R Log for Example Analyses Using Counties.dat in Problem #3.7

[similar to #3.5 and 3.6]

### ASCII Data  are comma-delimited: enter data accordingly

> counties = read.table("counties.dat", header=T, sep=",")
> names(counties)
 [1] "RN"       "STATE"    "COUNTY"   "LANDAREA" "TOTPOP"   "PHYSICIA"
 [7] "ENROLL"   "PERCPUB"  "CIVLABOR" "UNEMP"    "FARMPOP"  "NUMFARM"
[13] "FARMACRE" "FEDGRANT" "FEDCIV"   "MILIT"    "VETERANS" "PERCVIET"
> dim(counties)
[1] 100  18
> attach(counties)


Problem #3.7
============

> c(3141*mean(VETERANS), sqrt((3141*3041/100)*var(VETERANS)))
[1] 38476339 14703478

> 255077036*mean(VETERANS)/mean(TOTPOP)     ### Ratio estimator
1] 26361167

### Now for ratio estimator SE:
> sqrt((3141*3041/100)*var(VETERANS - TOTPOP*
           mean(VETERANS)/mean(TOTPOP)))
[1] 2389402  ### This is a LOT smaller than before !!!

> tmplm2 = lm(VETERANS ~ TOTPOP)
  c(3141*mean(VETERANS) + tmplm2$coef[2]*(255077036-3141*mean(TOTPOP)), 
      sqrt((3141*3041/100)*var(tmplm2$resid)))
[1] 27878518  1142010
                        #### these are Regression estimator & SE

> summary(tmplm2)$coef
                Estimate   Std. Error    t value      Pr(>|t|)
(Intercept) 1.534201e+03 3.808447e+02   4.028417  1.109188e-04
TOTPOP      9.040246e-02 7.114278e-04 127.071867 1.415724e-110

### Whenever regression estimator is much better than ratio
###   estimator, we should expect significant intercept;
###   whenever it is much better than the estimator which 
###   ignores auxiliary data, we should see signficant slope !