# linear discriminant analysi

d<-read.table("ExamA.dat")
a<-rbind(d[1:200,],d[1001:1200,])
names(a)<-c("x1","x2","y")

x1.max <- max(a$x1)
x1.min <- min(a$x1)
x2.max <- max(a$x2)
x2.min <- min(a$x2)

x1.lim = c(x1.min,x1.max)
x2.lim = c(x2.min,x2.max)

x<-seq(x1.min, x1.max, 0.5)
y<-seq(x2.min, x2.max, 0.5)

Xcon <- data.frame(rep(x,length(y)), rep(y, each=length(x)))
names(Xcon) <- c("x1","x2")



plot(a$x1,a$x2, xlim=x1.lim, ylim=x2.lim, col=a$y+1)

g <- lda( y ~ x1 + x2 , data = a)
Z <- predict(g, Xcon)
zp <- Z$post[,1] - Z$post[,2]
contour(x,y,matrix(zp,length(x),length(y)), add=T, levels=0, labex = 0)
title("LDA compared to Logistic Regression")


g.g <- glm( y ~ x1 + x2, data = a, family=binomial(logit))
Z.g <- predict(g.g, Xcon)
contour(x,y,matrix(Z.g,length(x),length(y)), add=T, lty=2, levels=0.5, labex = 0)