The SURVEYREG Procedure

## Example 62.1: Simple Random Sampling

This example investigates the relationship between the labor force participation rate (LFPR) of women in 1968 and 1972 in large cities in the United States. A simple random sample of 19 cities is drawn from a total of 200 cities. For each selected city, the LFPRs are recorded and saved in a SAS data set named Labor. The LFPR in 1972 is contained in the variable LFPR1972, and the LFPR in 1968 is identified by the variable LFPR1968.

   data Labor;
input City \$ 1-16 LFPR1972 LFPR1968;
datalines;
New York        .45     .42
Los Angeles     .50     .50
Chicago         .52     .52
Detroit         .46     .43
San Francisco   .55     .55
Boston          .60     .45
Pittsburgh      .49     .34
St. Louis       .35     .45
Connecticut     .55     .54
Washington D.C. .52     .42
Cincinnati      .53     .51
Baltimore       .57     .49
Newark          .53     .54
Minn/St. Paul   .59     .50
Buffalo         .64     .58
Houston         .50     .49
Patterson       .57     .56
Dallas          .64     .63
;


Assume that the LFPRs in 1968 and 1972 have a linear relationship, as shown in the following model. You can use PROC SURVEYREG to obtain the estimated regression coefficients and estimated standard errors of the regression coefficients. The following statements perform the regression analysis.

   title 'Study of Labor Force Participation Rates of Women';
proc surveyreg data=Labor total=200;
model LFPR1972 = LFPR1968;
run;


Here, the TOTAL=200 option specifies the finite population total from which the simple random sample of 19 cities is drawn. You can specify the same information by using the sampling rate option RATE=0.095 (19/200=.095).

Output 62.1.1: Summary of Regression Using Simple Random Sampling

 Study of Labor Force Participation Rates of Women

 The SURVEYREG Procedure Regression Analysis for Dependent Variable LFPR1972

 Data Summary Number of Observations 19 Mean of LFPR1972 0.52684 Sum of LFPR1972 10.01000

 Fit Statistics R-square 0.3970 Root MSE 0.05657 Denominator DF 18

 ANOVA for Dependent Variable LFPR1972 Source DF Sum of Squares Mean Square F Value Pr > F Model 1 0.035813 0.035813 11.19 0.0038 Error 17 0.054398 0.003200 Corrected Total 18 0.090211

Output 62.1.1 summarizes the data information, the fit information, and the ANOVA table.

Output 62.1.2: Regression Coefficient Estimates

 Study of Labor Force Participation Rates of Women

 The SURVEYREG Procedure Regression Analysis for Dependent Variable LFPR1972

 Tests of Model Effects Effect Num DF F Value Pr > F Model 1 13.84 0.0016 Intercept 1 4.63 0.0452 LFPR1968 1 13.84 0.0016

 NOTE: The denominator degrees of freedom for the F tests is 18.

 Estimated Regression Coefficients Parameter Estimate Standard Error t Value Pr > |t| Intercept 0.20331056 0.09444296 2.15 0.0452 LFPR1968 0.65604048 0.17635810 3.72 0.0016

 NOTE: The denominator degrees of freedom for the t tests is 18.

Output 62.1.2 presents the significance tests for the model effects and estimated regression coefficients. The F tests and t tests for the effects in the model are also presented in these tables.

From the regression performed by PROC SURVEYREG, you obtain a positive estimated slope for the linear relationship between the LFPR in 1968 and the LFPR in 1972. The regression coefficients are all significant at the 5% level. Effects Intercept and LFPR1968 are significant in the model at the 5% level. In this example, the F test for the overall model without intercept is the same as the effect LFPR1968.