 46 21 335 34.4
## 709 9 164 78 0 0 32.8
## 710 2 93 64 32 160 38.0
## 711 3 158 64 13 387 31.2
## 712 5 126 78 27 22 29.6
## 713 10 129 62 36 0 41.2
## 714 0 134 58 20 291 26.4
## 715 3 102 74 0 0 29.5
## 716 7 187 50 33 392 33.9
## 717 3 173 78 39 185 33.8
## 718 10 94 72 18 0 23.1
## 719 1 108 60 46 178 35.5
## 720 5 97 76 27 0 35.6
## 721 4 83 86 19 0 29.3
## 722 1 114 66 36 200 38.1
## 723 1 149 68 29 127 29.3
## 724 5 117 86 30 105 39.1
## 725 1 111 94 0 0 32.8
## 726 4 112 78 40 0 39.4
## 727 1 116 78 29 180 36.1
## 728 0 141 84 26 0 32.4
## 729 2 175 88 0 0 22.9
## 730 2 92 52 0 0 30.1
## 731 3 130 78 23 79 28.4
## 732 8 120 86 0 0 28.4
## 733 2 174 88 37 120 44.5
## 734 2 106 56 27 165 29.0
## 735 2 105 75 0 0 23.3
## 736 4 95 60 32 0 35.4
## 737 0 126 86 27 120 27.4
## 738 8 65 72 23 0 32.0
## 739 2 99 60 17 160 36.6
## 740 1 102 74 0 0 39.5
## 741 11 120 80 37 150 42.3
## 742 3 102 44 20 94 30.8
## 743 1 109 58 18 116 28.5
## 744 9 140 94 0 0 32.7
## 745 13 153 88 37 140 40.6
## 746 12 100 84 33 105 30.0
## 747 1 147 94 41 0 49.3
## 748 1 81 74 41 57 46.3
## 749 3 187 70 22 200 36.4
## 750 6 162 62 0 0 24.3
## 751 4 136 70 0 0 31.2
## 752 1 121 78 39 74 39.0
## 753 3 108 62 24 0 26.0
## 754 0 181 88 44 510 43.3
## 755 8 154 78 32 0 32.4
## 756 1 128 88 39 110 36.5
## 757 7 137 90 41 0 32.0
## 758 0 123 72 0 0 36.3
## 759 1 106 76 0 0 37.5
## 760 6 190 92 0 0 35.5
## 761 2 88 58 26 16 28.4
## 762 9 170 74 31 0 44.0
## 763 9 89 62 0 0 22.5
## 764 10 101 76 48 180 32.9
## 765 2 122 70 27 0 36.8
## 766 5 121 72 23 112 26.2
## 767 1 126 60 0 0 30.1
## 768 1 93 70 31 0 30.4
## DiabetesPedigreeFunction Age Outcome
## 1 0.627 50 1
## 2 0.351 31 0
## 3 0.672 32 1
## 4 0.167 21 0
## 5 2.288 33 1
## 6 0.201 30 0
## 7 0.248 26 1
## 8 0.134 29 0
## 9 0.158 53 1
## 10 0.232 54 1
## 11 0.191 30 0
## 12 0.537 34 1
## 13 1.441 57 0
## 14 0.398 59 1
## 15 0.587 51 1
## 16 0.484 32 1
## 17 0.551 31 1
## 18 0.254 31 1
## 19 0.183 33 0
## 20 0.529 32 1
## 21 0.704 27 0
## 22 0.388 50 0
## 23 0.451 41 1
## 24 0.263 29 1
## 25 0.254 51 1
## 26 0.205 41 1
## 27 0.257 43 1
## 28 0.487 22 0
## 29 0.245 57 0
## 30 0.337 38 0
## 31 0.546 60 0
## 32 0.851 28 1
## 33 0.267 22 0
## 34 0.188 28 0
## 35 0.512 45 0
## 36 0.966 33 0
## 37 0.420 35 0
## 38 0.665 46 1
## 39 0.503 27 1
## 40 1.390 56 1
## 41 0.271 26 0
## 42 0.696 37 0
## 43 0.235 48 0
## 44 0.721 54 1
## 45 0.294 40 0
## 46 1.893 25 1
## 47 0.564 29 0
## 48 0.586 22 0
## 49 0.344 31 1
## 50 0.305 24 0
## 51 0.491 22 0
## 52 0.526 26 0
## 53 0.342 30 0
## 54 0.467 58 1
## 55 0.718 42 0
## 56 0.248 21 0
## 57 0.254 41 1
## 58 0.962 31 0
## 59 1.781 44 0
## 60 0.173 22 0
## 61 0.304 21 0
## 62 0.270 39 1
## 63 0.587 36 0
## 64 0.699 24 0
## 65 0.258 42 1
## 66 0.203 32 0
## 67 0.855 38 1
## 68 0.845 54 0
## 69 0.334 25 0
## 70 0.189 27 0
## 71 0.867 28 1
## 72 0.411 26 0
## 73 0.583 42 1
## 74 0.231 23 0
## 75 0.396 22 0
## 76 0.140 22 0
## 77 0.391 41 0
## 78 0.370 27 0
## 79 0.270 26 1
## 80 0.307 24 0
## 81 0.140 22 0
## 82 0.102 22 0
## 83 0.767 36 0
## 84 0.237 22 0
## 85 0.227 37 1
## 86 0.698 27 0
## 87 0.178 45 0
## 88 0.324 26 0
## 89 0.153 43 1
## 90 0.165 24 0
## 91 0.258 21 0
## 92 0.443 34 0
## 93 0.261 42 0
## 94 0.277 60 1
## 95 0.761 21 0
## 96 0.255 40 0
## 97 0.130 24 0
## 98 0.323 22 0
## 99 0.356 23 0
## 100 0.325 31 1
## 101 1.222 33 1
## 102 0.179 22 0
## 103 0.262 21 0
## 104 0.283 24 0
## 105 0.930 27 0
## 106 0.801 21 0
## 107 0.207 27 0
## 108 0.287 37 0
## 109 0.336 25 0
## 110 0.247 24 1
## 111 0.199 24 1
## 112 0.543 46 1
## 113 0.192 23 0
## 114 0.391 25 0
## 115 0.588 39 1
## 116 0.539 61 1
## 117 0.220 38 1
## 118 0.654 25 0
## 119 0.443 22 0
## 120 0.223 21 0
## 121 0.759 25 1
## 122 0.260 24 0
## 123 0.404 23 0
## 124 0.186 69 0
## 125 0.278 23 1
## 126 0.496 26 1
## 127 0.452 30 0
## 128 0.261 23 0
## 129 0.403 40 1
## 130 0.741 62 1
## 131 0.361 33 1
## 132 1.114 33 1
## 133 0.356 30 1
## 134 0.457 39 0
## 135 0.647 26 0
## 136 0.088 31 0
## 137 0.597 21 0
## 138 0.532 22 0
## 139 0.703 29 0
## 140 0.159 28 0
## 141 0.268 55 0
## 142 0.286 38 0
## 143 0.318 22 0
## 144 0.272 42 1
## 145 0.237 23 0
## 146 0.572 21 0
## 147 0.096 41 0
## 148 1.400 34 0
## 149 0.218 65 0
## 150 0.085 22 0
## 151 0.399 24 0
## 152 0.432 37 0
## 153 1.189 42 1
## 154 0.687 23 0
## 155 0.137 43 1
## 156 0.337 36 1
## 157 0.637 21 0
## 158 0.833 23 0
## 159 0.229 22 0
## 160 0.817 47 1
## 161 0.294 36 0
## 162 0.204 45 0
## 163 0.167 27 0
## 164 0.368 21 0
## 165 0.743 32 1
## 166 0.722 41 1
## 167 0.256 22 0
## 168 0.709 34 0
## 169 0.471 29 0
## 170 0.495 29 0
## 171 0.180 36 1
## 172 0.542 29 1
## 173 0.773 25 0
## 174 0.678 23 0
## 175 0.370 33 0
## 176 0.719 36 1
## 177 0.382 42 0
## 178 0.319 26 1
## 179 0.190 47 0
## 180 0.956 37 1
## 181 0.084 32 0
## 182 0.725 23 0
## 183 0.299 21 0
## 184 0.268 27 0
## 185 0.244 40 0
## 186 0.745 41 1
## 187 0.615 60 1
## 188 1.321 33 1
## 189 0.640 31 1
## 190 0.361 25 1
## 191 0.142 21 0
## 192 0.374 40 0
## 193 0.383 36 1
## 194 0.578 40 1
## 195 0.136 42 0
## 196 0.395 29 1
## 197 0.187 21 0
## 198 0.678 23 1
## 199 0.905 26 1
## 200 0.150 29 1
## 201 0.874 21 0
## 202 0.236 28 0
## 203 0.787 32 0
## 204 0.235 27 0
## 205 0.324 55 0
## 206 0.407 27 0
## 207 0.605 57 1
## 208 0.151 52 1
## 209 0.289 21 0
## 210 0.355 41 1
## 211 0.290 25 0
## 212 0.375 24 0
## 213 0.164 60 0
## 214 0.431 24 1
## 215 0.260 36 1
## 216 0.742 38 1
## 217 0.514 25 1
## 218 0.464 32 0
## 219 1.224 32 1
## 220 0.261 41 1
## 221 1.072 21 1
## 222 0.805 66 1
## 223 0.209 37 0
## 224 0.687 61 0
## 225 0.666 26 0
## 226 0.101 22 0
## 227 0.198 26 0
## 228 0.652 24 1
## 229 2.329 31 0
## 230 0.089 24 0
## 231 0.645 22 1
## 232 0.238 46 1
## 233 0.583 22 0
## 234 0.394 29 0
## 235 0.293 23 0
## 236 0.479 26 1
## 237 0.586 51 1
## 238 0.686 23 1
## 239 0.831 32 1
## 240 0.582 27 0
## 241 0.192 21 0
## 242 0.446 22 0
## 243 0.402 22 1
## 244 1.318 33 1
## 245 0.329 29 0
## 246 1.213 49 1
## 247 0.258 41 0
## 248 0.427 23 0
## 249 0.282 34 0
## 250 0.143 23 0
## 251 0.380 42 0
## 252 0.284 27 0
## 253 0.249 24 0
## 254 0.238 25 0
## 255 0.926 44 1
## 256 0.543 21 1
## 257 0.557 30 0
## 258 0.092 25 0
## 259 0.655 24 0
## 260 1.353 51 1
## 261 0.299 34 0
## 262 0.761 27 1
## 263 0.612 24 0
## 264 0.200 63 0
## 265 0.226 35 1
## 266 0.997 43 0
## 267 0.933 25 1
## 268 1.101 24 0
## 269 0.078 21 0
## 270 0.240 28 1
## 271 1.136 38 1
## 272 0.128 21 0
## 273 0.254 40 0
## 274 0.422 21 0
## 275 0.251 52 0
## 276 0.677 25 0
## 277 0.296 29 1
## 278 0.454 23 0
## 279 0.744 57 0
## 280 0.881 22 0
## 281 0.334 28 1
## 282 0.280 39 0
## 283 0.262 37 0
## 284 0.165 47 1
## 285 0.259 52 1
## 286 0.647 51 0
## 287 0.619 34 0
## 288 0.808 29 1
## 289 0.340 26 0
## 290 0.263 33 0
## 291 0.434 21 0
## 292 0.757 25 1
## 293 1.224 31 1
## 294 0.613 24 1
## 295 0.254 65 0
## 296 0.692 28 0
## 297 0.337 29 1
## 298 0.520 24 0
## 299 0.412 46 1
## 300 0.840 58 0
## 301 0.839 30 1
## 302 0.422 25 1
## 303 0.156 35 0
## 304 0.209 28 1
## 305 0.207 37 0
## 306 0.215 29 0
## 307 0.326 47 1
## 308 0.143 21 0
## 309 1.391 25 1
## 310 0.875 30 1
## 311 0.313 41 0
## 312 0.605 22 0
## 313 0.433 27 1
## 314 0.626 25 0
## 315 1.127 43 1
## 316 0.315 26 0
## 317 0.284 30 0
## 318 0.345 29 1
## 319 0.150 28 0
## 320 0.129 59 1
## 321 0.527 31 0
## 322 0.197 25 1
## 323 0.254 36 1
## 324 0.731 43 1
## 325 0.148 21 0
## 326 0.123 24 0
## 327 0.692 30 1
## 328 0.200 37 0
## 329 0.127 23 1
## 330 0.122 37 0
## 331 1.476 46 0
## 332 0.166 25 0
## 333 0.282 41 1
## 334 0.137 44 0
## 335 0.260 22 0
## 336 0.259 26 0
## 337 0.932 44 0
## 338 0.343 44 1
## 339 0.893 33 1
## 340 0.331 41 1
## 341 0.472 22 0
## 342 0.673 36 0
## 343 0.389 22 0
## 344 0.290 33 0
## 345 0.485 57 0
## 346 0.349 49 0
## 347 0.654 22 0
## 348 0.187 23 0
## 349 0.279 26 0
## 350 0.346 37 1
## 351 0.237 29 0
## 352 0.252 30 0
## 353 0.243 46 0
## 354 0.580 24 0
## 355 0.559 21 0
## 356 0.302 49 1
## 357 0.962 28 1
## 358 0.569 44 1
## 359 0.378 48 0
## 360 0.875 29 1
## 361 0.583 29 1
## 362 0.207 63 0
## 363 0.305 65 0
## 364 0.520 67 1
## 365 0.385 30 0
## 366 0.499 30 0
## 367 0.368 29 1
## 368 0.252 21 0
## 369 0.306 22 0
## 370 0.234 45 1
## 371 2.137 25 1
## 372 1.731 21 0
## 373 0.545 21 0
## 374 0.225 25 0
## 375 0.816 28 0
## 376 0.528 58 1
## 377 0.299 22 0
## 378 0.509 22 0
## 379 0.238 32 1
## 380 1.021 35 0
## 381 0.821 24 0
## 382 0.236 22 0
## 383 0.947 21 0
## 384 1.268 25 0
## 385 0.221 25 0
## 386 0.205 24 0
## 387 0.660 35 1
## 388 0.239 45 1
## 389 0.452 58 1
## 390 0.949 28 0
## 391 0.444 42 0
## 392 0.340 27 1
## 393 0.389 21 0
## 394 0.463 37 0
## 395 0.803 31 1
## 396 1.600 25 0
## 397 0.944 39 0
## 398 0.196 22 1
## 399 0.389 25 0
## 400 0.241 25 1
## 401 0.161 31 1
## 402 0.151 55 0
## 403 0.286 35 1
## 404 0.280 38 0
## 405 0.135 41 1
## 406 0.520 26 0
## 407 0.376 46 1
## 408 0.336 25 0
## 409 1.191 39 1
## 410 0.702 28 1
## 411 0.674 28 0
## 412 0.528 25 0
## 413 1.076 22 0
## 414 0.256 21 0
## 415 0.534 21 1
## 416 0.258 22 1
## 417 1.095 22 0
## 418 0.554 37 1
## 419 0.624 27 0
## 420 0.219 28 1
## 421 0.507 26 0
## 422 0.561 21 0
## 423 0.496 21 0
## 424 0.421 21 0
## 425 0.516 36 1
## 426 0.264 31 1
## 427 0.256 25 0
## 428 0.328 38 1
## 429 0.284 26 0
## 430 0.233 43 1
## 431 0.108 23 0
## 432 0.551 38 0
## 433 0.527 22 0
## 434 0.167 29 0
## 435 1.138 36 0
## 436 0.205 29 1
## 437 0.244 41 0
## 438 0.434 28 0
## 439 0.147 21 0
## 440 0.727 31 0
## 441 0.435 41 1
## 442 0.497 22 0
## 443 0.230 24 0
## 444 0.955 33 1
## 445 0.380 30 1
## 446 2.420 25 1
## 447 0.658 28 0
## 448 0.330 26 0
## 449 0.510 22 1
## 450 0.285 26 0
## 451 0.415 23 0
## 452 0.542 23 1
## 453 0.381 25 0
## 454 0.832 72 0
## 455 0.498 24 0
## 456 0.212 38 1
## 457 0.687 62 0
## 458 0.364 24 0
## 459 1.001 51 1
## 460 0.460 81 0
## 461 0.733 48 0
## 462 0.416 26 0
## 463 0.705 39 0
## 464 0.258 37 0
## 465 1.022 34 0
## 466 0.452 21 0
## 467 0.269 22 0
## 468 0.600 25 0
## 469 0.183 38 1
## 470 0.571 27 0
## 471 0.607 28 0
## 472 0.170 22 0
## 473 0.259 22 0
## 474 0.210 50 0
## 475 0.126 24 0
## 476 0.231 59 0
## 477 0.711 29 1
## 478 0.466 31 0
## 479 0.162 39 0
## 480 0.419 63 0
## 481 0.344 35 1
## 482 0.197 29 0
## 483 0.306 28 0
## 484 0.233 23 0
## 485 0.630 31 1
## 486 0.365 24 1
## 487 0.536 21 0
## 488 1.159 58 0
## 489 0.294 28 0
## 490 0.551 67 0
## 491 0.629 24 0
## 492 0.292 42 0
## 493 0.145 33 0
## 494 1.144 45 1
## 495 0.174 22 0
## 496 0.304 66 0
## 497 0.292 30 0
## 498 0.547 25 0
## 499 0.163 55 1
## 500 0.839 39 0
## 501 0.313 21 0
## 502 0.267 28 0
## 503 0.727 41 1
## 504 0.738 41 0
## 505 0.238 40 0
## 506 0.263 38 0
## 507 0.314 35 1
## 508 0.692 21 0
## 509 0.968 21 0
## 510 0.409 64 0
## 511 0.297 46 1
## 512 0.207 21 0
## 513 0.200 58 0
## 514 0.525 22 0
## 515 0.154 24 0
## 516 0.268 28 1
## 517 0.771 53 1
## 518 0.304 51 0
## 519 0.180 41 0
## 520 0.582 60 0
## 521 0.187 25 0
## 522 0.305 26 0
## 523 0.189 26 0
## 524 0.652 45 1
## 525 0.151 24 0
## 526 0.444 21 0
## 527 0.299 21 0
## 528 0.107 24 0
## 529 0.493 22 0
## 530 0.660 31 0
## 531 0.717 22 0
## 532 0.686 24 0
## 533 0.917 29 0
## 534 0.501 31 0
## 535 1.251 24 0
## 536 0.302 23 1
## 537 0.197 46 0
## 538 0.735 67 0
## 539 0.804 23 0
## 540 0.968 32 1
## 541 0.661 43 1
## 542 0.549 27 1
## 543 0.825 56 1
## 544 0.159 25 0
## 545 0.365 29 0
## 546 0.423 37 1
## 547 1.034 53 1
## 548 0.160 28 0
## 549 0.341 50 0
## 550 0.680 37 0
## 551 0.204 21 0
## 552 0.591 25 0
## 553 0.247 66 0
## 554 0.422 23 0
## 555 0.471 28 0
## 556 0.161 37 0
## 557 0.218 30 0
## 558 0.237 58 0
## 559 0.126 42 0
## 560 0.300 35 0
## 561 0.121 54 1
## 562 0.502 28 1
## 563 0.401 24 0
## 564 0.497 32 0
## 565 0.601 27 0
## 566 0.748 22 0
## 567 0.412 21 0
## 568 0.085 46 0
## 569 0.338 37 0
## 570 0.203 33 1
## 571 0.270 39 0
## 572 0.268 21 0
## 573 0.430 22 0
## 574 0.198 22 0
## 575 0.892 23 0
## 576 0.280 25 0
## 577 0.813 35 0
## 578 0.693 21 1
## 579 0.245 36 0
## 580 0.575 62 1
## 581 0.371 21 1
## 582 0.206 27 0
## 583 0.259 62 0
## 584 0.190 42 0
## 585 0.687 52 1
## 586 0.417 22 0
## 587 0.129 41 1
## 588 0.249 29 0
## 589 1.154 52 1
## 590 0.342 25 0
## 591 0.925 45 1
## 592 0.175 24 0
## 593 0.402 44 1
## 594 1.699 25 0
## 595 0.733 34 0
## 596 0.682 22 1
## 597 0.194 46 0
## 598 0.559 21 0
## 599 0.088 38 1
## 600 0.407 26 0
## 601 0.400 24 0
## 602 0.190 28 0
## 603 0.100 30 0
## 604 0.692 54 1
## 605 0.212 36 1
## 606 0.514 21 0
## 607 1.258 22 1
## 608 0.482 25 0
## 609 0.270 27 0
## 610 0.138 23 0
## 611 0.292 24 0
## 612 0.593 36 1
## 613 0.787 40 1
## 614 0.878 26 0
## 615 0.557 50 1
## 616 0.207 27 0
## 617 0.157 30 0
## 618 0.257 23 0
## 619 1.282 50 1
## 620 0.141 24 1
## 621 0.246 28 0
## 622 1.698 28 0
## 623 1.461 45 0
## 624 0.347 21 0
## 625 0.158 21 0
## 626 0.362 29 0
## 627 0.206 21 0
## 628 0.393 21 0
## 629 0.144 45 0
## 630 0.148 21 0
## 631 0.732 34 1
## 632 0.238 24 0
## 633 0.343 23 0
## 634 0.115 22 0
## 635 0.167 31 0
## 636 0.465 38 1
## 637 0.153 48 0
## 638 0.649 23 0
## 639 0.871 32 1
## 640 0.149 28 0
## 641 0.695 27 0
## 642 0.303 24 0
## 643 0.178 50 1
## 644 0.610 31 0
## 645 0.730 27 0
## 646 0.134 30 0
## 647 0.447 33 1
## 648 0.455 22 1
## 649 0.260 42 1
## 650 0.133 23 0
## 651 0.234 23 0
## 652 0.466 27 0
## 653 0.269 28 0
## 654 0.455 27 0
## 655 0.142 22 0
## 656 0.240 25 1
## 657 0.155 22 0
## 658 1.162 41 0
## 659 0.190 51 0
## 660 1.292 27 1
## 661 0.182 54 0
## 662 1.394 22 1
## 663 0.165 43 1
## 664 0.637 40 1
## 665 0.245 40 1
## 666 0.217 24 0
## 667 0.235 70 1
## 668 0.141 40 1
## 669 0.430 43 0
## 670 0.164 45 0
## 671 0.631 49 0
## 672 0.551 21 0
## 673 0.285 47 0
## 674 0.880 22 0
## 675 0.587 68 0
## 676 0.328 31 1
## 677 0.230 53 1
## 678 0.263 25 0
## 679 0.127 25 1
## 680 0.614 23 0
## 681 0.332 22 0
## 682 0.364 26 1
## 683 0.366 22 0
## 684 0.536 27 1
## 685 0.640 69 0
## 686 0.591 25 0
## 687 0.314 22 0
## 688 0.181 29 0
## 689 0.828 23 0
## 690 0.335 46 1
## 691 0.856 34 0
## 692 0.257 44 1
## 693 0.886 23 0
## 694 0.439 43 1
## 695 0.191 25 0
## 696 0.128 43 1
## 697 0.268 31 1
## 698 0.253 22 0
## 699 0.598 28 0
## 700 0.904 26 0
## 701 0.483 26 0
## 702 0.565 49 1
## 703 0.905 52 1
## 704 0.304 41 0
## 705 0.118 27 0
## 706 0.177 28 0
## 707 0.261 30 1
## 708 0.176 22 0
## 709 0.148 45 1
## 710 0.674 23 1
## 711 0.295 24 0
## 712 0.439 40 0
## 713 0.441 38 1
## 714 0.352 21 0
## 715 0.121 32 0
## 716 0.826 34 1
## 717 0.970 31 1
## 718 0.595 56 0
## 719 0.415 24 0
## 720 0.378 52 1
## 721 0.317 34 0
## 722 0.289 21 0
## 723 0.349 42 1
## 724 0.251 42 0
## 725 0.265 45 0
## 726 0.236 38 0
## 727 0.496 25 0
## 728 0.433 22 0
## 729 0.326 22 0
## 730 0.141 22 0
## 731 0.323 34 1
## 732 0.259 22 1
## 733 0.646 24 1
## 734 0.426 22 0
## 735 0.560 53 0
## 736 0.284 28 0
## 737 0.515 21 0
## 738 0.600 42 0
## 739 0.453 21 0
## 740 0.293 42 1
## 741 0.785 48 1
## 742 0.400 26 0
## 743 0.219 22 0
## 744 0.734 45 1
## 745 1.174 39 0
## 746 0.488 46 0
## 747 0.358 27 1
## 748 1.096 32 0
## 749 0.408 36 1
## 750 0.178 50 1
## 751 1.182 22 1
## 752 0.261 28 0
## 753 0.223 25 0
## 754 0.222 26 1
## 755 0.443 45 1
## 756 1.057 37 1
## 757 0.391 39 0
## 758 0.258 52 1
## 759 0.197 26 0
## 760 0.278 66 1
## 761 0.766 22 0
## 762 0.403 43 1
## 763 0.142 33 0
## 764 0.171 63 0
## 765 0.340 27 0
## 766 0.245 30 0
## 767 0.349 47 1
## 768 0.315 23 06 Outlier: Data Pima Indian Diabetes
6.1 Pemeriksaan Data
setwd("D:/Kuliah/Mat/TSA Kominfo/Praktikum")
diabetes <- read.csv("pima-indians-diabeter-database.csv", sep = ',')
library(ggplot2)
library(mlbench) # data pima Indian Dataset
library(cowplot) # menampilkan plot dalam bentuk Grid
library(caret) # features scaling## Loading required package: lattice##
## Attaching package: 'caret'## The following objects are masked from 'package:DescTools':
##
## MAE, RMSEstr(diabetes)## 'data.frame': 768 obs. of 9 variables:
## $ Pregnancies : int 6 1 8 1 0 5 3 10 2 8 ...
## $ Glucose : int 148 85 183 89 137 116 78 115 197 125 ...
## $ BloodPressure : int 72 66 64 66 40 74 50 0 70 96 ...
## $ SkinThickness : int 35 29 0 23 35 0 32 0 45 0 ...
## $ Insulin : int 0 0 0 94 168 0 88 0 543 0 ...
## $ BMI : num 33.6 26.6 23.3 28.1 43.1 25.6 31 35.3 30.5 0 ...
## $ DiabetesPedigreeFunction: num 0.627 0.351 0.672 0.167 2.288 ...
## $ Age : int 50 31 32 21 33 30 26 29 53 54 ...
## $ Outcome : int 1 0 1 0 1 0 1 0 1 1 ...head(diabetes)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 6 148 72 35 0 33.6
## 2 1 85 66 29 0 26.6
## 3 8 183 64 0 0 23.3
## 4 1 89 66 23 94 28.1
## 5 0 137 40 35 168 43.1
## 6 5 116 74 0 0 25.6
## DiabetesPedigreeFunction Age Outcome
## 1 0.627 50 1
## 2 0.351 31 0
## 3 0.672 32 1
## 4 0.167 21 0
## 5 2.288 33 1
## 6 0.201 30 06.2 Ringkasan dan Sebaran Data
dim(diabetes)## [1] 768 9summary(diabetes)## Pregnancies Glucose BloodPressure SkinThickness
## Min. : 0.000 Min. : 0.0 Min. : 0.00 Min. : 0.00
## 1st Qu.: 1.000 1st Qu.: 99.0 1st Qu.: 62.00 1st Qu.: 0.00
## Median : 3.000 Median :117.0 Median : 72.00 Median :23.00
## Mean : 3.845 Mean :120.9 Mean : 69.11 Mean :20.54
## 3rd Qu.: 6.000 3rd Qu.:140.2 3rd Qu.: 80.00 3rd Qu.:32.00
## Max. :17.000 Max. :199.0 Max. :122.00 Max. :99.00
## Insulin BMI DiabetesPedigreeFunction Age
## Min. : 0.0 Min. : 0.00 Min. :0.0780 Min. :21.00
## 1st Qu.: 0.0 1st Qu.:27.30 1st Qu.:0.2437 1st Qu.:24.00
## Median : 30.5 Median :32.00 Median :0.3725 Median :29.00
## Mean : 79.8 Mean :31.99 Mean :0.4719 Mean :33.24
## 3rd Qu.:127.2 3rd Qu.:36.60 3rd Qu.:0.6262 3rd Qu.:41.00
## Max. :846.0 Max. :67.10 Max. :2.4200 Max. :81.00
## Outcome
## Min. :0.000
## 1st Qu.:0.000
## Median :0.000
## Mean :0.349
## 3rd Qu.:1.000
## Max. :1.0006.2.1 Jumlah Nilai NA
dari summary di bawah, terlihat tidak terdapat data NAdata.frame(colSums(is.na(diabetes)))## colSums.is.na.diabetes..
## Pregnancies 0
## Glucose 0
## BloodPressure 0
## SkinThickness 0
## Insulin 0
## BMI 0
## DiabetesPedigreeFunction 0
## Age 0
## Outcome 06.2.2 Jumlah Nilai 0
terlihat banyak kolom memiliki nilai 0 yang seharusnya tidak mungkin 0. Seperti glucose yang menunjukkan kadar gula atau pressure yang menunjukkan tekanan darah, serta kolom lainnya. Kondisi ini perlu ditangani karena merupakan informasi yang keliru.
data.frame(colSums(diabetes==0))## colSums.diabetes....0.
## Pregnancies 111
## Glucose 5
## BloodPressure 35
## SkinThickness 227
## Insulin 374
## BMI 11
## DiabetesPedigreeFunction 0
## Age 0
## Outcome 5006.2.3 Persentase Jumlah Nilai 0 di setiap kolom
data.frame(round(colSums(diabetes==0)/nrow(diabetes), 4)*100)## round.colSums.diabetes....0..nrow.diabetes...4....100
## Pregnancies 14.45
## Glucose 0.65
## BloodPressure 4.56
## SkinThickness 29.56
## Insulin 48.70
## BMI 1.43
## DiabetesPedigreeFunction 0.00
## Age 0.00
## Outcome 65.10library(gridExtra)
plot1 <- ggplot(diabetes, aes(x = Pregnancies)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("Pregnancies")
plot2 <- ggplot(diabetes, aes(x = Glucose)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("Glucose")
plot3 <- ggplot(diabetes, aes(x = BloodPressure)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("BloodPressure")
plot4 <- ggplot(diabetes, aes(x = SkinThickness)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("SkinThickness")
plot5 <- ggplot(diabetes, aes(x = Insulin)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("Insulin")
plot6 <- ggplot(diabetes, aes(x = BMI)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("BMI")
plot7 <- ggplot(diabetes, aes(x = DiabetesPedigreeFunction)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("DiabetesPedigreeFunction")
plot8 <- ggplot(diabetes, aes(x = Age)) +
geom_density(lwd=1, color="darkgreen") +
ggtitle("Age")
plot9 <- ggplot(diabetes, aes(x = Outcome)) +
geom_bar(fill="darkred") +
ggtitle("Outcome")
# Mengatur grid 3x3
grid.arrange(
plot1, plot2, plot3,
plot4, plot5, plot6,
plot7, plot8, plot9,
ncol = 3
)
plots <- lapply(names(diabetes), function(var_x){
p <-
ggplot(diabetes) +
aes_string(var_x)
if(var_x %in% names(diabetes)[1:8]) {
p <- p + geom_density(lwd=1, color="darkgreen")
} else if(var_x =="Outcome") {
p <- p + geom_bar(fill="darkred")
}
})## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation idioms with `aes()`.
## ℹ See also `vignette("ggplot2-in-packages")` for more information.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.plot_grid(plotlist = plots)
6.3 Kolom Pregnancies
library(ggplot2)
library(gridExtra)plot1 <- ggplot(diabetes, aes(x = Pregnancies)) +
geom_histogram(bins = 10, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = Pregnancies)) +
geom_boxplot(fill = "red", alpha=0.6) +theme_classic()
plot3 <- ggplot(diabetes, aes(x = Pregnancies, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(x = Pregnancies, group=Outcome)) +
geom_boxplot(aes(fill = Outcome)) +theme_classic()
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
summary(diabetes$Pregnancies)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.000 3.000 3.845 6.000 17.000Sebaran nilai Pregnancies cenderung menjulur jauh ke kanan.
Menurut visualisasi boxplot, terdapat beberapa data outlier namun secara umum masih dalam batas yang wajar. Apalagi jika melihat boxplot antara Pregnancies dan Outcome sebaran data relatif cukup baik.
Namun jika ingin dilakukan penanganan maka terdapat beberapa alternatif:
Menghapus data Outlier
Mengganti data dengan mean/ median data yang tidak outlier
Flooring & Capping: Mengganti data dengan nilai max teoritis (Misal Q1 - 1.5xIQR dan Q3 + 1.5xIQR)
6.3.1 Menghapus Data Outlier
Melihat dari boxplot tunggal, terdapat 3 titik data outlier, sedangkan jika melihat berdasarkan kelompok diabetes atau tidak maka terdapat dua outlier pada kelompok tidak diabetes. Misalkan kita menggunakan indikator dari boxplot tunggal, maka untuk menghapus data tersebut:
q1 <-quantile(diabetes$Pregnancies, prob = 0.25, names = F)
q3 <-quantile(diabetes$Pregnancies, prob = 0.75, names = F)
IQR <- q3 - q1
max <- q3 + 1.5*IQR# Hapus data yang lebih besar dari max yaitu
# R base
(diabetes[diabetes$Pregnancies > max,])## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 89 15 136 70 32 110 37.1
## 160 17 163 72 41 114 40.9
## 299 14 100 78 25 184 36.6
## 456 14 175 62 30 0 33.6
## DiabetesPedigreeFunction Age Outcome
## 89 0.153 43 1
## 160 0.817 47 1
## 299 0.412 46 1
## 456 0.212 38 1# dplyr
#library(dplyr)
#(diabetes %>% filter(Pregnancies > max))6.3.2 Mengganti dengan Mean/Median dari data yang tidak Outlier
non.outlier <- diabetes[diabetes$Pregnancies <= max, "Pregnancies"]
mean.non <- mean(non.outlier)
med.non <- median(non.outlier)
# Update outlier data menggunakan mean atau median
# R base
diabetes$Pregnancies <- ifelse(diabetes$Pregnancies > max, med.non, diabetes$Pregnancies)
# dplyr
# diabetes <- diabetes %>% mutate(pregnant = ifelse(pregnant > max, med.non, pregnant))6.3.3 Mengganti dengan Nilai Max dari data yang tidak Outlier
Sama seperti sebelumnya, cukup mengganti nilai outlier dengan nilai minimum/maksimum
# Update outlier data menggunakan nilai max
# R base
# diabetes$Pregnancies <- ifelse(diabetes$Pregnancies > max, max,
# diabetes$Pregnancies)
# dplyr
# diabetes <- diabetes %>% mutate(pregnant = ifelse(pregnant > max, max, pregnant))6.3.4 Plot Setelah Modifikasi
pl2 <- ggplot(diabetes, aes(y=Pregnancies))
pl2 +
geom_boxplot(fill="red", alpha=0.6) + coord_flip() + theme_classic()
6.4 Kolom Glucose
summary(diabetes$Glucose)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 99.0 117.0 120.9 140.2 199.0plot1 <- ggplot(diabetes, aes(x = Glucose)) +
geom_histogram(bins = 10, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = Glucose)) +
geom_boxplot(fill = "red", alpha=0.6) +theme_classic()
plot3 <- ggplot(diabetes, aes(x = Glucose, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(x = Glucose, group=Outcome)) +
geom_boxplot(aes(fill = Outcome)) +theme_classic()
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
Pada kolom ini sebaran data relatif simetris, dan secara umum tidak terdapat data outlier kecuali pada data bernilai 0.
Nilai Glucose menunjukkan kadar gula dalam darah, sehingga tidak mungkin bernilai 0. Perlu dicek juga apakah terdapat nilai-nilai lainnya yang tidak masuk akal (misalkan menurut Dokter).Namun pada contoh ini kita hanya akan fokus pada nilai 0 saja, kita anggap nilai lainnya masih masuk dalam rentang nilai yang memungkinkan.
Cek jumlah data bernilai 0:
length(which(diabetes$Glucose == 0))## [1] 5Terdapat 5 data yang memiliki nilai Glucose = 0 yang perlu ditangani. Jumlah ini relatif sedikit jadi dapat saja kita 5 baris ini atau alternatif lain kita amputasi misal dengan mean atau median.
6.4.1 Menghapus Data
# R base
# diabetes <- diabetes[diabetes$Glucose > 0,]
# dplyr
#diabetes <- diabetes %>% filter(Glucose > 0)6.4.2 Mengganti dengan Nilai Mean atau Median
Perlu diperhatikan, karena data bernilai 0 (bukan NA) maka perlu berhati-hati khususnya dalam menghitung mean.
Jika data bernilai NA, penghitungan mean dapat langsung dilakukan pada seluruh data, karena nilai NA akan diabaikan. Namun jika data 0 maka nilai tersebut akan dimasukkan dalam penghitungan rata-rata. Oleh karena itu, perlu difilter terlebih dahulu data yang tidak bernilai 0.
Pemilihan mean biasanya untuk data yang memiliki sebaran simetris, sementara untuk data dengan sebaran yang menjulur dapat menggunakan nilai median.
Melihat dari boxplot, tampat terdapat perbedaan sebaran nilai Glucose antara yang terkena diabetes dan yang tidak. Penderita Diabetes cenderung memiliki nilai Glucose yang lebih tinggi dibandingkan yang bukan penderita diabetes.
Opsi yang cocok adalah menggunakan mean atau median per kelompok. Data Glucose bernilai 0 mengacu pada kelompok diabetes diganti dengan mean atau median pada kelompok tersebut begitu pula sebaliknya.
# Mengambil data glucose yang tidak bernilai 0
glucose.pos <- diabetes[(diabetes$Glucose != 0) & (diabetes$Outcome == "1"), "Glucose"]
glucose.neg <- diabetes[(diabetes$Glucose != 0) & (diabetes$Outcome == "0"), "Glucose"]
# Menghitung mean glucose masing-masing kelompok
med.gluc.pos <- median(glucose.pos)
med.gluc.neg <- median(glucose.neg)
# Mengganti nilai 0 dengan mean
# R base
diabetes$Glucose <- ifelse(diabetes$Glucose == 0,
ifelse(diabetes$Outcome == "1", med.gluc.pos, med.gluc.neg),
diabetes$Glucose)
# dplyr
# diabetes <- diabetes %>% mutate(glucose = ifelse(glucose == 0,
# ifelse(diabetes=="pos",
# med.gluc.pos, med.gluc.neg),
# glucose))plot1 <- ggplot(diabetes, aes(x = Glucose)) +
geom_histogram(bins = 10, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = Glucose)) +
geom_boxplot(fill = "red", alpha=0.6) +theme_classic()
plot3 <- ggplot(diabetes, aes(x = Glucose, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(x = Glucose, group=Outcome)) +
geom_boxplot(aes(fill = Outcome)) +theme_classic()
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
summary(diabetes$Glucose)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 44.00 99.75 117.00 121.68 140.25 199.006.5 Kolom Blood Pressure
Kolom BloodPressure berisi data tekanan darah yang memuat nilai 0 (tidak mungkin terjadi)
Selain itu terdapat nilai-nilai outlier di kedua sisinya.
summary(diabetes$BloodPressure)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 62.00 72.00 69.11 80.00 122.00plot1 <- ggplot(diabetes, aes(x = BloodPressure)) +
geom_histogram(bins = 10, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = BloodPressure)) +
geom_boxplot(fill = "red", alpha=0.6) +theme_classic()
plot3 <- ggplot(diabetes, aes(x = BloodPressure, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(x = BloodPressure, group=Outcome)) +
geom_boxplot(aes(fill = Outcome)) +theme_classic()
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
6.5.1 Data bernilai 0
length(which(diabetes$BloodPressure == 0))## [1] 35library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:MASS':
##
## select## The following object is masked from 'package:gridExtra':
##
## combine## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionzero.BloodPressure <- diabetes %>%
filter(BloodPressure == 0) %>%
group_by(Outcome) %>%
summarise(count = length(BloodPressure))
zero.BloodPressure## # A tibble: 2 × 2
## Outcome count
## <int> <int>
## 1 0 19
## 2 1 16Terdapat 35 data dengan nilai BloodPressure == 0. Untuk kelompok penderita diabetes terdapat 16 data bernilai 0 sedangkan untuk kelompok bukan penderita diabetes terdapat 19 data bernilai 0. Melihat dari boxplot kelompok, tampaknya tidak terdapat perbedaan yang berarti antara sebaran nilai BloodPressure pada kelompok diabetes maupun tidak. Oleh karena itu, kita mungkin cukup menggunakan mean data keseluruhan (yang tidak bernilai 0) untuk imputasi data 0.
Pada data BloodPressure terindikasi terdapat beberapa amatan outlier, dapat pula dilakukan penanganan seperti pada bagian sebelumnya (pregnant). Namun di sini tidak akan dilakukan penanganan.
6.5.2 Mengganti nilai 0 dengan Nilai Mean
# Mengambil data BloodPressure yang tidak bernilai 0
BloodPressure <- diabetes[diabetes$BloodPressure != 0, "BloodPressure"]
# Menghitung mean pressure
mean.BloodPressure <- mean(diabetes$BloodPressure)
# Mengganti nilai 0 dengan mean
# R base
diabetes$BloodPressure <- ifelse(diabetes$BloodPressure == 0, mean.BloodPressure, diabetes$BloodPressure)
# dplyr
# diabetes <- diabetes %>% mutate(pressure = ifelse(pressure == 0, mean.pressure, pressure))6.5.3 Plot Setelah Imputasi
plot1 <- ggplot(diabetes, aes(x = BloodPressure)) +
geom_histogram(bins = 10, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = BloodPressure)) +
geom_boxplot(fill = "red", alpha=0.6) +theme_classic()
plot3 <- ggplot(diabetes, aes(x = BloodPressure, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(x = BloodPressure, group=Outcome)) +
geom_boxplot(aes(fill = Outcome)) +theme_classic()
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
6.6 Kolom Skin Thickness
Kolom SkinThickness menunjukkan ketebalan lipatan kulit(mm).
Data ini juga seharusnya tidak dapat bernilai 0.
summary(diabetes$SkinThickness)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 23.00 20.54 32.00 99.00plot1 <- ggplot(diabetes, aes(x = SkinThickness)) +
geom_histogram(bins = 10, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = SkinThickness)) +
geom_boxplot(fill = "red", alpha=0.6) +theme_classic()
plot3 <- ggplot(diabetes, aes(x = SkinThickness, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(x = SkinThickness, group=Outcome)) +
geom_boxplot(aes(fill = Outcome)) +theme_classic()
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
length(which(diabetes$SkinThickness == 0))## [1] 227length(which(diabetes$SkinThickness == 0))/length(diabetes$SkinThickness)## [1] 0.2955729Jumlah data bernilai 0 untuk kolom SkinThickness cukup besar yaitu sekitar 30%.
Dapat dilakukan imputasi seperti kolom sebelumnya. Namun, jika dirasa terlalu banyak yang diimputasi mungkin sebaiknya kolom ini dapat dibuang dari model.
6.6.1 Menghapus Kolom SkinThickness
diabetes$SkinThickness <- NULL6.7 Kolom Insulin
Sama seperti kolom SkinThickness, kolom Insulin juga tidak mungkin bernilai 0. Namun pada data terdapat nilai 0 yang sangat banyak bahkan hampir 50%.
Oleh karena itu, penanganan yang paling tepat adalah membuang kolom tersebut dari model.
summary(diabetes$Insulin)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 0.0 30.5 79.8 127.2 846.0length(which(diabetes$Insulin == 0))## [1] 374length(which(diabetes$Insulin == 0))/length(diabetes$Insulin)## [1] 0.48697926.7.1 Menghapus kolom Insulin
diabetes$Insulin <- NULL6.8 Kolom BMI
summary(diabetes$BMI)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 27.30 32.00 31.99 36.60 67.10plot1 <- ggplot(diabetes, aes(x = BMI)) +
geom_histogram(bins = 10, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = BMI)) +
geom_boxplot(fill = "red", alpha=0.6) +theme_classic()
plot3 <- ggplot(diabetes, aes(x = BMI, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(x = BMI, group=Outcome)) +
geom_boxplot(aes(fill = Outcome)) +theme_classic()
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
length(which(diabetes$BMI == 0))## [1] 11length(which(diabetes$BMI == 0))/length(diabetes$BMI)## [1] 0.014322926.8.1 Mengganti Nilai 0 dengan Nilai Mean
# Mengambil data mass yang tidak bernilai 0
BMI <- diabetes[diabetes$BMI != 0, "BMI"]
# Menghitung mean mass
mean.BMI <- mean(diabetes$BMI)
# Mengganti nilai 0 dengan mean
# R base
diabetes$BMI <- ifelse(diabetes$BMI == 0, mean.BMI, diabetes$BMI)
# dplyr
# diabetes <- diabetes %>% mutate(mass = ifelse(mass == 0, mean.mass, mass))6.8.2 Mengganti Nilai Data Outlier
Dalam kolom BMI ini, dianggap nilai BMI di atas (Q3 +1.5 IQR) merupakan nilai yang tidak masuk akal.
Maka akan dihapus amatan dengan BMI > 50 atau mengganti dengan nilai (Q3 + 1.5 IQR)
q1 <- quantile(diabetes$BMI, probs=0.25, names=F)
q3 <- quantile(diabetes$BMI, probs=0.75, names=F)
IQR <- q3 - q1
max <- q3 + 1.5*IQR
# R base
diabetes$BMI <- ifelse(diabetes$BMI > max, max, diabetes$BMI)
# dplyr
# diabetes <- diabetes %>% mutate(mass = ifelse(mass > max, max, mass))6.9 Setelah melakukan Imputasi Pada Kolom BMI
plot1 <- ggplot(diabetes, aes(x = BMI)) +
geom_histogram(bins = 10, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = BMI)) +
geom_boxplot(fill = "red", alpha=0.6) +theme_classic()
plot3 <- ggplot(diabetes, aes(x = BMI, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(x = BMI, group=Outcome)) +
geom_boxplot(aes(fill = Outcome)) +theme_classic()
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
6.10 Kolom Diabetes Pedigree Function
summary(diabetes$DiabetesPedigreeFunction)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0780 0.2437 0.3725 0.4719 0.6262 2.4200plot1 <- ggplot(diabetes, aes(x = DiabetesPedigreeFunction)) +
geom_histogram(bins = 10, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = DiabetesPedigreeFunction)) +
geom_boxplot(fill = "red", alpha=0.6) +theme_classic()
plot3 <- ggplot(diabetes, aes(x = DiabetesPedigreeFunction, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(x = DiabetesPedigreeFunction, group=Outcome)) +
geom_boxplot(aes(fill = Outcome)) +theme_classic()
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
length(which(diabetes$DiabetesPedigreeFunction == 0))## [1] 0Untuk melakukan penanganan outlier dapat menggunakan cara seperti sebelumnya. Namun pada kolom Diabetes Pedigree Function ini akan dibiarkan, karena nilai-nilai masih masuk dalam rentang nilai yang memungkinkan.
6.11 Kolom Age
summary(diabetes$Age)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 21.00 24.00 29.00 33.24 41.00 81.00plot1 <- ggplot(diabetes, aes(x = Age)) +
geom_histogram(bins = 10, fill = "red", alpha = 0.7)
plot2 <- ggplot(diabetes, aes(x = Age)) +
geom_boxplot(fill = "red", alpha=0.6) +theme_classic()
plot3 <- ggplot(diabetes, aes(x = Age, group=Outcome)) +
geom_density(lwd=0.1, aes(fill=Outcome), alpha= 0.5)
plot4 <- ggplot(diabetes, aes(x = Age, group=Outcome)) +
geom_boxplot(aes(fill = Outcome)) +theme_classic()
# Mengatur grid
grid.arrange(
plot1, plot2, plot3, plot4, ncol = 2
)
Tidak terdapat data yang aneh pada kolom Age sehingga akan dibiarkan apa adanya.
6.12 Features Scalling
Features Scalling adalah proses pengubahan skala pada pubah-peubah sehingga memiliki skala yang sama. Banyak algoritma machine learning, terutama yang berbasis jarak ataupun Neural Network akan bekerja lebih optimal jika skala setiap fitur sama.
Selain itu, dalam kasus model regresi, ada skala data yang sama, semakin besar nilai koefisiennya (mutlak) maka semakin besar pengaruhnya terhadap model.
Features Scalling tidak merubah pola hubungan antara peubah tersebut dengan peubah respon.
Contoh features scalling: 1. Standarize: mengubah setiap fitur menjadi distribusi dengan mean 0 dan variansi 1 dengan formula x_i scaled = (x_i - x_bar)/ s 2. Normalize: mengubah setiap fitur sehingga memiliki nilai pada rentang [0,1] dengan formula x_i scaled = (x_i - min(x))/(max(x) - min(x))
6.12.1 Standardized
summary(diabetes[,1:6])## Pregnancies Glucose BloodPressure BMI
## Min. : 0.000 Min. : 44.00 Min. : 24.00 Min. :18.20
## 1st Qu.: 1.000 1st Qu.: 99.75 1st Qu.: 64.00 1st Qu.:27.50
## Median : 3.000 Median :117.00 Median : 72.00 Median :32.00
## Mean : 3.783 Mean :121.68 Mean : 72.25 Mean :32.39
## 3rd Qu.: 6.000 3rd Qu.:140.25 3rd Qu.: 80.00 3rd Qu.:36.60
## Max. :13.000 Max. :199.00 Max. :122.00 Max. :50.25
## DiabetesPedigreeFunction Age
## Min. :0.0780 Min. :21.00
## 1st Qu.:0.2437 1st Qu.:24.00
## Median :0.3725 Median :29.00
## Mean :0.4719 Mean :33.24
## 3rd Qu.:0.6262 3rd Qu.:41.00
## Max. :2.4200 Max. :81.00sapply(diabetes[,1:6], sd)## Pregnancies Glucose BloodPressure
## 3.2706442 30.4641606 12.1159316
## BMI DiabetesPedigreeFunction Age
## 6.6676330 0.3313286 11.76023156.12.2 Standarisasi Fitur
preprocessParams <- preProcess(diabetes[,1:6], method=c("center", "scale"))
standardized <- predict(preprocessParams, diabetes[,1:6])
summary(standardized)## Pregnancies Glucose BloodPressure BMI
## Min. :-1.1565 Min. :-2.5498 Min. :-3.98276 Min. :-2.12804
## 1st Qu.:-0.8508 1st Qu.:-0.7198 1st Qu.:-0.68132 1st Qu.:-0.73324
## Median :-0.2393 Median :-0.1535 Median :-0.02103 Median :-0.05833
## Mean : 0.0000 Mean : 0.0000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.6780 3rd Qu.: 0.6097 3rd Qu.: 0.63926 3rd Qu.: 0.63157
## Max. : 2.8182 Max. : 2.5382 Max. : 4.10577 Max. : 2.67877
## DiabetesPedigreeFunction Age
## Min. :-1.1888 Min. :-1.0409
## 1st Qu.:-0.6885 1st Qu.:-0.7858
## Median :-0.2999 Median :-0.3606
## Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4659 3rd Qu.: 0.6598
## Max. : 5.8797 Max. : 4.0611sapply(standardized, sd)## Pregnancies Glucose BloodPressure
## 1 1 1
## BMI DiabetesPedigreeFunction Age
## 1 1 16.12.3 Normalize
# Normalisasi Fitur
preprocessParams <- preProcess(diabetes[,1:6], method=c("range"))
normalized <- predict(preprocessParams, diabetes[,1:6])
summary(normalized)## Pregnancies Glucose BloodPressure BMI
## Min. :0.00000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.07692 1st Qu.:0.3597 1st Qu.:0.4082 1st Qu.:0.2902
## Median :0.23077 Median :0.4710 Median :0.4898 Median :0.4306
## Mean :0.29097 Mean :0.5011 Mean :0.4924 Mean :0.4427
## 3rd Qu.:0.46154 3rd Qu.:0.6210 3rd Qu.:0.5714 3rd Qu.:0.5741
## Max. :1.00000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## DiabetesPedigreeFunction Age
## Min. :0.00000 Min. :0.0000
## 1st Qu.:0.07077 1st Qu.:0.0500
## Median :0.12575 Median :0.1333
## Mean :0.16818 Mean :0.2040
## 3rd Qu.:0.23409 3rd Qu.:0.3333
## Max. :1.00000 Max. :1.00006.12.4 Plot Sebaran Asal
plots <- lapply(names(diabetes[,1:6]), function(var_x){
p <-
ggplot(diabetes) +
aes_string(var_x)
if(is.numeric(diabetes[[var_x]])) {
p <- p + geom_density(lwd=1, color="darkgreen")
} else {
p <- p + geom_bar(fill="darkred")
}
})
plot_grid(plotlist = plots)
6.12.5 Hasil Standarisasi
Plot Sebaran Hasil Standarisasi
plots <- lapply(names(standardized), function(var_x){
p <-
ggplot(standardized) +
aes_string(var_x) +
geom_density(lwd=1, color="darkgreen")
})
plot_grid(plotlist = plots)
6.12.6 Hasil Normalisasi
Plot Sebaran Hasil Normalisasi
plots <- lapply(names(normalized), function(var_x){
p <-
ggplot(normalized) +
aes_string(var_x) +
geom_density(lwd=1, color="darkgreen")
})
plot_grid(plotlist = plots)
6.13 Transformasi Box-Cox
Transformasi umumnya digunakan untuk merubah sebaran suatu feature ketika feature tersebut tidak normal sehingga menjadi mendekati sebaran normal.
Box-Cox Transformation biasanya dilakukan pada variabel dependen (Y) dalam analisis regresi atau analisis varian (ANOVA). Ini dilakukan untuk memastikan bahwa variabel dependen memiliki distribusi yang lebih dekat dengan normal sehingga asumsi distribusi normal dalam model regresi atau ANOVA terpenuhi.
Transformasi ini juga dapat digunakan pada variabel independen (X) jika diperlukan, tergantung pada distribusi data dan tujuan analisis. Namun, transformasi pada variabel independen lebih jarang dilakukan karena memiliki implikasi terhadap interpretasi model akhir.
preprocessParams <- preProcess(diabetes[,1:6], method=c("BoxCox"))
print(preprocessParams)## Created from 768 samples and 5 variables
##
## Pre-processing:
## - Box-Cox transformation (5)
## - ignored (0)
##
## Lambda estimates for Box-Cox transformation:
## 0.1, 0.9, 0.3, -0.1, -1.1transformed <- predict(preprocessParams, diabetes[,1:6])
summary(transformed)## Pregnancies Glucose BloodPressure BMI
## Min. : 0.000 Min. :3.784 Min. : 24.00 Min. :4.626
## 1st Qu.: 1.000 1st Qu.:4.603 1st Qu.: 64.00 1st Qu.:5.676
## Median : 3.000 Median :4.762 Median : 72.00 Median :6.095
## Mean : 3.783 Mean :4.770 Mean : 72.25 Mean :6.087
## 3rd Qu.: 6.000 3rd Qu.:4.943 3rd Qu.: 80.00 3rd Qu.:6.482
## Max. :13.000 Max. :5.293 Max. :122.00 Max. :7.462
## DiabetesPedigreeFunction Age
## Min. :-2.5510 Min. :0.8772
## 1st Qu.:-1.4116 1st Qu.:0.8815
## Median :-0.9875 Median :0.8867
## Mean :-0.9599 Mean :0.8874
## 3rd Qu.:-0.4680 3rd Qu.:0.8938
## Max. : 0.8838 Max. :0.9019plots <- lapply(names(transformed), function(var_x){
p <-
ggplot(transformed) +
aes_string(var_x) +
geom_density(lwd=1, color="darkgreen")
})
plot_grid(plotlist = plots)