Some researchers tested whether arthritis in dogs could beimproved by supplementation with antioxidants and/or an aminosugarmixture (containing glucosamine and chondroitin). They gavecombinations of these supplements (each a factor with two levels:treatment and control) to equal numbers of test subjects in abalanced factorial design. They tested the effects of thesesupplements on levels of inflammation using a factorial ANOVA. TheANOVA table from their output is copied below.                                                                              

>model<-aov(inflammation~as.factor(antioxidant)*as.factor(aminosugar))

> anova(model)

	Df	SS	MS	F	P
antioxidant	1	385	385	17.5	0.0007
aminosugar	1	0.7	0.7	0.032	0.8581
antioxidant:aminosugar	1	1.3	1.3	0.059	0.7863
Residual	16	352	22

a) How many hypotheses did they test with this model?  

b) How many test subjects (i.e. replicates) did the researchershave?

c) Did the order in which antioxidant and aminosugar effectsentered this model affect their significance? Why?   

d) Name a measure of model fit that can be used to compare therelative fit of different models, while taking into account thenumber of parameters in each?

e) The researchers simplified their model by removing theinteraction term and the main effect of aminosugar. Fill in thetable below with the values of their new model.   

>model2<-aov(inflammation~as.factor(antioxidant))

> ANOVA(model)

	Df	SS	MS	F
antioxidant
Residual

f) Did the significance of antioxidant change by removing theother terms, and if so, did it become more or less significant?

g) By how much did the overall model R² change(explain whether it increased, decreased or no change, as well asthe amount)?    (show your working)