load(file='../../BookCode/nlrwr/data/ScotsPine.rda')

# Plot the data to get an idea of what it looks like:
#
plot(ScotsPine$age, ScotsPine$lai, xlab='age', ylab='lai')
grid()

# Guess at some initial values:
#
a0 = min(ScotsPine$lai)* 0.95
y = log(ScotsPine$lai - a0)
x = ScotsPine$age
lm_fit = lm(y ~ x)
cs = as.double(coefficients(lm_fit))
b0 = exp(cs[1])
c0 = -1/cs[2]
print(c( b0, c0 ))

fit = nls(lai ~ a + b * exp(-age/c), data=ScotsPine, start=c(a=a0, b=b0, c=c0), trace=FALSE)

# Plot the curve and the fit:
#
ageVals = with(ScotsPine, seq(min(age), max(age), length.out=100))
lai_predicted = predict(fit, newdata=data.frame(age=ageVals))
plot(ScotsPine$age, ScotsPine$lai, xlab='age', ylab='lai')
lines(ageVals, lai_predicted, col='blue')
grid()

print(summary(fit))
#print(confint(fit)) # this does not seem to converge