Multivariante - Holding

x1=matrix(c(2,12,4,10,3,8),byrow=T,nrow=3)
x2=matrix(c(5,7,3,9,4,5),byrow=T,nrow=3)
barx1=as.matrix(colMeans(x1))
barx2=as.matrix(colMeans(x2))
s1=2*cov(x1)
s2=2*cov(x2)
s.pooled=1/4 * (s1+s2)
hat.a=barx1-barx2

hat.y=t(hat.a)%*%solve(s.pooled)
hat.y
bar.y1=t(hat.a)%*%barx1
bar.y2=t(hat.a)%*%barx2

m=1/2*(bar.y1+bar.y2)

p=c(0,0,0)

clasifica=function(m){
  for (i in 1:dim(m)[1]){
    if(t(hat.a)%*%m[i,]>=22){
      p[i]=1
    } else{
      p[i]=2
    }
  }
  print(p)
}

clasifica(x1)
clasifica(x2)

#Primera observación de x1

obs1x1=as.matrix(x1[1,])
x1h1=x1[2:3,]
barx1h1=as.matrix(colMeans(x1h1))
s1h1=cov(x1h1)

s.hpooled1h1=1/3 * (s1h1+s2)
solve(s.hpooled1h1)

t(obs1x1-barx1h1)%*%solve(s.hpooled1h1)%*%(obs1x1-barx1h1)
t(obs1x1-barx2)%*%solve(s.hpooled1h1)%*%(obs1x1-barx2)

#Segunda observación de x1

obs1x2=as.matrix(x1[2,])
x1h2=x1[c(1,3),]
barx1h2=as.matrix(colMeans(x1h2))
s1h2=cov(x1h2)

s.hpooled1h2 = 1/3 * (s1h2+s2)
solve(s.hpooled1h2)

t(obs1x2-barx1h2)%*%solve(s.hpooled1h2)%*%(obs1x2-barx1h2)
t(obs1x2-barx2)%*%solve(s.hpooled1h2)%*%(obs1x2-barx2)

#Tercera observación de x1

obs1x3=as.matrix(x1[3,])
x1h3=x1[1:2,]
barx1h3=as.matrix(colMeans(x1h3))
s1h3=cov(x1h3)

s.hpooled1h3 = 1/3 * (s1h3+s2)
solve(s.hpooled1h3)

t(obs1x3-barx1h3)%*%solve(s.hpooled1h3)%*%(obs1x3-barx1h3)
t(obs1x3-barx2)%*%solve(s.hpooled1h3)%*%(obs1x3-barx2)

#Primera observación de x2

obs2x1=as.matrix(x2[1,])
x2h1=x2[2:3,]
barx2h1=as.matrix(colMeans(x2h1))
s2h1=cov(x2h1)

s.hpooled2h1 = 1/3 * (s1+s2h1)
solve(s.hpooled2h1)

t(obs2x1-barx1)%*%solve(s.hpooled2h1)%*%(obs2x1-barx1)
t(obs2x1-barx2h1)%*%solve(s.hpooled2h1)%*%(obs2x1-barx2h1)

#Segunda observación de x2

obs2x2=as.matrix(x2[2,])
x2h2=x2[c(1,3),]
barx2h2=as.matrix(colMeans(x2h2))
s2h2=cov(x2h2)

s.hpooled2h2 = 1/3 * (s1+s2h2)
solve(s.hpooled2h2)

t(obs2x2-barx1)%*%solve(s.hpooled2h2)%*%(obs2x2-barx1)
t(obs2x2-barx2h2)%*%solve(s.hpooled2h2)%*%(obs2x2-barx2h2)

#Tercera observación de x3

obs2x3=as.matrix(x2[3,])
x2h3=x2[1:2,]
barx2h3=as.matrix(colMeans(x2h3))
s2h3=cov(x2h3)

s.hpooled2h3 = 1/3 * (s1+s2h3)
solve(s.hpooled2h3)

t(obs2x3-barx1)%*%solve(s.hpooled2h3)%*%(obs2x3-barx1)
t(obs2x3-barx2h3)%*%solve(s.hpooled2h3)%*%(obs2x3-barx2h3)