#
# Epage 143
#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

# version$language == "R" for R version$language == NULL for SPlus

if(is.null(version$language) == FALSE) require(alr3) else library(alr3)

if(is.null(version$language) == FALSE) data(turk0)
attach(turk0)

# do a quadratic OLS regression on yBar:
#
m2 <- lm( Gain ~ A + I(A^2) ) 

# we can use the ALR3 package "delta.method" (but we need to specify the parameter names correctly):
delta.method(m2,"-b1/(2*b2)")

# lets do the same problem via the bootstrap (first generate coefficients):
#
bCoefficients <- boot.case( m2, B=2000 )

# next compute the maximum:
maxs <- -bCoefficients[,2]/(2*bCoefficients[,3])

print(mean(maxs))
print(sqrt(var(maxs)))