##### Code for F-Drop tests


###Importing data
datum=read.csv(file.choose())
head(datum)


### Plotting the data


plot(Biomass~Cows,data=datum) # In this case, R saws numbers in the 'Cows' column and treated the variable as continuous
plot(Biomass~as.factor(Cows),data=datum) # use the as.factor function to get R to treat 'Cows' as a categorical variable


### Run a regression - treat Cows as continuous


results=lm(Biomass~Cows,data=datum) #Cows is continuous because R saw numbers for that variable
summary(results)
plot(residuals(results)~datum$Cows)


### Run an ANOVA - treat Cows as categorical


results2=lm(Biomass~as.factor(Cows),data=datum) #use the as.factor function to get R to treat 'Cows' as continuous
summary(results)


### Conduct the f-drop test


anova(results,results3) #the two models you want to compare are included as arguments
# Usually, you should list the more complicated model first, but in this case it doesn't matter
# Note that the two models can't have the same number of parameters
# A significant p-value means the more complex model is a significant improvement in fit
# A non-significant p-value means the simpler model is adequate
# Note that RSS (which is the same thing as SSE) is always lower in the more complex model


### BONUS: How to fit a quadratic curve to data when x is continuous

results3=lm(Bioamss~Cows+I(Cows^2),data=datum)
anova(results3,results)