library(ggplot2)
g <- function (x, a,b,c) a * (1-exp(-(x-c)/abs(b)))
X1 <- c(129.08,109.92,85.83,37.72)
Y1 <- c(0.7,0.5,0.39,-1.36)
dt1 <- data.frame(x1=X1,y1=Y1)
model1 <- nls(Y1 ~ g(X1, a, b, c),
          start = list(a=0.5, b=60, c=50),control=nls.control(maxiter = 200))

ggplot(data = dt1,aes(x = x1, y = y1)) +
     theme_bw() + geom_point() +
     geom_smooth(data=dt1, method="nls", formula=y~g(x, a, b, c),
       se=F, start=list(a=0.5, b=60, c=50))


f <- function (x, a, b, c) a*(x^2)+b*x+c
X2 <- c(589.62,457.92,370.16,295.98,243.99,199.07,159.91,142.63,
124.15, 101.98, 87.93, 83.16, 82.2, 74.48, 47.68, 37.51, 31,
27.9, 21.24,18.28)
Y2 <- c(0.22,0.37,0.49,0.65,0.81,0.83,1,0.81,0.65,0.44,0.55,0.63,
0.65,0.55,0.37,0.32,0.27,0.22,0.17,0.14)
dt2 <- data.frame(x2=X2,y2=Y2)
model2 <- nls(Y2 ~ f(X2, a, b, c),
           start = list(a=-1, b=3, c=0),control=nls.control(maxiter = 200))
ggplot(data = dt2,aes(x = x2, y = y2)) +
      theme_bw() + geom_point() +
      geom_smooth(data=dt2, method="nls", formula=y~f(x, a, b, c),
       se=F, start=list(a=-1, b=3, c=0))

library(nls2)
summary(as.lm(model))

as.lm.nls <- function(object, ...) {
    if (!inherits(object, "nls")) {
        w <- paste("expected object of class nls but got object of class:",
        paste(class(object), collapse = " "))
        warning(w)
    }

    gradient <- object$m$gradient()
    if (is.null(colnames(gradient))) {
        colnames(gradient) <- names(object$m$getPars())
    }

    response.name <- if (length(formula(object)) == 2) "0" else
        as.character(formula(object)[[2]])

    lhs <- object$m$lhs()
    L <- data.frame(lhs, gradient)
    names(L)[1] <- response.name

    fo <- sprintf("%s ~ %s - 1", response.name,
    paste(colnames(gradient), collapse = "+"))
    fo <- as.formula(fo, env = as.proto.list(L))

    do.call("lmst(fo, offset = substitute(fitted(object))))
}

predCI <- predict(as.lm.nls(fittednls), interval = “confidence”, level = 0.95)

predictNLS <- function(
object,
newdata,
level = 0.95,
nsim = 10000,
...
)
{
  require(MASS, quietly = TRUE)

  ## get right-hand side of formula
  RHS <- as.list(object$call$formula)[[3]]
  EXPR <- as.expression(RHS)

  ## all variables in model
  VARS <- all.vars(EXPR)

  ## coefficients
  COEF <- coef(object)

  ## extract predictor variable
  predNAME <- setdiff(VARS, names(COEF))

  ## take fitted values, if 'newdata' is missing
  if (missing(newdata)) {
    newdata <- eval(object$data)[predNAME]
    colnames(newdata) <- predNAME
  }

  ## check that 'newdata' has same name as predVAR
  if (names(newdata)[1] != predNAME) stop("newdata should have name '", predNAME, "'!")

  ## get parameter coefficients
  COEF <- coef(object)

  ## get variance-covariance matrix
  VCOV <- vcov(object)

  ## augment variance-covariance matrix for 'mvrnorm'
  ## by adding a column/row for 'error in x'
  NCOL <- ncol(VCOV)
  ADD1 <- c(rep(0, NCOL))
  ADD1 <- matrix(ADD1, ncol = 1)
  colnames(ADD1) <- predNAME
  VCOV <- cbind(VCOV, ADD1)
  ADD2 <- c(rep(0, NCOL + 1))
  ADD2 <- matrix(ADD2, nrow = 1)
  rownames(ADD2) <- predNAME
  VCOV <- rbind(VCOV, ADD2)

  ## iterate over all entries in 'newdata' as in usual 'predict.' functions
  NR <- nrow(newdata)
  respVEC <- numeric(NR)
  seVEC <- numeric(NR)
  varPLACE <- ncol(VCOV)

  ## define counter function
  counter <- function (i)
  {
    if (i%%10 == 0)
      cat(i)
    else cat(".")
    if (i%%50 == 0)
      cat("n")
    flush.console()
  }

  outMAT <- NULL

  for (i in 1:NR) {
    counter(i)

    ## get predictor values and optional errors
    predVAL <- newdata[i, 1]
    if (ncol(newdata) == 2) predERROR <- newdata[i, 2] else predERROR <- 0
    names(predVAL) <- predNAME
    names(predERROR) <- predNAME

    ## create mean vector for 'mvrnorm'
    MU <- c(COEF, predVAL)

    ## create variance-covariance matrix for 'mvrnorm'
    ## by putting error^2 in lower-right position of VCOV
    newVCOV <- VCOV
    newVCOV[varPLACE, varPLACE] <- predERROR^2

    ## create MC simulation matrix
    simMAT <- mvrnorm(n = nsim, mu = MU, Sigma = newVCOV, empirical = TRUE)

    ## evaluate expression on rows of simMAT
    EVAL <- try(eval(EXPR, envir = as.data.frame(simMAT)), silent = TRUE)
    if (inherits(EVAL, "try-error")) stop("There was an error evaluating the simulations!")

    ## collect statistics
    PRED <- data.frame(predVAL)
    colnames(PRED) <- predNAME
    FITTED <- predict(object, newdata = data.frame(PRED))
    MEAN.sim <- mean(EVAL, na.rm = TRUE)
    SD.sim <- sd(EVAL, na.rm = TRUE)
    MEDIAN.sim <- median(EVAL, na.rm = TRUE)
    MAD.sim <- mad(EVAL, na.rm = TRUE)
    QUANT <- quantile(EVAL, c((1 - level)/2, level + (1 - level)/2))
    RES <- c(FITTED, MEAN.sim, SD.sim, MEDIAN.sim, MAD.sim, QUANT[1], QUANT[2])
    outMAT <- rbind(outMAT, RES)
  }

  colnames(outMAT) <- c("fit", "mean", "sd", "median", "mad", names(QUANT[1]), names(QUANT[2]))
  rownames(outMAT) <- NULL

  cat("n")

  return(outMAT)
}