#### Stochastik IV, Übungsblatt 7

### Aufgabe 3

library(ellipse)

# Einlesen und Auswahl der Daten und Einbinden in Suchpfad

data.crabs <- 
read.table("D:/Univ Augsburg/Lehre/SS07/VO_MultiVar/Datensaetze/crabs.txt",
head = TRUE, sep = "\t", quote = "")

crabs.bl <- subset(data.crabs, sp == 1)

attach(crabs.bl)

# Scatterplot

plot(FL, RW, main = "Scatterplot mit 95%-Konfidenzellipsen", 
     xlim = c(6, 23), ylim = c(6, 19),
     pch = sex, col = sex, cex = 1.5)

## Teilaufgabe (a)

lines(ellipse(cov(cbind(FL[sex == 1], RW[sex == 1])), 
              centre = c(mean(FL[sex == 1]), mean(RW[sex == 1])), 
              level = 0.95), 
      col = 1, lwd = 2)

lines(ellipse(cov(cbind(FL[sex == 2], RW[sex == 2])), 
              centre = c(mean(FL[sex == 2]), mean(RW[sex == 2])), 
              level = 0.95), 
      col = 2, lwd = 2)

## Teilaufgabe (b)

cov.pooled <- (( cov(cbind(FL[sex == 1], RW[sex == 1])) + 
                 cov(cbind(FL[sex == 2], RW[sex == 2])) ) / 2)

lines(ellipse(cov.pooled, 
              centre = c(mean(FL[sex == 1]), mean(RW[sex == 1])), 
              level = 0.95), 
      col = 1, lty = 2, lwd = 2)

lines(ellipse(cov.pooled, 
              centre = c(mean(FL[sex == 2]), mean(RW[sex == 2])), 
              level = 0.95),
      col = 2, lty = 2, lwd = 2)

## Teilaufgabe (c)

lines(ellipse(cov(cbind(FL, RW)), 
              centre = c(mean(FL), mean(RW)), 
              level = 0.95), 
      col = 3, lwd = 2)

# Legende

legend( 14, 9, lty = c(1, 1, 2, 2, 1), col = c(1, 2, 1, 2, 3), 
        c("Teilaufgabe (a): Blue Male", "Teilaufgabe (a): Blue Female",
          "Teilaufgabe (b): Blue Male", "Teilaufgabe (b): Blue Female",
          "Teilaufgabe (c): Blue Male AND Female") )