Tugas Pertemuan Minggu 4-5: Asumsi Regresi Linier Sederhana

Membaca Data

handheight<-read.table("C:/Users/LENOVO/OneDrive/Documents/Learning R/Semester 2/handheight.txt", header = TRUE)
head(handheight)

##      Sex Height HandSpan
## 1 Female     68     21.5
## 2   Male     71     23.5
## 3   Male     73     22.5
## 4 Female     64     18.0
## 5   Male     68     23.5
## 6 Female     59     20.0

Eksplorasi data

summary(handheight)

##      Sex                Height         HandSpan    
##  Length:167         Min.   :57.00   Min.   :16.00  
##  Class :character   1st Qu.:65.00   1st Qu.:19.50  
##  Mode  :character   Median :68.00   Median :21.00  
##                     Mean   :68.07   Mean   :20.86  
##                     3rd Qu.:71.00   3rd Qu.:22.00  
##                     Max.   :78.00   Max.   :25.50

plot(handheight$Height, handheight$HandSpan, xlab="Height", ylab="HandSpan", pch=10)

Persamaan Regresi

model2 <- lm(HandSpan ~ Height, data = handheight)
summary(model2)

## 
## Call:
## lm(formula = HandSpan ~ Height, data = handheight)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3888 -0.9348  0.0135  1.0365  2.6629 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -3.00161    1.69394  -1.772   0.0782 .  
## Height       0.35057    0.02484  14.113   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.301 on 165 degrees of freedom
## Multiple R-squared:  0.5469, Adjusted R-squared:  0.5442 
## F-statistic: 199.2 on 1 and 165 DF,  p-value: < 2.2e-16

Asumsi 1: Rata-rata galat diasumsikan bernilai nol

plot(handheight$Height, handheight$HandSpan, 
     xlab="Height", ylab="HandSpan", pch=10, 
     main="Plot Uji Asumsi Rata-rata Galat bernilai nol")

Asumsi 2: Galat saling bebas

c <- (1:167)
handheight <- cbind(handheight, c)
head(handheight)

##      Sex Height HandSpan c
## 1 Female     68     21.5 1
## 2   Male     71     23.5 2
## 3   Male     73     22.5 3
## 4 Female     64     18.0 4
## 5   Male     68     23.5 5
## 6 Female     59     20.0 6

plot(handheight$c, model2$residuals,
     xlab = "amatan", ylab = "residuals", type = "l",
     main = "Plot Uji Asumsi Galat Saling Bebas")

plot(handheight$c,model2$residuals,
     xlab="Amatan",ylab="Residuals",
     main="Plot Uji Asumsi Galat Saling Bebas")

Asumsi 3: Galat berdistribusi normal

c <- (1:167)
ytopi <- model2$fitted.values
ei <- model2$residuals
eiterurut <- sort(model2$residuals)
anova(model2)

## Analysis of Variance Table
## 
## Response: HandSpan
##            Df Sum Sq Mean Sq F value    Pr(>F)    
## Height      1 337.08  337.08  199.17 < 2.2e-16 ***
## Residuals 165 279.25    1.69                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

hi<-sqrt(1.69)*qnorm((c-0.375)/(167+0.25))
Hi<-cbind(handheight, ytopi, ei, eiterurut, hi)
head(Hi)

##      Sex Height HandSpan c    ytopi          ei eiterurut        hi
## 1 Female     68     21.5 1 20.83708  0.66291514 -3.388792 -3.477447
## 2   Male     71     23.5 2 21.88879  1.61120802 -3.187654 -3.038280
## 3   Male     73     22.5 3 22.58993 -0.08993006 -2.791068 -2.797719
## 4 Female     64     18.0 4 19.43481 -1.43480870 -2.687654 -2.626440
## 5   Male     68     23.5 5 20.83708  2.66291514 -2.584240 -2.491399
## 6 Female     59     20.0 6 17.68196  2.31803650 -2.538223 -2.378873

plot(hi,eiterurut,
     xlab="hi",ylab="eiterurut",
     main="Plot Uji Galat Berdistribusi Normal")

Atau gunakan fungsi qqnorm dan qqline di R berikut

qqnorm(model2$residuals, ylab = "raw residuals")
qqline(model2$residuals)

Histogram

hist(model2$residuals, main="Histogram Uji Galat Berdistribusi Normal")

Histogram untuk interval data = 167

hist(model2$residuals, 167, main="Histogram Uji Galat Berdistribusi Normal untuk Interval Data = 167")

Boxplot

boxplot(model2$residuals, main="Boxplot")

Asumsi 4: Ragam galat diasumsikan konstan

ytopi<-model2$fitted.values
ei<-model2$residuals
plot(ytopi,ei,
     xlab="fitted values", ylab="residuals",
     main="Plot Uji Ragam Galat Konstan")

Asumsi 5: X dan Y berhubungan linear

plot(handheight$Height, handheight$HandSpan, main="Plot Data")

Asumsi 6: Tidak ada outlier

plot(handheight$Height, handheight$HandSpan, main="Plot Data")

Nama Anggota

1. Fiki Vania Arun Fadila (23031030003)
2. Nariza Rahmadani Putri Mawardi (23031030012)
3. Sahda Huwaidah Estiningtyas (23031030019)
4. Sekar Ayu Nida Nur Afifah (23031030028)
5. Qurrota A’yun Zahirah (23031030029)