UJI ASUMSI REGRESI LINEAR SEDERHANA

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# ASUMSI REGRESI LINEAR SEDERHANA

library(readxl)
ANREGP4<-read_excel("C:/Users/Me/Downloads/ANREGP4.xlsx")
head(ANREGP4)

## # A tibble: 6 × 3
##   Sex    Height HandSpan
##   <chr>  <chr>  <chr>   
## 1 Female 68     21.5    
## 2 Male   71     23.5    
## 3 Male   73     22.5    
## 4 Female 64     18      
## 5 Male   68     23.5    
## 6 Female 59     20

# Eksplorasi data
summary(ANREGP4)

##      Sex               Height            HandSpan        
##  Length:167         Length:167         Length:167        
##  Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character

plot(ANREGP4$Height, ANREGP4$HandSpan,xlab="Height",ylab="HandSpan",pch=16)

model2 <- lm(HandSpan~Height, data=ANREGP4)
summary(model2)

## 
## Call:
## lm(formula = HandSpan ~ Height, data = ANREGP4)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.1429 -0.7273  0.0000  0.8536  2.4333 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   16.000      1.295  12.354  < 2e-16 ***
## Height59       4.000      1.832   2.184 0.030614 *  
## Height60       2.333      1.496   1.560 0.120932    
## Height61       2.000      1.586   1.261 0.209429    
## Height61.5     2.750      1.586   1.734 0.085146 .  
## Height62       2.125      1.448   1.468 0.144446    
## Height63       3.500      1.374   2.548 0.011903 *  
## Height63.75    5.500      1.832   3.003 0.003162 ** 
## Height64       3.036      1.341   2.264 0.025062 *  
## Height64.25    6.000      1.832   3.276 0.001324 ** 
## Height64.5     3.500      1.832   1.911 0.058035 .  
## Height65       3.812      1.374   2.775 0.006258 ** 
## Height66       3.727      1.353   2.755 0.006632 ** 
## Height67       4.605      1.329   3.466 0.000700 ***
## Height67.5     4.500      1.496   3.009 0.003102 ** 
## Height68       5.067      1.338   3.788 0.000224 ***
## Height69       5.143      1.341   3.836 0.000187 ***
## Height70       6.000      1.385   4.333 2.76e-05 ***
## Height71       5.433      1.338   4.062 8.02e-05 ***
## Height72       5.722      1.365   4.191 4.85e-05 ***
## Height73       6.650      1.358   4.896 2.63e-06 ***
## Height74       7.650      1.358   5.632 9.23e-08 ***
## Height75       6.625      1.448   4.575 1.03e-05 ***
## Height76       7.667      1.496   5.126 9.49e-07 ***
## Height78       9.500      1.832   5.187 7.24e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.295 on 142 degrees of freedom
## Multiple R-squared:  0.6135, Adjusted R-squared:  0.5482 
## F-statistic: 9.393 on 24 and 142 DF,  p-value: < 2.2e-16

 # Asumsi 1 : Rata-rata galat diasumsikan bernilai nol
plot(ANREGP4$Height,model2$residuals,
     xlab="Height (X)",ylab="Residuals",
     main="Plot Uji Asumsi Rata-rata Galat bernilai nol")

# Asumsi 2 : Galat saling bebas
c<-(1:167)
ANREGP4<-cbind(ANREGP4,c)
head(ANREGP4)

##      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 4
## 5   Male     68     23.5 5
## 6 Female     59       20 6

plot(ANREGP4$c,model2$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) #baca nilai KTG

## Analysis of Variance Table
## 
## Response: HandSpan
##            Df Sum Sq Mean Sq F value    Pr(>F)    
## Height     24 378.14 15.7558   9.393 < 2.2e-16 ***
## Residuals 142 238.19  1.6774                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

hi<-sqrt(1.6774)*qnorm((c-0.375)/(168+0.25))
Hi<-cbind(ANREGP4,ytopi,ei,eiterurut,hi)
head(Hi)

##      Sex Height HandSpan c    ytopi            ei eiterurut        hi
## 1 Female     68     21.5 1 21.06667  4.333333e-01 -3.142857 -3.467047
## 2   Male     71     23.5 2 21.43333  2.066667e+00 -3.000000 -3.029818
## 3   Male     73     22.5 3 22.65000 -1.500000e-01 -3.000000 -2.790347
## 4 Female     64       18 4 19.03571 -1.035714e+00 -2.933333 -2.619858
## 5   Male     68     23.5 5 21.06667  2.433333e+00 -2.642857 -2.485451
## 6 Female     59       20 6 20.00000 -7.077672e-15 -2.605263 -2.373459

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

hist(model2$residuals,5)

#Atau gunakan fungsi qqnorm dan qqline di R sebagai berikut
qqnorm(model2$residuals,ylab = "Raw Residuals")
qqline(model2$residuals)

hist(model2$residuals,168) #interval data ada 168

boxplot(model2$residuals)

# 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(ANREGP4$Height,ANREGP4$HandSpan,main="Plot Data")

# Asumsi 6 : Tidak ada outlier
plot(ANREGP4$Height,ANREGP4$HandSpan,main="Plot Data")

UJI ASUMSI REGRESI LINEAR SEDERHANA

Anggraini berta

2026-06-10

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