(CD<-read.csv('CobbDouglas.csv'))

y<-log(as.numeric(gsub(",","",as.character(CD$Y))))
x1<-log(as.numeric(gsub(",","",as.character(CD$X2))))
x2<-log(as.numeric(gsub(",","",as.character(CD$X3))))

pairs(cbind(y,x1,x2))

par(mfrow=c(1,2))
plot(x1,y,pch=19)
plot(x2,y,pch=19)
dev.print(device=pdf,file='CD-Data.pdf',width=11,height=7)

Cobb<-data.frame(y,x1,x2)

fit12<-lm(y~x1+x2,data=Cobb)
summary(fit12)
summary(fit12)$sigma

summary(fit12)$df[2]*summary(fit12)$sigma^2

anova(fit12)[,2]

fit21<-lm(y~x2+x1,data=Cobb)
anova(fit21)

anova(lm(y~1,data=Cobb))[1,2]
anova(lm(y~1,data=Cobb))[1,3]
anova(lm(y~x1,data=Cobb))[2,2]

SSRes0<-anova(lm(y~1,data=Cobb))[1,2]
MSRes012<-anova(lm(y~x1+x2,data=Cobb))[3,3]
SSRes01<-anova(lm(y~x1,data=Cobb))[2,2]
F<-((SSRes0-SSRes01)/1)/MSRes012

SSRes0
MSRes012
SSRes01
F

summary(lm(y~x1,data=Cobb))
anova(lm(y~x1,data=Cobb))


SSRes01<-anova(lm(y~x1,data=Cobb))[2,2]
MSRes012<-anova(lm(y~x1+x2,data=Cobb))[3,3]
SSRes012<-anova(lm(y~x1+x2,data=Cobb))[3,2]
F<-((SSRes01-SSRes012)/1)/MSRes012

SSRes0
MSRes012
SSRes01
F

############################################
SSRes0<-anova(lm(y~1,data=Cobb))[1,2]
MSRes012<-anova(lm(y~x1+x2,data=Cobb))[3,3]
SSRes02<-anova(lm(y~x2,data=Cobb))[2,2]
(F<-((SSRes0-SSRes01)/1)/MSRes012)


SSRes02<-anova(lm(y~x2,data=Cobb))[2,2]
MSRes012<-anova(lm(y~x1+x2,data=Cobb))[3,3]
SSRes012<-anova(lm(y~x1+x2,data=Cobb))[3,2]
(F<-((SSRes02-SSRes012)/1)/MSRes012)

############################################

fit12<-lm(y~x1+x2,data=Cobb)
drop1(fit12,test='F')

mval<-which.max(residuals(fit12))
NM<-as.character(CD[mval,1])

plot(x1,residuals(fit12),pch=19,ylim=range(-1.5,1.5));abline(h=0,lty=2)
text(x1[mval],residuals(fit12)[mval]+0.1,NM)
plot(x2,residuals(fit12),pch=19,ylim=range(-1.5,1.5))
text(x2[mval],residuals(fit12)[mval]+0.1,NM);abline(h=0,lty=2)