#LM 01 PRINCIPAL AXIS REGRESSION:
setwd("c:/DATA/Models")
K=read.table("SR15.2.txt")
K
S=cov(K)
S
R=cor(K)
R
e=eigen(S)
e
b0=e$vectors[1,1]/e$vectors[1,2]
b0
b1=e$vectors[1,2]/e$vectors[2,2]
b1
X=K$V1
Y=K$V2
X=X-mean(X)
Y=Y-mean(Y)
Int0=mean(X)-b0*mean(Y)
Int0
Int1=mean(X)-b1*mean(Y)
Int1

#PLOT OF PRINCIPAL AXIS REGRESSION CALCULATED
plot(X,Y)
abline(a=0,b=-b1,col="blue")

#RMA REGRESSION
Lxx=t(X)%*%X # Matrix multiplication for SS
Lxx
Lyy=t(Y)%*%Y # Matrix multiplication for SS
Lyy
bv=sqrt(Lyy/Lxx)
bv
#PLOTTING RMA REGRESSION CALCULATED
abline(a=0,b=bv,col="red")

#PLOT USING slope.com{smatr}
#FUNCTION ALSO INCLUDES CONF INTERVALS
library(smatr)
g=rep(1,length(X))
slope.com(Y,X,g)
CS=slope.com(Y,X,g, method="SMA")
bb=CS$b
abline(a=0,b=bb,col="green")

CS=slope.com(Y,X,g, method="MA")
bb=CS$b
abline(a=0,b=bb,col="magenta")