Getting Started | SAS.STAT 9.1 Users Guide (Vol. 5)

Longley Data

The labor statistics data set of Longley (1967) is noted for being ill conditioned. Both the ORTHOREG and GLM procedures are applied for comparison (only portions of the PROC GLM results are shown). Note: The results from this example vary from machine to machine, depending on floating-point configuration.

The following statements read the data into the SAS data set Longley .

  title 'PROC ORTHOREG used with Longley data';   data Longley;   input Employment Prices GNP Jobless Military PopSize Year;   datalines;   60323  83.0 234289 2356 1590 107608 1947   61122  88.5 259426 2325 1456 108632 1948   60171  88.2 258054 3682 1616 109773 1949   61187  89.5 284599 3351 1650 110929 1950   63221  96.2 328975 2099 3099 112075 1951   63639  98.1 346999 1932 3594 113270 1952   64989  99.0 365385 1870 3547 115094 1953   63761 100.0 363112 3578 3350 116219 1954   66019 101.2 397469 2904 3048 117388 1955   67857 104.6 419180 2822 2857 118734 1956   68169 108.4 442769 2936 2798 120445 1957   66513 110.8 444546 4681 2637 121950 1958   68655 112.6 482704 3813 2552 123366 1959   69564 114.2 502601 3931 2514 125368 1960   69331 115.7 518173 4806 2572 127852 1961   70551 116.9 554894 4007 2827 130081 1962   ;   run;

The data set contains one dependent variable, Employment (total derived employment) and six independent variables : Prices (GNP implicit price deflator with year 1954 = 100), GNP (gross national product), Jobless (unemployment), Military ( size of armed forces), PopSize (non-institutional population aged 14 and over), and Year (year).

The following statements use the ORTHOREG procedure to model the Longley data using a quadratic model in each independent variable, without interaction:

  proc orthoreg data=Longley;   model Employment = Prices   Prices*Prices   GNP      GNP*GNP   Jobless  Jobless*Jobless   Military Military*Military   PopSize  PopSize*PopSize   Year     Year*Year;   run;

Figure 53.1 shows the resulting analysis.

  PROC ORTHOREG used with Longley data   The ORTHOREG Procedure   Dependent Variable: Employment   Sum of   Source                 DF         Squares     Mean Square    F Value    Pr > F   Model                  12     184864508.5    15405375.709     320.24    0.0003   Error                   3    144317.49568    48105.831895   Corrected Total        15       185008826   Root MSE    219.33041717   R-Square    0.9992199426   Standard   Parameter      DF    Parameter Estimate           Error    t Value    Pr > t   Intercept       1      186931078.640064    154201839.66       1.21      0.3122   Prices          1      1324.50679362465    916.17455832       1.45      0.2440   Prices**2       1   6.61923922845326    4.7891445654   1.38      0.2609   GNP             1   0.12768642156234    0.0738897784   1.73      0.1824   GNP**2          1    3.1369569286214E-8    8.7167753E-8       0.36      0.7428   Jobless         1   4.35507653558748    1.3851792402   3.14      0.0515   Jobless**2      1      0.00022132944101    0.0001763541       1.26      0.2983   Military        1       4.9116201456086     1.826715856       2.69      0.0745   Military**2     1   0.00113707146734    0.0003539971   3.21      0.0489   PopSize         1   0.03039972343344    5.9272538242   0.01      0.9962   PopSize**2      1   1.212511414593E-6    0.0000237262   0.05      0.9625   Year            1   194907.139041683    157739.28757   1.24      0.3045   Year**2         1      50.8067603538103    40.279878944       1.26      0.2963

Figure 53.1: PROC ORTHOREG Results

The estimates in Figure 53.1 compare very well with the best estimates available; for additional information, refer to Longley (1967) and Beaton et al. (1976).

The following statements request the same analysis from the GLM procedure:

  proc glm data=Longley;   model Employment = Prices   Prices*Prices   GNP      GNP*GNP   Jobless  Jobless*Jobless   Military Military*Military   PopSize  PopSize*PopSize   Year     Year*Year;   ods select OverallANOVA   FitStatistics   ParameterEstimates   Notes;   run;

Figure 53.2 contains the over-all ANOVA table and the parameter estimates produced by PROC GLM. Notice that the ORTHOREG fit achieves a somewhat smaller root mean square error (RMSE) and also that the GLM procedure detects spurious singularities.

  PROC ORTHOREG used with Longley data   The GLM Procedure   Dependent Variable: Employment   Sum of   Source                     DF        Squares    Mean Square   F Value   Pr > F   Model                      11    184791061.6     16799187.4    308.58   <.0001   Error                       4       217764.4        54441.1   Corrected Total            15    185008826.0   R-Square     Coeff Var      Root MSE    Employment Mean   0.998823      0.357221      233.3262           65317.00   Standard   Parameter                 Estimate             Error    t Value    Pr > t   Intercept   3598851.832 B     1327335.647   2.71      0.0535   Prices                     523.802           688.979       0.76      0.4894   Prices*Prices   2.326             3.507   0.66      0.5434   GNP   0.138             0.078   1.76      0.1526   GNP*GNP                      0.000             0.000       0.24      0.8218   Jobless   4.599             1.459   3.15      0.0344   Jobless*Jobless              0.000             0.000       1.14      0.3183   Military                     4.994             1.942       2.57      0.0619   Military*Military   0.001             0.000      -3.15      0.0346   PopSize   4.246             5.156      -0.82      0.4565   PopSize*PopSize              0.000 B           0.000       0.81      0.4655   Year                         0.000 B            .           .         .   Year*Year                    1.038             0.419       2.48      0.0683   NOTE: The X'X matrix has been found to be singular, and a generalized inverse   was used to solve the normal equations. Terms whose estimates are   followed by the letter 'B' are not uniquely estimable.

Figure 53.2: Partial PROC GLM Results