Kuis TPG Nomor 2

Input Data

x<-c(525,500,550,575,495,490,525,550,13,14,13,11,15,14,12,12)
data<-matrix(x,, ncol=2)
data

##      [,1] [,2]
## [1,]  525   13
## [2,]  500   14
## [3,]  550   13
## [4,]  575   11
## [5,]  495   15
## [6,]  490   14
## [7,]  525   12
## [8,]  550   12

Rata-rata kolom

xbar <- colMeans(data)
xbar

## [1] 526.25  13.00

Matrix kovarian

cov <- cov(data)
cov

##          [,1]       [,2]
## [1,] 926.7857 -35.000000
## [2,] -35.0000   1.714286

Selang kepercyaan 95% 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

#Selang untuk X1
T.ci(mu=xbar, Sigma=cov, n=n, avec=c(1,0),level=0.95)

##    lower    upper 
## 488.9635 563.5365

#Selang untuk X2
T.ci(mu=xbar, Sigma=cov, n=n, avec=c(0,1),level=0.95)

##    lower    upper 
## 11.39637 14.60363

Selang kepercayaan 95% elips

library(ellipse)

## 
## Attaching package: 'ellipse'

## The following object is masked from 'package:graphics':
## 
##     pairs

n = 8 # Jumlah Amatan
p = 2 # Jumlah Peubah
plot(ellipse(cov,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])

#mencari x1=520 dan x2=13
points(520,13,col = "red")