Growth_curve_1.R

dat <- list(
  "N" = 27,  
  "x" =
    c(1, 1.5, 1.5, 1.5, 2.5, 4, 5, 5, 7, 8, 8.5, 9, 9.5, 9.5, 10, 
      12, 12, 13, 13, 14.5, 15.5, 15.5, 16.5, 17, 22.5, 29, 31.5),
  "Y" =
    c(1.8, 1.85, 1.87, 1.77, 2.02, 2.27, 2.15, 2.26, 2.47, 2.19, 
      2.26, 2.4, 2.39, 2.41, 2.5, 2.32, 2.32, 2.43, 2.47, 2.56, 2.65, 
      2.47, 2.64, 2.56, 2.7, 2.72, 2.57))

nlm <- nls(Y ~ alpha - beta * lambda^x, data=dat,
           start=list(alpha=1, beta=1, lambda=0.9))
summary(nlm)
## 
## Formula: Y ~ alpha - beta * lambda^x
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## alpha   2.65807    0.06151   43.21  < 2e-16 ***
## beta    0.96352    0.06968   13.83  6.3e-13 ***
## lambda  0.87146    0.02460   35.42  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09525 on 24 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.574e-06