x2<-c(1,2,3,2)
x3<-c(2,1,1,2)
y0<-c(1,1,2,3)
n<-length(y0)

olsx2<-lm(x2~x3)
resx2<-resid(olsx2)
ols2<-lm(y0~resx2+x3)
summary(ols2)

olsx3<-lm(x3~x2)
resx3<-resid(olsx3)
ols3<-lm(y0~x2+resx3)
summary(ols3)

ols4<-lm(y0~x2+x3)
summary(ols4)

y0bar<-mean(y0)
x2bar<-mean(x2)
x3bar<-mean(x3)
y0sd<-sqrt(var(y0))
x2sd<-sqrt(var(x2))
x3sd<-sqrt(var(x3))
sy0<-(y0-y0bar)/y0sd
sx2<-(x2-x2bar)/x2sd
sx3<-(x3-x3bar)/x3sd
sols<-lm(sy0~sx2+sx3-1)
summary(sols)

y0sd
x2sd
x3sd

beta2hat<-summary(sols)$coef[1,1]*(y0sd/x2sd)
beta3hat<-summary(sols)$coef[2,1]*(y0sd/x3sd)
beta2hat
beta3hat