###################################################
#                                                 #
#     Simulation: Curve Data (Chen&Li, 1998)      #
#     Author: Han-Ming Wu                         #
#     2007/05/23                                  #
###################################################
# model formula
# y=sign(beta1'X + sigma * epsilon1)*log(|beta2'X + alpha + sigma2*epsilon2|)
# x=(x1,...,x15) ~iid Normal(0, 1)
# epsilon1, epsilon2 ~iid Normal(0, 1)
# n=300, p=15

beta1 <- matrix(c(1,1,1,1,1,1,1,1,1,0,0,0,0,0,0), ncol=1)
beta2 <- matrix(c(0,0,0,0,0,0,0,0,0,1,1,1,1,1,1), ncol=1)
alpha <-5
p <-15
n <-300
epsilon1 <- matrix(c(rnorm(n)), ncol=1)
epsilon2 <- matrix(c(rnorm(n)), ncol=1)
x <- matrix(0, nrow=n, ncol=p)
for(i in 1:p){
   x[,i] <- rnorm(n)
}

sigma1 <-1
sigma2 <-1

y <- sign(x%*%beta1 + sigma1*epsilon1)*log(abs(x%*%beta2+alpha +sigma2*epsilon2))
mydataF <- data.frame(y, x)
write.table(mydataF, "Curves_300x15.txt", quote=FALSE, sep='\t')

mylm <- lm(y~., data=mydataF)
print(summary(mylm)$r.squared)