[R] R-Square in WLS

[frespider]

Hi,

I am fitting a weighted least square regression and trying to compute
SSE,SST and SSReg but I am not getting SST = SSReg + SSE and I dont know
what I am coding wrong. Can you help please?

xnam <-colnames(X) # colnames Design Matrix                                                                       
fmla1 <- as.formula(paste("Y ~",paste(xnam, collapse= "+"),"-1",sep=""))
fitlm <- lm(formula=fmla1,data = data.frame(cbind(X,Y)))
ResiSqr <- (residuals(fitlm))*(residuals(fitlm))
fmla2 <- as.formula(paste("ResiSqr ~ ", paste(xnam, collapse=
"+"),"-1",sep=""))
fitResi <- lm(formula=fmla2,data = data.frame(cbind(x,ResiSqr))) # This fit
is to calculate the weights
bResi <- coef(fitResi)
Sigma2 <- X%*%bResi                               # Var(Y)
Weights <- 1/Sigma2
for(i in 1:length(Weights)){
Weights[which(ifelse(Weights<=0.5,TRUE,FALSE))] <- 0.5
Weights[which(ifelse(Weights>=200,TRUE,FALSE))] <- 200
Sigma2[which(ifelse(Sigma2<=0,TRUE,FALSE))] <- 0                    # set
-ve Var(Y) to zero
#+++++++++++++++++++++++++++ Fit WLS
+++++++++++++++++++++++++++++++++++++++++++
fitwls <- lm(formula = fmla1,weights = Weights,data =
data.frame(cbind(X,Y)))
bhat <- coef(fitwls)

############################## Y = Log(Z) Scale
####################################
Yhat <- X%*%bhat                 # predicted values
mu <- mean(Y)
To <- Y - mu
Er <- Y - Yhat
Re <- Yhat - mu
lgSST <- sum(Weights*(To)^2)                # log SST
lgSSE <- sum(Weights*(Er)^2)                # log SSE
lgSSR <- sum(Weights*(Re)^2)                # log SSR
lgR-sq <- lgSSR/lgSST
###############################  Z Scale
######################################
Z <- exp(Y)
muZ <- mean(Z)
Zhat <- exp(Yhat+0.5*Sigma2)
ToZ <- Z-muZ
ErZ <- Z - Zhat
ReZ <- Zhat - muZ
SST <- sum(Weights*(ToZ)^2)          # SST
SSE <- sum(Weights*(ErZ)^2)          # SSE 
SSR <- sum(Weights*(ReZ)^2)          # SSR
Rsq <- SSR/SST

I don't understand what is wrong with the code.  The sum square regression
plus the sum square error do not add up to the sum square total in both the
Y scale and Z scale.  Y is a normal distribution and Z is log normally
distributed.  Where is the error? 
Also, is there a way to calculate the weighted sum square?
 



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