library(survey)

# Regression estimation

x <- c(94,74,82,58,86,94,63,86,69,72,85,86,88,72,74,61,90,89,68,76,78,90)
y <- c(130,51,80,28,80,110,33,90,36,38,84,83,70,61,54,44,106,84,39,42,57,102)

ci.level = .95   # confidence level
p = 2            # number of parameters in the model
n = length(x)
df = n - p
corr.fctr = sqrt((n-1)/df)

regdata <- data.frame(x,y)

regdsgn <- svydesign(id=~1,data=regdata)
regdsgn

svyreg <- svyglm(y~x,design=regdsgn)
svyreg
atmean <- c(1,90)

# Assign names to each term in the model

names(atmean) <- c("(Intercept)","x")
atmean <- as.data.frame(t(atmean))

meanwgt <- predict(svyreg,newdata=atmean,total=1)
meanwgt

# Enter standard error 
se.meanwgt = 4.0207

# Compute confidence interval for mean with correction factor
meanwgt + c(-1,1)*corr.fctr*qt(ci.level+(1-ci.level)/2,df)*se.meanwgt