# January 27, 2009


#	try some linear regression examples

eg.0910 <- function() {
    set.seed(478); x = c(rnorm(50,.2,.06),rnorm(50,.5,.06),rnorm(50,.8,.06))
    y1=rep(1,50); y0=rep(0,50); X = cbind(rep(1,150),x)
    Y = cbind(c(y1,y0,y0),c(y0,y1,y0),c(y0,y0,y1))
    Yh = X %*% solve(t(X)%*%X) %*% t(X) %*% Y

    plot(X[,2],Y %*% c(1,2,3),main="K=3 groups",xlim=range(X[,1],0,1))
		 browser()

    plot(X[,2],Yh[,1],pch=16,main="linear scores",xlim=range(X[,1],0,1)); rug(X[,2])
    points(X[,2],Yh[,2],pch=16,col=5);  points(X[,2],Yh[,3],pch=16,col=6);
       abline(h=c(0,1),lty=2)
		 browser()

    X = cbind(X,X[,2]^2)
    Yh = X %*% solve(t(X)%*%X) %*% t(X) %*% Y
    plot(X[,2],Yh[,1],pch=16,main="linear scores w/ quadratic",xlim=range(X[,1],0,1),
	ylim=range(Yh)); rug(X[,2]); abline(h=c(0,1),lty=2)
    points(X[,2],Yh[,2],pch=16,col=5); points(X[,2],Yh[,3],pch=16,col=6)
		 browser()

    X = cbind(X,X[,2]^3)
    Yh = X %*% solve(t(X)%*%X) %*% t(X) %*% Y
    plot(X[,2],Yh[,1],pch=16,main="linear scores w/cubic",xlim=range(X[,1],0,1),
	ylim=range(Yh)); rug(X[,2]); abline(h=c(0,1),lty=2)
    points(X[,2],Yh[,2],pch=16,col=5); points(X[,2],Yh[,3],pch=16,col=6)
		 browser()

    X = cbind(X,X[,2]^4)
    Yh = X %*% solve(t(X)%*%X) %*% t(X) %*% Y
    plot(X[,2],Yh[,1],pch=16,main="linear scores w/quartic",xlim=range(X[,1],0,1),
	ylim=range(Yh)); rug(X[,2]); abline(h=c(0,1),lty=2)
    points(X[,2],Yh[,2],pch=16,col=5); points(X[,2],Yh[,3],pch=16,col=6)

}



eg.0910()