#LOAD PACKAGES
require(ISwR)
require(car)

#LOAD DATA FROM ISwR
data(cystfibr)
attach(cystfibr)
cystfibr

#FITTING FULL MODEL
FM=lm(pemax~age+sex+height+weight+bmp+fev1+rv+frc+tlc)
FM

#OVERALL F TEST & PARTIAL t/F TESTS
summary(FM)

#FITTING REDUCED MODEL - ONLY "age","sex","weight" ,"bmp"
RM=lm(pemax~age+sex+weight+bmp)
#GLM F TEST of RM vs FM
anova(RM,FM)

#FITTING REDUCED MODEL - EVERYTHING BUT "tlc"
RM=lm(pemax~age+sex+height+weight+bmp+fev1+frc)
#GLM F TEST of RM vs FM
anova(RM,FM)

#Anova{car} SET FOR TYPE II SS
#RETURNS REGRESSION SS DIFFERENCE FOR EACH VAR
#AND RESIDUAL SS WHEN ALL VARS ARE INCLUDED
#RESIDUAL SS SAME AS IN TYPE I
Anova(FM,type="2")

#anova{stats} = TYPE I SS
#RETURNS DIFFERENCE IN REGRESSION SS
#AT TIME OF ENTRY INTO THE MODEL IN ORDER FROM TOP TO BOTTOM
anova(FM)

#COMPARING RM & FM FOR PARTIAL F-TEST
RM=lm(pemax~age+sex+height+weight+bmp+fev1)
FM=lm(pemax~age+sex+height+weight+bmp+fev1+rv+frc+tlc)
anova(RM,FM)

#COMPARING RM & FM UPON ENTRY OF "fev1"
FM=lm(pemax~age+sex+height+weight+bmp+fev1)
RM=lm(pemax~age+sex+height+weight+bmp)
anova(RM,FM)

#EQUIVALENT anova{stats} APPROACH
#INVOLVING A LIMITED FM IGNORING LAST ENTERED VARIABLES
FM=lm(pemax~age+sex+height+weight+bmp+fev1)
anova(FM)

#RECOVERY OF TYPE II SS USING drop1{stats}
#RSS RETURNS RESIDUAL SS WHEN SPECIFIC VAR IS EXCLUDED
FM=lm(pemax~age+sex+height+weight+bmp+fev1+rv+frc+tlc)
drop1(FM)

#CREATING RM - EXCLUDING ONLY "rv"
RM=lm(pemax~age+sex+height+weight+bmp+fev1+frc+tlc)
anova(RM,FM)

#CREATING RM - WITH ONLY "age"
RM=lm(pemax~age)
#MARGINAL COMPARISION BY ADDING EACH VARIABLE IN TURN
add1(RM,~age+sex+height+weight+bmp+fev1+rv+frc+tlc)

#COMPARING SINGLE ADDITION OF "fev1"
FM=lm(pemax~age+fev1)
anova(RM,FM)

#SIMPLE REGRESSIONS WITH add1{stats}
#NOTE IN MODEL 1=include constant, -1=no constant
RM=lm(pemax~1)
add1(RM,~age+sex+height+weight+bmp+fev1+rv+frc+tlc)

#SIMPLE REGRESSION FOR WEIGHT ONLY
anova(lm(pemax~weight))