Input Data

dt<-c(525, 500, 550, 575,495,490, 525, 550, 13, 14, 13, 11, 15, 14, 12, 12)
data<-matrix(dt, nrow=8, ncol=2)
datadf= as.data.frame(data)
colnames(datadf) <- c("IHSG", "TSB")
datadf
##   IHSG TSB
## 1  525  13
## 2  500  14
## 3  550  13
## 4  575  11
## 5  495  15
## 6  490  14
## 7  525  12
## 8  550  12

Menghitung vektor rataan dan matriks covarians

xbar = apply(datadf[,1:2], 2, mean)
xbar
##   IHSG    TSB 
## 526.25  13.00
cov_m = cov(datadf[,1:2])
cov_m
##          IHSG        TSB
## IHSG 926.7857 -35.000000
## TSB  -35.0000   1.714286

Menggambar Elips Kepercayaan

library(ellipse)
## Warning: package 'ellipse' was built under R version 4.3.3
## 
## Attaching package: 'ellipse'
## The following object is masked from 'package:graphics':
## 
##     pairs
n = 8 # Jumlah Amatan
p = 2 # Jumlah Peubah
plot(ellipse(cov_m,centre=xbar,level = 0.95, t=sqrt(((n-1)*p/(n*(n-p)))*qf(0.95,p,n-p))),type="l",main = "Ellips Kepercayaan 95%")
points(xbar[1],xbar[2])

Selang Kepercayaan Simultan

T.ci = function(mu, Sigma, n, avec=rep(1,length(mu)), level=0.95){
p = length(mu)
cval = qf(level, p, n-p) * p * (n-1) / (n-p)
zhat = crossprod(avec, mu)
zvar = crossprod(avec, Sigma %*% avec) / n
const = sqrt(cval * zvar)
c(lower = zhat - const, upper = zhat + const)
}

n = 8 # Jumlah Amatan

#IHSG
T.ci(mu=xbar, Sigma=cov_m, n=n, avec=c(1,0),level=0.95)
##    lower    upper 
## 488.9635 563.5365
#Tingkat Suku Bunga
T.ci(mu=xbar, Sigma=cov_m, n=n, avec=c(0,1),level=0.95)
##    lower    upper 
## 11.39637 14.60363

Dari hasil diatas dapat dilihat bahwa batas bawah IHSG berada di angka 488,9635 dan batas atas IHSG 563.5365, sedangkan batas bawah TSB 11,08957 dan batas atas TSB 14,66043