# nllsqt2.r                         October 2007, 2008
 #
 # test problem for nonlinear least squares
 # from Gallant (1975)
 #
  all <- matrix(scan("gallant.dat"),30,5, byrow=TRUE)
 #
 # make a data frame
  gallant <- data.frame( y=all[,2], x1=all[,3], x2=all[,4], x3=all[,5] )
  print(gallant)                    # see data frame
 #
 #               another way is to define residual function
   res <- function(th1,th2,th3,th4,y,x1,x2,x3,x4) {
      res <- y - th1*x1 - th2*x2 - th4*exp(th3*x3) } 
 #
 #               nonlinear least squares
  that1 <- nls(  ~res(th1,th2,th3,th4,y,x1,x2,x3) , data=gallant,
         start=list( th1=-.05, th2=1.04, th3=-1.2, th4=-.53), trace=TRUE )
 #               results
  that1
 #
  thfin <- coef(that1)
  print("coefficients")
  print(thfin)
 #              summary
  summary(that1)
 #
 #               done
  rm(list=ls())
  q()