#Lecture 4 - testing the position of Johnson et al. 2006

### Import the data

datum=read.csv(file.choose())

head(datum) #Make sure that it is imported correctly

### run the model - know what the model is, so I'll just run the 
### correct model
results=glm(Presence~Medium+High+Elevation,data=datum,family=binomial)
summary(results)

### use coefficients from results to generate a predicted
### probability of use (will be proportional to true probability of use)
testing=exp(0.2771073-1.5640112*datum$Medium-1.3587885*datum$High
	-0.0046661*datum$Elevation)

head(testing) ### make sure it worked

plot(testing,datum$Proportion) #Plot relationship between estimated
### probability of use and true probability of use

### Run regression between true probability of use and estimated
### probability of use
results=lm(datum$Proportion~testing)
summary(results)
### estimate of slope is "proportionality constant" that converts
### estimated probability of use to true probability of use
### Note that you will never be able to calculate what this
### proportionality constant is
### this exercise just demonstrates that the estimated probability 
### of use is indeed proportional to the true probability of use.