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R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> pdf("rpd15_1r.pdf")
> 
> grimes <- matrix(c(
+    1,      0.45,    0.34170,  
+    2,      0.45,   -0.00438,  
+    3,      0.45,    0.82531,  
+    4,      1.30,    1.77967,  
+    5,      1.30,    0.95384,  
+    6,     1.30,    0.64080,  
+    7,      2.40,    1.75136,  
+    8,      2.40,    1.27497,  
+    9,      2.40,    1.17332,  
+   10,      4.00,    3.12273,  
+   11,      4.00,   2.60958,  
+   12,      4.00,    2.57429,  
+   13,      6.10,    3.17881,  
+   14,      6.10,    3.00782,  
+   15,      6.10,    2.67061, 
+   16,      8.05,    3.05959, 
+   17,      8.05,    3.94321, 
+   18,      8.05,    3.43726, 
+   19,     11.15,    4.80735, 
+   20,     11.15,    3.35583, 
+   21,     11.15,    2.78309, 
+   22,     13.15,    5.13825, 
+   23,     13.15,    4.70274, 
+   24,     13.15,    4.25702, 
+   25,     15.00,    3.60404, 
+   26,     15.00,    4.15029,
+   27,     15.00,   3.42484),byrow=T,ncol=3)
> 
> t <- as.matrix(grimes[,2])
> y <- as.matrix(grimes[,3])
> 
> 
> 
> ca.nlreg <- nls(y ~ a*(1-exp(-(t/d)^g)),start=c(a=5,d=2,g=1))
> 
> summary(ca.nlreg)

Formula: y ~ a * (1 - exp(-(t/d)^g))

Parameters:
  Estimate Std. Error t value Pr(>|t|)    
a   4.2835     0.4747   9.024 3.51e-09 ***
d   4.7326     1.2712   3.723  0.00106 ** 
g   1.0156     0.2272   4.469  0.00016 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.5576 on 24 degrees of freedom

Number of iterations to convergence: 6 
Achieved convergence tolerance: 9.706e-07 

> theta <- as.matrix(coef(ca.nlreg))
> vtheta <- vcov(ca.nlreg)
> setheta <- sqrt(diag(vtheta))
> setheta <- diag(setheta)
> 
> corrtheta <- solve(setheta) %*% vtheta %*% solve(setheta)
> corrtheta
           [,1]       [,2]       [,3]
[1,]  1.0000000  0.9329968 -0.7775717
[2,]  0.9329968  1.0000000 -0.7167829
[3,] -0.7775717 -0.7167829  1.0000000
> 
> vec <- seq(0,15,0.1)
> 
> plot(t,y,xlim=c(0,15),ylim=c(0,6))
> lines(vec,theta[1]*(1-exp(-(vec/theta[2])^theta[3])))
> 
> 
> # Proportional Response estimates
> 
> n <- nrow(y)
> p <- nrow(theta)
> 
> ht <- matrix(c(1,5,15),ncol=1)
> 
> httheta <- 1-exp(-(ht/theta[2])^theta[3])
> 
> 
> dhb1 <- 0*ht
> dhb2 <- -(theta[3]/theta[2])*((ht/theta[2])^theta[3])*exp(-(ht/theta[2])^theta[3])
> dhb3 <- (log(ht/theta[2]))*((ht/theta[2])^theta[3])*exp(-(ht/theta[2])^theta[3])
> 
> dhb <- cbind(dhb1,dhb2,dhb3)
> 
> 
> 
> s2h <- dhb %*% vtheta %*% t(dhb)
> 
> seh <- sqrt(diag(s2h))
> 
> seh <- as.matrix(seh)
> 
> 
> 
> ciht <- qt(.975,n-p)*seh
> 
> 
> 
> htthetalo <- httheta - ciht
> htthetahi <- httheta + ciht
> 
> print(cbind(ht,httheta,htthetalo,htthetahi))
     [,1]      [,2]      [,3]      [,4]
[1,]    1 0.1863579 0.1007847 0.2719310
[2,]    5 0.6526456 0.4389562 0.8663351
[3,]   15 0.9603278 0.8293647 1.0912908
> 
> dev.off() 
null device 
          1 
> 
>