"wt.adair"<-
function(y, p, K1, K2, K3, K4)
{
# weight oxygen saturation data, y = f(p), uniformly for 
# hill function, log(y/(1-y))
# 
# var(log(y/(1-y))) = (d/dy (log(y/(1-y)))^2 * var(y)
#                   = (1/(y(1-y)))^2 * var(y)
#
# by assumption
#
# var(log(y/(1-y))) = constant = 1
#
# therefore the residuals^2 should be weighted by
#
# wt^2 = 1/var(y) 
#      = (1/(y(1-y)))^2 
#
	wt <- 1/(y * (1 - y))
	resp <- (K1 * p + 3 * K1 * K2 * p^2 + 3 * K1 * K2 * K3 * p^3 + K1 * K2 * 
		K3 * K4 * p^4)/(1 + 4 * K1 * p + 6 * K1 * K2 * p^2 + 4 * K1 * 
		K2 * K3 * p^3 + K1 * K2 * K3 * K4 * p^4)
	(y - resp) * wt
}
"wt.mwc"<-
function(y, p, L, Kt, Kr)
{
# weight oxygen saturation data, y = f(p), uniformly for
# hill function, log(y/(1-y))
#
# var(log(y/(1-y))) = (d/dy (log(y/(1-y)))^2 * var(y)
#                   = (1/(y(1-y)))^2 * var(y)
#
# by assumption
#
# var(log(y/(1-y))) = constant = 1
#
# therefore the residuals^2 should be weighted by
#
# wt^2 = 1/var(y)
#      = (1/(y(1-y)))^2
#
	wt <- 1/(y * (1 - y))
	pred <- (L/Kt * p * (1 + p/Kt)^3 + p/Kr * (1 + p/Kr)^3)/(L * (1 + p/Kt)^
		4 + (1 + p/Kr)^4)
	(y - pred) * wt
}