Latihan MSC 1

Data Soal 1

beratBadan <- c(49,65,60,50,45,75,53,64,54,71)
tinggiBadan <- c(150,161,155,150,160,170,155,154,145,165)
soalmsc1 <- data.frame(beratBadan, tinggiBadan)
head(soalmsc1)

Persamaan Regresi Linier Sederhana Metode MKT manual

soalmsc1$xdif <- soalmsc1$beratBadan-mean(soalmsc1$beratBadan)
soalmsc1$ydif <- soalmsc1$tinggiBadan-mean(soalmsc1$tinggiBadan)
soalmsc1$crp <- soalmsc1$xdif * soalmsc1$ydif
soalmsc1$xsq <- soalmsc1$xdif^2
b1 <- sum(soalmsc1$crp)/sum(soalmsc1$xsq)
b1

## [1] 0.5253785

b0 <- mean(soalmsc1$tinggiBadan)-b1*mean(soalmsc1$beratBadan)
b0

## [1] 125.7128

Persamaan Regresi Linier Sederhana dengan R function

lmsoal1 <- lm(tinggiBadan ~ beratBadan, data = soalmsc1)
summary(lmsoal1)

## 
## Call:
## lm(formula = tinggiBadan ~ beratBadan, data = soalmsc1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.0833 -2.1721 -0.1594  1.8495 10.6451 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 125.7128    11.4312  10.997 4.16e-06 ***
## beratBadan    0.5254     0.1926   2.728   0.0259 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.772 on 8 degrees of freedom
## Multiple R-squared:  0.482,  Adjusted R-squared:  0.4172 
## F-statistic: 7.443 on 1 and 8 DF,  p-value: 0.02592

Berdasarkan perhitungan diatas, didapat perhitungan keduanya sama dan menghasilkan persamaan regresinya yaitu : 125.7128 + 0.5253785x

Data Soal 2

head(soalmsc1)

Koefisien Determinasi

JKG <- sum((soalmsc1$tinggiBadan-lmsoal1$fitted.values)^2)
JKG

## [1] 266.5214

JKR <- sum((lmsoal1$fitted.values-mean(soalmsc1$tinggiBadan))^2)
JKR

## [1] 247.9786

JKT <- sum((soalmsc1$tinggiBadan-mean(soalmsc1$tinggiBadan))^2)
JKT

## [1] 514.5

r_sqr <- (JKT-JKG)/JKT
r_sqr

## [1] 0.4819798

Koefisien Korelasi Metode manual

x1_x1bar <- soalmsc1$beratBadan-mean(soalmsc1$beratBadan)
x2_x2bar <- soalmsc1$tinggiBadan-mean(soalmsc1$tinggiBadan)
A <- sum(x1_x1bar*x2_x2bar)
varx1 <- sum((x1_x1bar)^2)
varx2 <- sum((x2_x2bar)^2)
B <- sqrt(varx1*varx2)
corr <- A/B
corr

## [1] 0.6942477

Koefisien Korelasi menggunakan R

cor(soalmsc1$beratBadan,soalmsc1$tinggiBadan)

## [1] 0.6942477

Berdasarkan perhitungan diatas, didapat perhitungan keduanya sama dan menghasilkan koefisien korelasinya yaitu 0.6942477

Data Soal 3

skorTes <- c(75,60,65,75,65,80,75,80,65,80)
nilaiUjian <- c(85,75,75,90,80,92,82,95,80,90)
soalmsc2 <- data.frame(skorTes,nilaiUjian)
head(soalmsc2)

Uji Ketidakpasan

lmsoal2 <- lm(nilaiUjian ~ skorTes, data = soalmsc2)
summary(lmsoal2)

## 
## Call:
## lm(formula = nilaiUjian ~ skorTes, data = soalmsc2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.0000 -1.8333  0.8333  1.6667  3.6667 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  22.0000     9.5670   2.300 0.050504 .  
## skorTes       0.8667     0.1322   6.554 0.000178 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.986 on 8 degrees of freedom
## Multiple R-squared:  0.843,  Adjusted R-squared:  0.8234 
## F-statistic: 42.96 on 1 and 8 DF,  p-value: 0.0001776

library(alr3)

## Loading required package: car

## Loading required package: carData

pureErrorAnova(lmsoal2)

qf(0.95, df1 = 2, df2 = 6)

## [1] 5.143253

Karena Fhit < Ftabel maka H0 diterima yang artinya tidak ada ketidakpasan atau bisa dikatakan model regresi sederhana cocok digunakan.

Soal 4: 6 Asumsi

Asumsi 1: Rata - rata galat diasumsikan bernilai nol

plot(soalmsc2$skorTes,lmsoal2$residuals, xlab = "Skor Tes (X)", ylab = "Residuals", main = "Plot Uji Asumsi Rata - rata Galat bernilai nol")

Asumsi 2: Galat Saling Bebas

c <- (1:10)
soalmsc2 <- cbind(soalmsc2,c)
head(soalmsc2)

plot(soalmsc2$c, lmsoal2$Residuals,xlab= "Amatan",ylab="Residuals",type="l",main="Plot Uji Asumsi Galat Saling Bebas")

plot(soalmsc2$c, lmsoal2$Residuals,xlab= "Amatan",ylab="Residuals",main="Plot Uji Asumsi Galat Saling Bebas")

Asumsi 3: Galat berdistribusi normal

c <- (1:10)
ytopi <- lmsoal2$fitted.values
ei <- lmsoal2$residuals
eiterurut <- sort(lmsoal2$residuals)

hi <- sqrt(8.92)*qnorm((c-0.375)/(10+0.25))
Hi <- cbind(soalmsc2,ytopi,ei,eiterurut,hi)
head(Hi)

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

Asumsi 4: Ragam Galat diasumsikan Konstan

ytopi<-lmsoal2$fitted.values
ei<-lmsoal2$residuals
plot(ytopi,ei,
xlab="fitted values",ylab="residuals",
main="Plot Uji Ragam Galat Konstan")

Asumsi 5: X dan Y berhubungan linier

plot(soalmsc2$skorTes,soalmsc2$nilaiUjian,main="Plot Data")

Asumsi 6: Tidak ada outlier

plot(soalmsc2$skorTes,soalmsc2$nilaiUjian,main="Plot Data")