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; datalines; 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.