Finding the Regresion estimate of the population total

Here is some R code that finds the point and 95% interval regression estimates for the population total. We first generate a example simple population.

For a sample we will calculate the regression estimate and find its absolute error as an estimate of the population total We will also find the usual 95% confidence interval, its length and check to see if it contains the true population total.

The command set.seed lets you set the seed of the random number generator in R so that you can generate the same population again and again.

regtot<-function(smp,popy,popx) { xsamp<-popx[smp] ysamp<-popy[smp] mnpopx<-mean(popx) mny<-mean(popy) trtot<-sum(popy) n <- length(xsamp) N<-length(popy) ff <- n/N out <- lsfit(xsamp, ysamp) bb<-as.numeric(out$coef) res <- out$residuals mnxsamp <- mean(xsamp) mnysamp <- mean(ysamp) esttot <- N*(mnysamp + bb[2] * (mnpopx - mnxsamp)) abserr <- abs(esttot - trtot) dum1 <- N*N*((1 - ff)/(n*(n-2))) estvr <- dum1*sum(res * res) lwbd <- esttot - 1.96 * sqrt(estvr) upbd <-esttot + 1.96 * sqrt(estvr) if(lwbd <= trtot & trtot <= upbd) { cov<-1} else {cov<-0} ans<-c(esttot,abserr,lwbd,upbd - lwbd,cov) return(ans) } set.seed(1999) popx<-rgamma(500,5) popy<-rnorm(500,75 + 3*popx,20) cor(popx,popy) plot(popx,popy) smp<-sample(1:500,25) regtot(smp,popy,popx) out<-lsfit(popx[smp],popy[smp]) names(out) as.numeric(out$coef)

External Data Entry

Enter a Dataset URL :