# For the general linear test approach 
#         by Yu-Ling Tseng on 20090430


ch6pr18 <- matrix(scan("ch06pr18.txt"),ncol=5, byrow=T) ;
# y <- ch6pr18[,1];
# x1 <- ch6pr18[,2];
# x2 <- ch6pr18[,3];
# x3 <- ch6pr18[,4];
# x4 <- ch6pr18[,5];
dum <- data.frame(ch6pr18)
names(dum) <- c("Rates","Age","OET","VR","TSF")
# dum <- data.frame("Rates"=y,"Age"=x1,"OET"=x2,"VR"=x3,"TSF"=x4)
attach(dum)
fm1234 <- lm(Rates~Age+OET+VR+TSF, dum)
SSE1234<-sum((Rates-fitted(fm1234))^2)
SSE1234
anova(fm1234)

# Ex 1
fm12 <- lm(Rates~Age+OET, dum)   # reduced model has only two predictors X1, X2
SSE12<-sum((Rates-fitted(fm12))^2)
SSE12
anova(fm12)
F34 <- ((SSE12-SSE1234)/2)/(SSE1234/76)   # F stat for testing H0: beta3=0 and beta4=0
F34           
qf(.95,2,76)                              # level of the test = 0.05

# Ex 2 
fm3 <- lm(Rates~VR, dum)       # reduced model has only one predictor X3
SSE3<-sum((Rates-fitted(fm3))^2)
SSE3
anova(fm3)  
F124 <- ((SSE3-SSE1234)/3)/(SSE1234/76)  # F stat fpr testing H0: beta1=beta2=beta4=0
F124
qf(.95,3,76)

# Ex 3 
fm124 <- lm(Rates~Age+OET+TSF, dum)       # reduced model has three predictors X1 2 4
SSE124<-sum((Rates-fitted(fm124))^2)
SSE124
anova(fm124)  
F3 <- ((SSE124-SSE1234)/1)/(SSE1234/76)  # F stat fpr testing H0: beta3=0
F3
qf(.95,1,76)
# If so......    As usual, before you leave R ......    #
detach()
rm(list=ls())