Example 62.3: Regresson Estimator for Simple Random Sample

The SURVEYREG Procedure

Example 62.3: Regresson Estimator for Simple Random Sample

Using auxilary information, you can construct the regression estimators to provide more accurate estimates of the population characteristics that are of interest. With ESTIMATE statements in PROC SURVEYREG, you can speciofy a regression estimator as a linear function of the regression parameters to estimate the population total. This example illustrates this application, using the data in the previous example.

In this sample, a linear model between the Swedish populations in 1975 and in 1985 is established.

${{\hv Population85}}=\alpha+\beta *{{\hv Population75}}+{{\rm error}}$

Assuming that the total population in 1975 is known to be 8200 (in thousands), you can use the ESTIMATE statement to predict the 1985 total population using the following statements.

   title1 'Regression Analysis for Swedish Municipalities';
   title2 'Estimate Total Population';
   proc surveyreg data=Municipalities total=50;
      cluster Cluster;
      model Population85=Population75;
      estimate '1985 population' Intercept 284 Population75 8200;
   run;

Since each observation in the sample is a municipality, and there is a total of 284 municipalities in Sweden, the coefficient for Intercept ( $\alpha$ ) in the ESTIMATE statement is 284, and the coefficient for Population75 ( $\beta$ ) is the total population in 1975 (8.2 million).

Output 62.3.1: Use the Regression Estimator to Estimate the Population Total

Regression Analysis for Swedish Municipalities

Estimate Total Population

The SURVEYREG Procedure

Regression Analysis for Dependent Variable Population85

Analysis of Estimable Functions
Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
1985 population	8642.49485	258.558613	33.43	<.0001

NOTE:

The denominator degrees of freedom for the t tests is 4.

Output 62.3.1 displays the regression results and the estimation of the total population. Using the linear model, you can predict the total population in 1985 to be 8.64 million, with a standard error of 0.26 million.

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