###################hw 2######################################
##prob 1
#regression line
library(SDaA)
library(survey)
data(anthuneq)
finger<-anthuneq$finger
height<-anthuneq$height
prob<-anthuneq$prob
weight<-1/prob
duneq<-svydesign(id=~1,weight=weight,data=anthuneq)
duneq
myfit<-svyglm(height~finger,design=duneq)
myfit
#jackknife fit
b_0<-myfit$coef[1]
b_1<-myfit$coef[2]
slope<-rep(0,200)
sum<-0
for(i in 1:200){
   data<-anthuneq[-i,]
   prob<-data$prob
   wt<-(200/199)*(1/prob)
   duneq<-svydesign(id=~1,weight=wt,data=anthuneq[-i,])
   fit1<-svyglm(height~finger,design=duneq)
   slope[i]<-fit1$coef[2]
   sum<-sum+(slope[i]-b_1)^2
}
varjk<-(199/200)*sum
varjk

##problem 2
library(survey)
data(api)
dapistrat<-svydesign(id=~1,strata=~stype,weight=~pw,data=apistrat,fpc=~fpc)
nrow(apistrat)
apistrat[1:2,]
svyplot(api00~emer,design=dapistrat,xlab="emer",ylab="api00",style="bubble")
myfit<-svyglm(api00~emer,design=dapistrat)
summary(myfit)
#What confounding variables measuring socioeconomic status of students should
#be included in the model?
#meals, not.hsg, hsg, some.col, col.grad,grad.sch, avg.ed
help(apistrat) #to see the definitions of variables
pairs(api00 ~ emer+meals+not.hsg+some.col+col.grad+grad.sch+avg.ed,data=apistrat)
##variable selection