##### Code for running a nonlinear model and comparing to 
#a linear model using the marginal Sum of Squares test 
#(This is a true lack of fit test)




#### Note this code assumes you have already imported data and created
# a regression object and an ANOVA object

###Importing data
#datum=read.csv(file.choose())
#head(datum)
### Run a regression - treat Protein as continuous
#results2=lm(Mass~Protein) #Protein is continuous 
#summary(results)


###Run a nonlinear model

results3=lm(Mass~Protein+I(Protein^2),data=datum)
summary(results3)

#The 'I' function tells R to do whatever the math is
# inside the parantheses


### Conduct the f-drop test


anova(results3,result2) 

### the two models you want to compare are included as arguments 
### order doesn't usually matter, but it's best to put the more complicated
### model first for those few cases where it does
### 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



######## Not run as part of class

### Run a cubic or higher order polynomial

# results4=lm(Mass~Protein+I(Protein^2)+I(Protein^3),data=datum)
# summary(results4)
# anova(results4,results3)

### Alternative parameterization that uses polynomial contrasts
### eliminates collinearity among terms

# results5=lm(Mass~poly(Protein,5),data=datum)
# summary(results5)
# anova(results5,results4)