> ### Fit the transformed linear model for starting values:
> ### Y = g0*exp(g1*X)  =>  Y' = ln(Y) =ln(g0) + (g1*X)  =g0' + (g1'*X')
> ### where  g0 = exp(g0')  g1=g1' X=X'
> 
> si.mod0 <- lm(log(prognosis) ~ days)          # R uses  log(*)  for  ln(*)
> 
> (g0.lm <- exp(si.mod0$coef[1]))
(Intercept) 
   56.66512 
> (g1.lm <- si.mod0$coef[2])
       days 
-0.03797418 
> 
> g0.lm <- g0.lm[[1]]         # [[1]] takes coefficent, not label (Intercept)
> g1.lm <- g1.lm[[1]]         # [[1]] takes coefficient, not label (days)
> 
> ### Use regression coefficients (transformed back) as inputs to NLS
> 
> si.mod1 <- nls(prognosis ~ g0 * exp(g1*days), start=c(g0=g0.lm, g1=g1.lm))
> 
> summary(si.mod1)

Formula: prognosis ~ g0 * exp(g1 * days)

Parameters:
    Estimate Std. Error t value Pr(>|t|)    
g0 58.606531   1.472159   39.81 5.70e-15 ***
g1 -0.039586   0.001711  -23.13 6.01e-12 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 1.951 on 13 degrees of freedom

Number of iterations to convergence: 3 
Achieved convergence tolerance: 8.973e-06 

> vcov(si.mod1)
             g0            g1
g0  2.167253342 -1.781512e-03
g1 -0.001781512  2.928520e-06
> 
> plot(days,prognosis,xlab="days",ylab="prognosis")
> 
> days1 <- 0:70
> 
> lines(days1,predict(si.mod1,list(days=days1)))
>