#POLYNOMIAL REGRESSION
# READ STRUCTURED DATA TABLE
K=read.table("c:/2008LinearModelsData/PowerCellsR.txt")
K
attach(K)
options(digits=10)

#SCALE AND SQUARE/MULTIPLY X DATA ONLY 
x1=scale(X1,center=T,scale=0.4)
x2=scale(X2,center=T,scale=10)
x1s=x1^2
x2s=x2^2
x1x2=x1*x2

#REFORMAT AS DATAFRAME
Kscaled=data.frame(Y,x1,x2,x1s,x2s,x1x2)
Kscaled
detach(K)
attach(Kscaled)

#FITTING FULL LINEAR MODEL
FM=lm(Y~x1+x2+x1s+x2s+x1x2)
summary(FM)

#PARTIAL F TEST FOR HIGHER ORDER VARIABLES
anova(FM)
529+284.928+1645.967
F=((529+284.928+1645.967)/3)/1048.088
F
qf(0.95,3,5)

#GLM TEST FOR HIGHER ORDER VARIABLES
FM=lm(Y~x1+x2+x1s+x2s+x1x2)
RM=lm(Y~x1+x2)
anova(RM,FM)

#++++++++++++++++++++++++++++++++++++++++++++++

#INTERACTIONS REGRESSION
# READ A STRUCTURED DATA TABLE
K=read.table("c:/2008LinearModelsData/BodyFatR.txt")
K
attach(K)

#CENTERING X VALUES
X=cbind(X1,X2,X3)
Xc=data.frame(scale(X,center=T,scale=FALSE))
Xc
attach(Xc)

#MAKING INTERACTION VARIABLES
X1X2=X1*X2
X1X3=X1*X3
X2X3=X2*X3

#FIT OF THE FULL LINEAR MODEL AND REPORT
FM=lm(Y~X1+X2+X3+X1X2+X1X3+X2X3)
summary(FM)

#PARTIAL F TEST FOR HIGHER ORDER VARIABLES
anova(FM)
F=((6.51484+2.70433+1.49572)/3)/6.74538
F
qf(0.95,3,13)

#GLM TEST FOR HIGHER ORDER VARIABLES
FM=lm(Y~X1+X2+X3+X1X2+X1X3+X2X3)
RM=lm(Y~X1+X2+X3)
anova(RM,FM)

#+++++++++++++++++++++++++++++++++++++++
#USING FORMULA OPTIONS IN R:
options(digits=7)

#FULLY CROSSED MODEL WITH ALL HIGHER-ORDER VARIABLES
FM=lm(Y~X1*X2*X3)
summary(FM)
anova(FM)

#SPECIFYING HIGHER-ORDER VARIABLES
FM=lm(Y~X1+X2+X3+X1:X2+X1:X3+X2:X3)
summary(FM)
anova(FM)