attach(spruce)

south.slope <- -.1326
north.slope <- .45
south.int <- -.2381
north.int <- -4.48

## elevation has been divided by 100
## I think these parameter estimates might be right, but you should check

elevation.values_seq(from=6,to=18,by=.1) # these are where we evaluate the function

logit.back.transform <- function(X) exp(X)/(1+exp(X))

south.fit.logscale <- south.int+south.slope*elevation.values
north.fit.logscale <- north.int+north.slope*elevation.values
  
south.fit <- logit.back.transform(south.fit.logscale)
north.fit <- logit.back.transform(north.fit.logscale)

plot(elevation,percent,ylim=c(0,1)) ## this can also be a coded scatterplot of data values

lines(elevation.values,north.fit,lty=1)
lines(elevation.values,south.fit,lty=2)

## don't worry about the warning messages this produces