##### General Code for calculating predictions and prediction intervals in R


### import the data


datum=read.csv(file.choose()) #imports data
head(datum) #displays the column headings of data plus first 6 rows


### Run analysis - Cannot make predictions until model has been run


results=lm(Y~X,data=datum) #runs a linear model between 'Y' and 'X' from 'datum', call results 'results
# 'Y' is the response in your excel file. BE SURE TO CHANGE THE NAME
# 'X' is the x-variable in your excel file. BE SURE TO CHANGE THE NAME
# in example, I used results=lm(Biomass~Rainfall,data=datum)
summary(results) # gives output.


##### Generating Predictions


### Generate a new data frame of X-values that you want predictions for


# in this case, I'm just getting predictions across the x-range
summary(datum) ###get min and max values for X
help(seq) ### help file for seq function - useful for creating sequences of values
x=seq(from=min,to=max,by=interval) 
# where 'min' is minimum value of X, 
#'max' is maximum value of x
# 'interval' is the distance between individual x values
# be sure to input values for min, max, and interval
# in example, I used x=seq(from=0,to=10,by=0.1)
NewX=data.frame(X=x) ### where 'X' is the x-variable from your excel file. BE SURE TO CHANGE THE NAME
###Example: NewX = data.frame(Biomass=x) where 'x' is the sequence of values
head(NewX) ###make sure it made the new data.frame
predictions=predict(results,NewX,interval="prediction") ### generates a vector of y predictions and prediction intervals
predictions=as.data.frame(predictions) ###convert 'predictions' to a data.frame
predictions$X=NewX$X ###Add column of X values to predictions 


### plot predictions for easy viewing




plot(Y~X,data=datum) ### plot original X and Y data - replace X and Y as appriopriate
lines(fit~X,data=predictions) ### plots best fit line as a line
lines(lwr~X,data=predictions) ### plots lower prediction interval
lines(upr~X,data=predictions) ### plots upper prediction interval