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SAS FAQ
How can I do regression estimation with survey data?

This example is taken from Lehtonen and Pahkinen's Practical Methods for Design and Analysis of Complex Surveys.

simple random sample without replacement for regression estimation

page 107 Table 3.14  Model-assisted estimation results for the population total of ue91 from an SRS sample of eight elements drawn from the Province'91 population.

data page106;
  input id str clu wt ue91 meanz hou85 diffhou85 smplrat;
  fpc = 32;
  cards;
  1 1 1 4 4123 2867 26881 -24014 .25
  2 1 4 4 760 2867 4896 -2029 .25
  3 1 5 4 721 2867 3730 -863 .25
  4 1 15 4 142 2867 556 2311 .25
  5 1 18 4 187 2867 1463 1404 .25
  6 1 26 4 331 2867 1946 921 .25
  7 1 30 4 127 2867 834 2033 .25
  8 1 31 4 219 2867 932 1935 .25
  ;
run;

The code below produces the estimate of b-hat, 0.152, shown in the middle of page 106.

proc surveyreg data = page106 r = .25 ;
  weight wt;
  strata str;
  cluster clu;
  model ue91 = hou85;
run;

The SURVEYREG Procedure

Regression Analysis for Dependent Variable ue91

            Data Summary

Number of Observations             8
Sum of Weights              32.00000
Weighted Mean of ue91      826.25000
Weighted Sum of ue91         26440.0


         Design Summary

Number of Strata               1
Number of Clusters             8

      Fit Statistics

R-square            0.9982
Root MSE           61.2713
Denominator DF           7

                   ANOVA for Dependent Variable ue91

                                 Sum of        Mean
Source                   DF     Squares      Square    F Value    Pr > F

Model                     1    51365266    51365266    3420.55    <.0001
Error                     6       90100       15017
Corrected Total           7    51455366

         Tests of Model Effects

Effect       Num DF    F Value    Pr > F

Model             1    38527.9    <.0001
Intercept         1       3.70    0.0960
hou85             1    38527.9    <.0001

NOTE: The denominator degrees of freedom for the F tests is 7.

Regression Analysis for Dependent Variable ue91

             Estimated Regression Coefficients

                             Standard
Parameter      Estimate         Error    t Value    Pr > |t|

Intercept    42.6546808    22.1860968       1.92      0.0960
hou85         0.1520142     0.0007745     196.29      <.0001

NOTE: The denominator degrees of freedom for the t tests is 7.

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