Example 86.1 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 Labor. In the following DATA step, 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 
   Philadelphia    .45     .45 
   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 86.1.1 summarizes the data information and the fit information.