data lntrans;
input case x1 x2 x3 x4 y logy;
cards;
01   6.7  62   81  2.59  200  2.3010
02   5.1  59   66  1.70  101  2.0043
03   7.4  57   83  2.16  204  2.3096
04   6.5  73   41  2.01  101  2.0043
05   7.8  65  115  4.30  509  2.7067
06   5.8  38   72  1.42   80  1.9031
07   5.7  46   63  1.91   80  1.9031
08   3.7  68   81  2.57  127  2.1038
09   6.0  67   93  2.50  202  2.3054
10   3.7  76   94  2.40  203  2.3075
11   6.3  84   83  4.13  329  2.5172
12   6.7  51   43  1.86   65  1.8129
13   5.8  96  114  3.95  830  2.9191
14   5.8  83   88  3.95  330  2.5185
15   7.7  62   67  3.40  168  2.2253
16   7.4  74   68  2.40  217  2.3365
17   6.0  85   28  2.98   87  1.9395
18   3.7  51   41  1.55   34  1.5315
19   7.3  68   74  3.56  215  2.3324
20   5.6  57   87  3.02  172  2.2355
21   5.2  52   76  2.85  109  2.0374
22   3.4  83   53  1.12  136  2.1335
23   6.7  26   68  2.10   70  1.8451
24   5.8  67   86  3.40  220  2.3424
25   6.3  59  100  2.95  276  2.4409
26   5.8  61   73  3.50  144  2.1584
27   5.2  52   86  2.45  181  2.2577
28  11.2  76   90  5.59  574  2.7589
29   5.2  54   56  2.71   72  1.8573
30   5.8  76   59  2.58  178  2.2504
31   3.2  64   65  0.74   71  1.8513
32   8.7  45   23  2.52   58  1.7634
33   5.0  59   73  3.50  116  2.0645
34   5.8  72   93  3.30  295  2.4698
35   5.4  58   70  2.64  115  2.0607
36   5.3  51   99  2.60  184  2.2648
37   2.6  74   86  2.05  118  2.0719
38   4.3   8  119  2.85  120  2.0792
39   4.8  61   76  2.45  151  2.1790
40   5.4  52   88  1.81  148  2.1703
41   5.2  49   72  1.84   95  1.9777
42   3.6  28   99  1.30   75  1.8751
43   8.8  86   88  6.40  483  2.6840
44   6.5  56   77  2.85  153  2.1847
45   3.4  77   93  1.48  191  2.2810
46   6.5  40   84  3.00  123  2.0899
47   4.5  73  106  3.05  311  2.4928
48   4.8  86  101  4.10  398  2.5999
49   5.1  67   77  2.86  158  2.1987
50   3.9  82  103  4.55  310  2.4914
51   6.6  77   46  1.95  124  2.0934
52   6.4  85   40  1.21  125  2.0969
53   6.4  59   85  2.33  198  2.2967
54   8.8  78   72  3.20  313  2.4955
;
proc chart;
 hbar x1 x2 x3 x4 y logy;

proc reg simple corr;
model y=x1 x2 x3 x4 /adjrsq corrb dw stb tol vif r pcorr2 scorr2 sse mse;
	output out=resid student=sresid;
	plot (y)*(x1 x2 x3 x4) (residual.)*(x1 x2 x3 x4) 
		residual.*predicted. / hplots=2 vplots=2;
proc chart data=resid;
        vbar sresid;
proc univariate plot;
        var sresid;

proc reg;
	model y=x1 x2 x3 x4 /adjrsq stb tol selection=forward sle=.05;
	model y=x1 x2 x3 x4 / adjrsq stb tol selection=backward sle=.1;
	model y=x1 x2 x3 x4 / adjrsq stb tol selection=stepwise sle=.05;


proc reg simple corr;
model logy=x1 x2 x3 x4 /adjrsq corrb dw stb tol vif r pcorr2 scorr2 sse 
	mse;
	output out=resid2 student=sresid2;
	plot (logy)*(x1 x2 x3 x4) (residual.)*(x1 x2 x3 x4) 
		residual.*predicted. / hplots=2 vplots=2;
proc chart data=resid2;
        vbar sresid2;
proc univariate plot;
        var sresid2;

proc reg;
	model logy=x1 x2 x3 x4 / adjrsq stb tol selection=forward sle=.05;
	model logy=x1 x2 x3 x4 / adjrsq stb tol selection=backward sle=.1;
	model logy=x1 x2 x3 x4 / adjrsq stb tol selection=stepwise sle=.05;

proc reg;
model x1 = x2 x3 x4 /adjrsq stb;
model x2 = x1 x3 x4 /adjrsq stb;
model x3 = x1 x2 x4 /adjrsq stb;
model x4 = x1 x2 x3 /adjrsq stb;

run;











The SAS System                             14:43 Thursday, December 23, 1999   1

  X1                                     Cum.              Cum.
Midpoint                           Freq  Freq  Percent  Percent
       |
 3.0   |********                      8     8    14.81    14.81
       |
 4.5   |************                 12    20    22.22    37.04
       |
 6.0   |*************************    25    45    46.30    83.33
       |
 7.5   |*****                         5    50     9.26    92.59
       |
 9.0   |***                           3    53     5.56    98.15
       |
10.5   |*                             1    54     1.85   100.00
       |
       -----+----+----+----+----+
            5    10   15   20   25

                Frequency

The SAS System                             14:43 Thursday, December 23, 1999   2

X2                                                Cum.              Cum.
Midpoint                                    Freq  Freq  Percent  Percent
     |
15   |**                                       1     1     1.85     1.85
     |
30   |****                                     2     3     3.70     5.56
     |
45   |**********************                  11    14    20.37    25.93
     |
60   |************************************    18    32    33.33    59.26
     |
75   |****************************            14    46    25.93    85.19
     |
90   |****************                         8    54    14.81   100.00
     |
     ----+---+---+---+---+---+---+---+---+
         2   4   6   8   10  12  14  16  18

                   Frequency

The SAS System                             14:43 Thursday, December 23, 1999   3

   X3                                              Cum.              Cum.
Midpoint                                     Freq  Freq  Percent  Percent
        |
 22.5   |****                                   2     2     3.70     3.70
        |
 37.5   |********                               4     6     7.41    11.11
        |
 52.5   |********                               4    10     7.41    18.52
        |
 67.5   |**************************            13    23    24.07    42.59
        |
 82.5   |**********************************    17    40    31.48    74.07
        |
 97.5   |********************                  10    50    18.52    92.59
        |
112.5   |********                               4    54     7.41   100.00
        |
        ----+---+---+---+---+---+---+---+--
            2   4   6   8   10  12  14  16

                     Frequency

The SAS System                             14:43 Thursday, December 23, 1999   4

X4                                                      Cum.              Cum.
Midpoint                                          Freq  Freq  Percent  Percent
     |
 1   |************                                   6     6    11.11    11.11
     |
 2   |********************************              16    22    29.63    40.74
     |
 3   |******************************************    21    43    38.89    79.63
     |
 4   |****************                               8    51    14.81    94.44
     |
 5   |**                                             1    52     1.85    96.30
     |
 6   |****                                           2    54     3.70   100.00
     |
     ----+---+---+---+---+---+---+---+---+---+--
         2   4   6   8   10  12  14  16  18  20

                      Frequency

The SAS System                             14:43 Thursday, December 23, 1999   5

  Y                                     Cum.              Cum.
Midpoint                          Freq  Freq  Percent  Percent
      |
 75   |*************************    25    25    46.30    46.30
      |
225   |*******************          19    44    35.19    81.48
      |
375   |******                        6    50    11.11    92.59
      |
525   |***                           3    53     5.56    98.15
      |
675   |                              0    53     0.00    98.15
      |
825   |*                             1    54     1.85   100.00
      |
      -----+----+----+----+----+
           5    10   15   20   25

               Frequency

The SAS System                             14:43 Thursday, December 23, 1999   6

 LOGY                                                  Cum.              Cum.
Midpoint                                         Freq  Freq  Percent  Percent
        |
1.625   |**                                         1     1     1.85     1.85
        |
1.875   |********************                      10    11    18.52    20.37
        |
2.125   |**************************************    19    30    35.19    55.56
        |
2.375   |**********************************        17    47    31.48    87.04
        |
2.625   |**********                                 5    52     9.26    96.30
        |
2.875   |****                                       2    54     3.70   100.00
        |
        ----+---+---+---+---+---+---+---+---+--
            2   4   6   8   10  12  14  16  18

                       Frequency

The SAS System                             14:43 Thursday, December 23, 1999   7

Descriptive Statistics

Variables                 Sum                Mean      Uncorrected SS

INTERCEP                   54                   1                  54
X1                      312.3        5.7833333333             1942.33
X2                       3415        63.240740741              231109
X3                       4164        77.111111111              345032
X4                     148.19        2.7442592593            467.3919
Y                       10647        197.16666667             3218165


Variables            Variance       Std Deviation

INTERCEP                    0                   0
X1               2.5697169811        1.6030336806
X2               285.69566737        16.902534347
X3               451.72327044        21.253782497
X4               1.1456626485        1.0703563185
Y                21111.915094        145.29939812


Correlation

CORR             X1             X2             X3             X4              Y

X1           1.0000         0.0901        -0.1496         0.5024         0.3725
X2           0.0901         1.0000        -0.0236         0.3690         0.5540
X3          -0.1496        -0.0236         1.0000         0.4164         0.5802
X4           0.5024         0.3690         0.4164         1.0000         0.7223
Y            0.3725         0.5540         0.5802         0.7223         1.0000

The SAS System                             14:43 Thursday, December 23, 1999   8

Model: MODEL1  
Dependent Variable: Y                                                  

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            4 936264.53767 234066.13442       62.788       0.0001
Error           49 182666.96233   3727.89719
C Total         53    1118931.5

    Root MSE      61.05651     R-square       0.8367
    Dep Mean     197.16667     Adj R-sq       0.8234
    C.V.          30.96695

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1   -621.597550   64.80042601        -9.592        0.0001
X1         1     33.163828    7.01727463         4.726        0.0001
X2         1      4.271860    0.56338454         7.582        0.0001
X3         1      4.125738    0.51116093         8.071        0.0001
X4         1     14.091563   12.52532754         1.125        0.2661

                                 Squared       Squared
              Standardized  Semi-partial       Partial              
Variable  DF      Estimate  Corr Type II  Corr Type II     Tolerance

INTERCEP   1    0.00000000     .             .             .        
X1         1    0.36588406    0.07441368    0.31310333    0.55586050
X2         1    0.49694120    0.19155106    0.53988110    0.77566563
X3         1    0.60349558    0.21704434    0.57072538    0.59593691
X4         1    0.10380630    0.00421697    0.02518072    0.39133899

                  Variance
Variable  DF     Inflation

INTERCEP   1    0.00000000
X1         1    1.79901252
X2         1    1.28921530
X3         1    1.67802997
X4         1    2.55532933



Correlation of Estimates

CORRB         INTERCEP            X1            X2            X3            X4

INTERCEP        1.0000       -0.7167       -0.6382       -0.7516        0.5155
X1             -0.7167        1.0000        0.2464        0.4958       -0.6535
X2             -0.6382        0.2464        1.0000        0.2987       -0.4668
X3             -0.7516        0.4958        0.2987        1.0000       -0.6248
X4              0.5155       -0.6535       -0.4668       -0.6248        1.0000


The SAS System                             14:43 Thursday, December 23, 1999   9

Durbin-Watson D             1.720
(For Number of Obs.)           54
1st Order Autocorrelation   0.134


The SAS System                             14:43 Thursday, December 23, 1999  10

        Dep Var   Predict   Std Err             Std Err   Student
  Obs      Y        Value   Predict  Residual  Residual  Residual

    1     200.0     236.1    12.166  -36.1374    59.832    -0.604
    2     101.0   95.8321    11.742    5.1679    59.917     0.086
    3     204.0     240.2    19.814  -36.1848    57.752    -0.627
    4     101.0     103.3    17.502   -2.2924    58.494    -0.039
    5     509.0     449.8    21.570   59.1952    57.120     1.036
    6   80.0000   50.1465    17.392   29.8535    58.527     0.510
    7   80.0000   50.7782    13.299   29.2218    59.591     0.490
    8     127.0     162.0    14.930  -34.9952    59.203    -0.591
    9     202.0     282.5    14.780  -80.5226    59.241    -1.359
   10     203.0     247.4    16.756  -44.4091    58.712    -0.756
   11     329.0     346.8    15.652  -17.8052    59.016    -0.302
   12   65.0000   22.0820    17.433   42.9180    58.515     0.733
   13     830.0     506.8    24.210     323.2    56.052     5.765
   14     330.0     344.0    15.035  -14.0437    59.177    -0.237
   15     168.0     223.0    13.683  -54.9550    59.504    -0.924
   16     217.0     254.3    17.396  -37.3024    58.526    -0.637
   17   87.0000   98.0070    26.476  -11.0070    55.018    -0.200
   18   34.0000  -90.0293    23.686     124.0    56.275     2.204
   19     215.0     266.5    11.990  -51.4555    59.868    -0.859
   20     172.0     209.1    10.051  -37.1116    60.224    -0.616
   21     109.0     126.7    12.691  -17.7081    59.723    -0.297
   22     136.0   80.1705    22.860   55.8295    56.615     0.986
   23   70.0000   21.8109    21.503   48.1891    57.145     0.843
   24     220.0     259.7    10.194  -39.6921    60.200    -0.659
   25     276.0     293.5    14.435  -17.5182    59.326    -0.295
   26     144.0     181.8    14.160  -37.8355    59.392    -0.637
   27     181.0     162.3    10.802   18.6711    60.093     0.311
   28     574.0     524.6    31.422   49.4130    52.350     0.944
   29   72.0000   50.7643    17.528   21.2357    58.486     0.363
   30     178.0     175.2    12.671    2.8112    59.727     0.047
   31   71.0000   36.5265    19.833   34.4735    57.746     0.597
   32   58.0000  -10.4358    28.677   68.4358    53.903     1.270
   33     116.0     146.8    18.272  -30.7607    58.258    -0.528
   34     295.0     308.5    11.367  -13.5224    59.989    -0.225
   35     115.0     131.3    10.286  -16.2584    60.184    -0.270
   36     184.0     217.1    13.783  -33.1217    59.481    -0.557
   37     118.0     164.4    19.870  -46.4472    57.733    -0.805
   38     120.0   86.3056    34.172   33.6944    50.598     0.666
   39     151.0     146.3    10.028    4.7473    60.227     0.079
   40     148.0     168.2    15.094  -20.1945    59.161    -0.341
   41   95.0000   83.1571    11.924   11.8429    59.881     0.198
   42   75.0000   44.1714    23.515   30.8286    56.347     0.547
   43     483.0     490.9    31.129   -7.8751    52.525    -0.150
   44     153.0     191.0     9.945  -38.0343    60.241    -0.631
   45     191.0     224.6    22.221  -33.6418    56.869    -0.592
   46     123.0     153.7    15.811  -30.6784    58.974    -0.520
   47     311.0     319.8    16.127   -8.7930    58.888    -0.149
   48     398.0     379.4    19.382   18.5563    57.898     0.320
   49     158.0     191.7    10.007  -33.7363    60.231    -0.560
   50     310.0     347.1    26.016  -37.1015    55.236    -0.672
   51     124.0     143.5    17.903  -19.4794    58.373    -0.334
   52     125.0     135.8    25.418  -10.8394    55.514    -0.195
   53     198.0     226.2    13.676  -28.2118    59.505    -0.474
   54     313.0     345.6    21.471  -32.5954    57.157    -0.570

The SAS System                             14:43 Thursday, December 23, 1999  11

                          Cook's
  Obs    -2-1-0 1 2            D

    1  |     *|      |     0.003
    2  |      |      |     0.000
    3  |     *|      |     0.009
    4  |      |      |     0.000
    5  |      |**    |     0.031
    6  |      |*     |     0.005
    7  |      |      |     0.002
    8  |     *|      |     0.004
    9  |    **|      |     0.023
   10  |     *|      |     0.009
   11  |      |      |     0.001
   12  |      |*     |     0.010
   13  |      |******|     1.240
   14  |      |      |     0.001
   15  |     *|      |     0.009
   16  |     *|      |     0.007
   17  |      |      |     0.002
   18  |      |****  |     0.172
   19  |     *|      |     0.006
   20  |     *|      |     0.002
   21  |      |      |     0.001
   22  |      |*     |     0.032
   23  |      |*     |     0.020
   24  |     *|      |     0.002
   25  |      |      |     0.001
   26  |     *|      |     0.005
   27  |      |      |     0.001
   28  |      |*     |     0.064
   29  |      |      |     0.002
   30  |      |      |     0.000
   31  |      |*     |     0.008
   32  |      |**    |     0.091
   33  |     *|      |     0.005
   34  |      |      |     0.000
   35  |      |      |     0.000
   36  |     *|      |     0.003
   37  |     *|      |     0.015
   38  |      |*     |     0.040
   39  |      |      |     0.000
   40  |      |      |     0.002
   41  |      |      |     0.000
   42  |      |*     |     0.010
   43  |      |      |     0.002
   44  |     *|      |     0.002
   45  |     *|      |     0.011
   46  |     *|      |     0.004
   47  |      |      |     0.000
   48  |      |      |     0.002
   49  |     *|      |     0.002
   50  |     *|      |     0.020
   51  |      |      |     0.002
   52  |      |      |     0.002
   53  |      |      |     0.002
   54  |     *|      |     0.009


The SAS System                             14:43 Thursday, December 23, 1999  12

Sum of Residuals                      0
Sum of Squared Residuals    182666.9623
Predicted Resid SS (Press)  247880.7920


The SAS System                             14:43 Thursday, December 23, 1999  13

       ---+----+----+----+----+----+---        ---+----+----+----+----+----+---
       |                              |        |                              |
  1000 +                              +   1000 +                              +
       |                              |        |                              |
       |                              |        |                              |
       |            1                 |        |                          1   |
   800 +                              +    800 +                              +
       |                              |        |                              |
Y      |                              | Y      |                              |
       |                              |        |                              |
   600 +                              +    600 +                              +
       |                         1    |        |                     1        |
       |                 1 1          |        |                  1     1     |
       |                              |        |                              |
   400 +         1                    +    400 +                        1     +
       |            11                |        |                       2      |
       |       11   11     1          |        |                 1  2 11      |
       |                              |        |                              |
   200 +      2   2 31112             +    200 +               21113 4        +
       |      2  11212  1             |        |               12212   2      |
       |    1 1 1 42221               |        |    1    1  2 21 3  12 1      |
       |     11   1   2    1          |        |         1   1 21 1           |
     0 +                              +      0 +                              +
       |                              |        |                              |
       ---+----+----+----+----+----+---        ---+----+----+----+----+----+---
          2    4    6    8   10   12              0   20   40   60   80   100
 
                   X1                                      X2
 
       ---+----+----+----+----+----+---        -+------+------+------+------+--
       |                              |        |                              |
  1000 +                              +   1000 +                              +
       |                              |        |                              |
       |                              |        |                              |
       |                          1   |        |              1               |
   800 +                              +    800 +                              +
       |                              |        |                              |
Y      |                              | Y      |                              |
       |                              |        |                              |
   600 +                              +    600 +                              +
       |                    1         |        |                    1         |
       |                   1      1   |        |               1      1       |
       |                              |        |                              |
   400 +                      1       +    400 +              1               +
       |                  11          |        |              2               |
       |               1    1 111     |        |          121   1             |
       |                              |        |                              |
   200 +            1 1 1122211       +    200 +     1  45  2                 +
       |       1  1   1131 2          |        |    2 1  2212                 |
       |    1  1 1   1141 11  1    1  |        |     224 1311                 |
       |   1   11  1 11               |        |   1 1 2 2                    |
     0 +                              +      0 +                              +
       |                              |        |                              |
       ---+----+----+----+----+----+---        -+------+------+------+------+--
         20   40   60   80   100  120           0      2      4      6      8
 
                   X3                                      X4
 

The SAS System                             14:43 Thursday, December 23, 1999  14

       ---+----+----+----+----+----+---        ---+----+----+----+----+----+---
       |                              |        |                              |
   400 +                              +    400 +                              +
       |                              |        |                              |
       |                              |        |                              |
       |            1                 |        |                          1   |
   300 +                              +    300 +                              +
       |                              |        |                              |
R      |                              | R      |                              |
E      |                              | E      |                              |
S  200 +                              + S  200 +                              +
I      |                              | I      |                              |
D      |                              | D      |                              |
U      |      1                       | U      |               1              |
A  100 +                              + A  100 +                              +
L      |                   1          | L      |             1                |
       |      1       2  1       1    |        |         1     1  1  1 1      |
       |     11 11211                 |        |    1    1  1 111 1     1     |
     0 +        112 22     1          +      0 +              1  2  21 21     +
       |      21  43242 2  1          |        |            1  324121313      |
       |    1 1     21 11             |        |                1112 2        |
       |            1                 |        |                   1          |
  -100 +                              +   -100 +                              +
       |                              |        |                              |
       ---+----+----+----+----+----+---        ---+----+----+----+----+----+---
          2    4    6    8   10   12              0   20   40   60   80   100
 
                   X1                                      X2
 
       ---+----+----+----+----+----+---        -+------+------+------+------+--
       |                              |        |                              |
   400 +                              +    400 +                              +
       |                              |        |                              |
       |                              |        |                              |
       |                          1   |        |              1               |
   300 +                              +    300 +                              +
       |                              |        |                              |
R      |                              | R      |                              |
E      |                              | E      |                              |
S  200 +                              + S  200 +                              +
I      |                              | I      |                              |
D      |                              | D      |                              |
U      |       1                      | U      |     1                        |
A  100 +                              + A  100 +                              +
L      |   1                          | L      |         1                    |
       |        1 1   1     1     1   |        |    1  2       1    1         |
       |           1 2 1   1  2    1  |        |   1 2 1 21   1               |
     0 +    1  2    1 111  1    1     +      0 +    1 21 211          1       +
       |         1    1322432 21      |        |     11134332 2 1             |
       |              112  2 1        |        |       11 1 4                 |
       |                    1         |        |         1                    |
  -100 +                              +   -100 +                              +
       |                              |        |                              |
       ---+----+----+----+----+----+---        -+------+------+------+------+--
         20   40   60   80   100  120           0      2      4      6      8
 
                   X3                                      X4
 

The SAS System                             14:43 Thursday, December 23, 1999  15

       -+------+------+------+------+--
       |                              |
   400 +                              +
       |                              |
       |                              |
       |                         1    |
   300 +                              +
       |                              |
R      |                              |
E      |                              |
S  200 +                              +
I      |                              |
D      |                              |
U      |    1                         |
A  100 +                              +
L      |       1                      |
       |        2 1            1 1    |
       |        141  1      1         |
     0 +          3121    1     1     +
       |           142251114          |
       |             2113             |
       |                 1            |
  -100 +                              +
       |                              |
       -+------+------+------+------+--
      -200     0     200    400    600
 
                   PRED
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

The SAS System                             14:43 Thursday, December 23, 1999  16

Frequency

   |               *****                                                        
   |               *****                                                        
30 +               *****                                                        
   |               *****                                                        
   |               *****                                                        
   |               *****                                                        
   |               *****                                                        
25 +               *****                                                        
   |               *****                                                        
   |               *****                                                        
   |               *****                                                        
   |               *****                                                        
20 +               *****                                                        
   |               *****                                                        
   |               *****                                                        
   |               *****                                                        
   |               *****                                                        
15 +               *****                                                        
   |               *****                                                        
   |     *****     *****                                                        
   |     *****     *****                                                        
   |     *****     *****                                                        
10 +     *****     *****                                                        
   |     *****     *****                                                        
   |     *****     *****                                                        
   |     *****     *****     *****                                              
   |     *****     *****     *****                                              
 5 +     *****     *****     *****                                              
   |     *****     *****     *****                                              
   |     *****     *****     *****                                              
   |     *****     *****     *****                                              
   |     *****     *****     *****     *****                         *****      
   ----------------------------------------------------------------------------
          -1.2      0.0       1.2       2.4       3.6       4.8       6.0

                               Studentized Residual

The SAS System                             14:43 Thursday, December 23, 1999  17

Univariate Procedure

Variable=SRESID        Studentized Residual

                 Moments

 N                54  Sum Wgts         54
 Mean        0.01449  Sum        0.782471
 Std Dev    1.036889  Variance    1.07514
 Skewness   3.486046  Kurtosis   17.50163
 USS        56.99373  CSS         56.9824
 CV           7155.8  Std Mean   0.141103
 T:Mean=0   0.102692  Pr>|T|       0.9186
 Num ^= 0         54  Num > 0          20
 M(Sign)          -7  Pr>=|M|      0.0759
 Sgn Rank     -137.5  Pr>=|S|      0.2400


            Quantiles(Def=5)

 100% Max  5.765284       99%  5.765284
  75% Q3   0.363088       95%  1.269614
  50% Med  -0.25373       90%  0.943893
  25% Q1   -0.59156       10%  -0.67169
   0% Min  -1.35925        5%  -0.85949
                           1%  -1.35925
 Range      7.12453                    
 Q3-Q1     0.954651                    
 Mode      -1.35925                    


                 Extremes

    Lowest    Obs     Highest    Obs
  -1.35925(       9) 0.986117(      22)
  -0.92356(      15) 1.036339(       5)
  -0.85949(      19) 1.269614(      32)
  -0.80452(      37) 2.203981(      18)
  -0.75638(      10) 5.765284(      13)



The SAS System                             14:43 Thursday, December 23, 1999  18

Univariate Procedure

Variable=SRESID        Studentized Residual

   Stem Leaf                     #  Boxplot
      5 8                        1     *   
      5                                    
      4                                    
      4                                    
      3                                    
      3                                    
      2                                    
      2 2                        1     0   
      1                                    
      1 003                      3     |   
      0 55567789                 8     |   
      0 0112334                  7  +--+--+
     -0 3333332222110           13  *-----*
     -0 99887766666666666555    20  +-----+
     -1 4                        1     |   
        ----+----+----+----+              


                       Normal Probability Plot              
    5.75+                                                *  
        |                                                   
        |                                                   
        |                                                   
        |                                                   
        |                                                   
        |                                                 ++
    2.25+                                            *++++  
        |                                        +++++      
        |                                   +++++* *        
        |                              +++*******           
        |                         ++++****                  
        |                     +*******                      
        |      * * ************                             
   -1.25+  *        +++++                                   
         +----+----+----+----+----+----+----+----+----+----+
             -2        -1         0        +1        +2     



The SAS System                             14:43 Thursday, December 23, 1999  19

Forward Selection Procedure for Dependent Variable Y       

Step 1   Variable X4 Entered        R-square = 0.52175569   C(p) = 93.54543578

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       1        583808.87323857  583808.87323857      56.73   0.0001
Error           52        535122.62676143   10290.81974541
Total           53        1118931.5000000

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP     -71.92123497     38.30031842   36287.70264864       3.53   0.0660
X4            98.05483965     13.01843184  583808.87323857      56.73   0.0001

Bounds on condition number:            1,            1
--------------------------------------------------------------------------------

Step 2   Variable X2 Entered        R-square = 0.61738863   C(p) = 66.84112703

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       2        690815.58520223  345407.79260112      41.15   0.0001
Error           51        428115.91479777    8394.42970192
Total           53        1118931.5000000

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP    -207.06423185     51.27700590  136885.06002868      16.31   0.0002
X2             2.86025069      0.80111375  107006.71196366      12.75   0.0008
X4            81.38681690     12.65078976  347427.38408526      41.39   0.0001

Bounds on condition number:     1.157648,     4.630594
--------------------------------------------------------------------------------

Step 3   Variable X3 Entered        R-square = 0.76233507   C(p) = 25.33532953

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       3        853000.72546101  284333.57515367      53.46   0.0001
Error           50        265930.77453899    5318.61549078
Total           53        1118931.5000000

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP    -402.09953137     53.97534792  295171.77519430      55.50   0.0001
X2             3.61581816      0.65218694  163481.10413865      30.74   0.0001
X3             2.92792762      0.53021756  162185.14025877      30.49   0.0001
X4            52.77323058     11.32476709  115496.12099960      21.72   0.0001

Bounds on condition number:     1.464174,     11.82183
--------------------------------------------------------------------------------

The SAS System                             14:43 Thursday, December 23, 1999  20

Step 4   Variable X1 Entered        R-square = 0.83674875   C(p) =  5.00000000

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       4        936264.53766549  234066.13441637      62.79   0.0001
Error           49        182666.96233451    3727.89719050
Total           53        1118931.5000000

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP    -621.59755029     64.80042601  343025.80578100      92.02   0.0001
X1            33.16382813      7.01727463   83263.81220448      22.34   0.0001
X2             4.27185982      0.56338454  214332.51418236      57.49   0.0001
X3             4.12573829      0.51116093  242857.75291129      65.15   0.0001
X4            14.09156259     12.52532754    4718.50099971       1.27   0.2661

Bounds on condition number:     2.555329,     29.28635
--------------------------------------------------------------------------------

All variables have been entered into the model.

Summary of Forward Selection Procedure for Dependent Variable Y       

        Variable   Number   Partial     Model
Step    Entered        In      R**2      R**2        C(p)           F   Prob>F

   1    X4              1    0.5218    0.5218     93.5454     56.7310   0.0001
   2    X2              2    0.0956    0.6174     66.8411     12.7473   0.0008
   3    X3              3    0.1449    0.7623     25.3353     30.4939   0.0001
   4    X1              4    0.0744    0.8367      5.0000     22.3353   0.0001

The SAS System                             14:43 Thursday, December 23, 1999  21

Model: MODEL1  
Dependent Variable: Y                                                  

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            4 936264.53767 234066.13442       62.788       0.0001
Error           49 182666.96233   3727.89719
C Total         53    1118931.5

    Root MSE      61.05651     R-square       0.8367
    Dep Mean     197.16667     Adj R-sq       0.8234
    C.V.          30.96695

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1   -621.597550   64.80042601        -9.592        0.0001
X1         1     33.163828    7.01727463         4.726        0.0001
X2         1      4.271860    0.56338454         7.582        0.0001
X3         1      4.125738    0.51116093         8.071        0.0001
X4         1     14.091563   12.52532754         1.125        0.2661

              Standardized              
Variable  DF      Estimate     Tolerance

INTERCEP   1    0.00000000     .        
X1         1    0.36588406    0.55586050
X2         1    0.49694120    0.77566563
X3         1    0.60349558    0.59593691
X4         1    0.10380630    0.39133899


The SAS System                             14:43 Thursday, December 23, 1999  22

Backward Elimination Procedure for Dependent Variable Y       

Step 0    All Variables Entered     R-square = 0.83674875   C(p) =  5.00000000

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       4        936264.53766549  234066.13441637      62.79   0.0001
Error           49        182666.96233451    3727.89719050
Total           53        1118931.5000000

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP    -621.59755029     64.80042601  343025.80578100      92.02   0.0001
X1            33.16382813      7.01727463   83263.81220448      22.34   0.0001
X2             4.27185982      0.56338454  214332.51418236      57.49   0.0001
X3             4.12573829      0.51116093  242857.75291129      65.15   0.0001
X4            14.09156259     12.52532754    4718.50099971       1.27   0.2661

Bounds on condition number:     2.555329,     29.28635
--------------------------------------------------------------------------------

Step 1   Variable X4 Removed        R-square = 0.83253178   C(p) =  4.26572723

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       3        931546.03666578  310515.34555526      82.85   0.0001
Error           50        187385.46333422    3747.70926668
Total           53        1118931.5000000

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP    -659.17941990     55.67408110  525372.16182084     140.18   0.0001
X1            38.32274412      5.32589144  194041.43220438      51.78   0.0001
X2             4.56773202      0.49955913  313323.76018378      83.60   0.0001
X3             4.48503622      0.40017410  470760.31016036     125.61   0.0001

Bounds on condition number:     1.030813,     9.186356
--------------------------------------------------------------------------------

All variables left in the model are significant at the 0.1000 level.

Summary of Backward Elimination Procedure for Dependent Variable Y       

        Variable   Number   Partial     Model
Step    Removed        In      R**2      R**2        C(p)           F   Prob>F

   1    X4              3    0.0042    0.8325      4.2657      1.2657   0.2661

The SAS System                             14:43 Thursday, December 23, 1999  23

Model: MODEL2  
Dependent Variable: Y                                                  

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            3 931546.03667 310515.34556       82.855       0.0001
Error           50 187385.46333   3747.70927
C Total         53    1118931.5

    Root MSE      61.21854     R-square       0.8325
    Dep Mean     197.16667     Adj R-sq       0.8225
    C.V.          31.04913

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1   -659.179420   55.67408110       -11.840        0.0001
X1         1     38.322744    5.32589144         7.196        0.0001
X2         1      4.567732    0.49955913         9.144        0.0001
X3         1      4.485036    0.40017410        11.208        0.0001

              Standardized              
Variable  DF      Estimate     Tolerance

INTERCEP   1    0.00000000     .        
X1         1    0.42280044    0.97010805
X2         1    0.53135972    0.99177367
X3         1    0.65605216    0.97750637


The SAS System                             14:43 Thursday, December 23, 1999  24

Stepwise Procedure for Dependent Variable Y       

Step 1   Variable X4 Entered        R-square = 0.52175569   C(p) = 93.54543578

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       1        583808.87323857  583808.87323857      56.73   0.0001
Error           52        535122.62676143   10290.81974541
Total           53        1118931.5000000

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP     -71.92123497     38.30031842   36287.70264864       3.53   0.0660
X4            98.05483965     13.01843184  583808.87323857      56.73   0.0001

Bounds on condition number:            1,            1
--------------------------------------------------------------------------------

Step 2   Variable X2 Entered        R-square = 0.61738863   C(p) = 66.84112703

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       2        690815.58520223  345407.79260112      41.15   0.0001
Error           51        428115.91479777    8394.42970192
Total           53        1118931.5000000

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP    -207.06423185     51.27700590  136885.06002868      16.31   0.0002
X2             2.86025069      0.80111375  107006.71196366      12.75   0.0008
X4            81.38681690     12.65078976  347427.38408526      41.39   0.0001

Bounds on condition number:     1.157648,     4.630594
--------------------------------------------------------------------------------

Step 3   Variable X3 Entered        R-square = 0.76233507   C(p) = 25.33532953

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       3        853000.72546101  284333.57515367      53.46   0.0001
Error           50        265930.77453899    5318.61549078
Total           53        1118931.5000000

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP    -402.09953137     53.97534792  295171.77519430      55.50   0.0001
X2             3.61581816      0.65218694  163481.10413865      30.74   0.0001
X3             2.92792762      0.53021756  162185.14025877      30.49   0.0001
X4            52.77323058     11.32476709  115496.12099960      21.72   0.0001

Bounds on condition number:     1.464174,     11.82183
--------------------------------------------------------------------------------

The SAS System                             14:43 Thursday, December 23, 1999  25

Step 4   Variable X1 Entered        R-square = 0.83674875   C(p) =  5.00000000

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       4        936264.53766549  234066.13441637      62.79   0.0001
Error           49        182666.96233451    3727.89719050
Total           53        1118931.5000000

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP    -621.59755029     64.80042601  343025.80578100      92.02   0.0001
X1            33.16382813      7.01727463   83263.81220448      22.34   0.0001
X2             4.27185982      0.56338454  214332.51418236      57.49   0.0001
X3             4.12573829      0.51116093  242857.75291129      65.15   0.0001
X4            14.09156259     12.52532754    4718.50099971       1.27   0.2661

Bounds on condition number:     2.555329,     29.28635
--------------------------------------------------------------------------------

Step 5   Variable X4 Removed        R-square = 0.83253178   C(p) =  4.26572723

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       3        931546.03666578  310515.34555526      82.85   0.0001
Error           50        187385.46333422    3747.70926668
Total           53        1118931.5000000

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP    -659.17941990     55.67408110  525372.16182084     140.18   0.0001
X1            38.32274412      5.32589144  194041.43220438      51.78   0.0001
X2             4.56773202      0.49955913  313323.76018378      83.60   0.0001
X3             4.48503622      0.40017410  470760.31016036     125.61   0.0001

Bounds on condition number:     1.030813,     9.186356
--------------------------------------------------------------------------------

All variables left in the model are significant at the 0.1500 level.
No other variable met the 0.0500 significance level for entry into the model.

Summary of Stepwise Procedure for Dependent Variable Y       

       Variable        Number   Partial    Model
Step   Entered Removed     In      R**2     R**2      C(p)          F   Prob>F

   1   X4                   1    0.5218   0.5218   93.5454    56.7310   0.0001
   2   X2                   2    0.0956   0.6174   66.8411    12.7473   0.0008
   3   X3                   3    0.1449   0.7623   25.3353    30.4939   0.0001
   4   X1                   4    0.0744   0.8367    5.0000    22.3353   0.0001
   5           X4           3    0.0042   0.8325    4.2657     1.2657   0.2661

The SAS System                             14:43 Thursday, December 23, 1999  26

Model: MODEL3  
Dependent Variable: Y                                                  

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            3 931546.03667 310515.34556       82.855       0.0001
Error           50 187385.46333   3747.70927
C Total         53    1118931.5

    Root MSE      61.21854     R-square       0.8325
    Dep Mean     197.16667     Adj R-sq       0.8225
    C.V.          31.04913

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1   -659.179420   55.67408110       -11.840        0.0001
X1         1     38.322744    5.32589144         7.196        0.0001
X2         1      4.567732    0.49955913         9.144        0.0001
X3         1      4.485036    0.40017410        11.208        0.0001

              Standardized              
Variable  DF      Estimate     Tolerance

INTERCEP   1    0.00000000     .        
X1         1    0.42280044    0.97010805
X2         1    0.53135972    0.99177367
X3         1    0.65605216    0.97750637


The SAS System                             14:43 Thursday, December 23, 1999  27

Descriptive Statistics

Variables                 Sum                Mean      Uncorrected SS

INTERCEP                   54                   1                  54
X1                      312.3        5.7833333333             1942.33
X2                       3415        63.240740741              231109
X3                       4164        77.111111111              345032
X4                     148.19        2.7442592593            467.3919
LOGY                 119.1318        2.2061444444        266.79473098


Variables            Variance       Std Deviation

INTERCEP                    0                   0
X1               2.5697169811        1.6030336806
X2               285.69566737        16.902534347
X3               451.72327044        21.253782497
X4               1.1456626485        1.0703563185
LOGY              0.074957967        0.2737845267


Correlation

CORR             X1             X2             X3             X4           LOGY

X1           1.0000         0.0901        -0.1496         0.5024         0.3464
X2           0.0901         1.0000        -0.0236         0.3690         0.5929
X3          -0.1496        -0.0236         1.0000         0.4164         0.6651
X4           0.5024         0.3690         0.4164         1.0000         0.7262
LOGY         0.3464         0.5929         0.6651         0.7262         1.0000

The SAS System                             14:43 Thursday, December 23, 1999  28

Model: MODEL1  
Dependent Variable: LOGY                                               

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            4      3.86300      0.96575      431.097       0.0001
Error           49      0.10977      0.00224
C Total         53      3.97277

    Root MSE       0.04733     R-square       0.9724
    Dep Mean       2.20614     Adj R-sq       0.9701
    C.V.           2.14541

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1      0.488756    0.05023319         9.730        0.0001
X1         1      0.068520    0.00543978        12.596        0.0001
X2         1      0.009254    0.00043673        21.189        0.0001
X3         1      0.009475    0.00039625        23.910        0.0001
X4         1      0.001925    0.00970961         0.198        0.8436

                                 Squared       Squared
              Standardized  Semi-partial       Partial              
Variable  DF      Estimate  Corr Type II  Corr Type II     Tolerance

INTERCEP   1    0.00000000     .             .             .        
X1         1    0.40119198    0.08946853    0.76404020    0.55586050
X2         1    0.57131764    0.25318025    0.90160386    0.77566563
X3         1    0.73550521    0.32238275    0.92105814    0.59593691
X4         1    0.00752741    0.00002217    0.00080187    0.39133899

                  Variance
Variable  DF     Inflation

INTERCEP   1    0.00000000
X1         1    1.79901252
X2         1    1.28921530
X3         1    1.67802997
X4         1    2.55532933



Correlation of Estimates

CORRB         INTERCEP            X1            X2            X3            X4

INTERCEP        1.0000       -0.7167       -0.6382       -0.7516        0.5155
X1             -0.7167        1.0000        0.2464        0.4958       -0.6535
X2             -0.6382        0.2464        1.0000        0.2987       -0.4668
X3             -0.7516        0.4958        0.2987        1.0000       -0.6248
X4              0.5155       -0.6535       -0.4668       -0.6248        1.0000


The SAS System                             14:43 Thursday, December 23, 1999  29

Durbin-Watson D             2.146
(For Number of Obs.)           54
1st Order Autocorrelation  -0.073


The SAS System                             14:43 Thursday, December 23, 1999  30

        Dep Var   Predict   Std Err             Std Err   Student
  Obs    LOGY       Value   Predict  Residual  Residual  Residual

    1    2.3010    2.2940     0.009   0.00698     0.046     0.150
    2    2.0043    2.0128     0.009  -0.00849     0.046    -0.183
    3    2.3096    2.3138     0.015  -0.00424     0.045    -0.095
    4    2.0043    2.0020     0.014   0.00229     0.045     0.050
    5    2.7067    2.7226     0.017   -0.0159     0.044    -0.359
    6    1.9031    1.9227     0.013   -0.0196     0.045    -0.433
    7    1.9031    1.9056     0.010  -0.00248     0.046    -0.054
    8    2.1038    2.1439     0.012   -0.0401     0.046    -0.875
    9    2.3054    2.4058     0.011   -0.1004     0.046    -2.187
   10    2.3075    2.3408     0.013   -0.0333     0.046    -0.732
   11    2.5172    2.4921     0.012    0.0251     0.046     0.548
   12    1.8129    1.8308     0.014   -0.0179     0.045    -0.394
   13    2.9191    2.8623     0.019    0.0568     0.043     1.308
   14    2.5185    2.4956     0.012    0.0229     0.046     0.499
   15    2.2253    2.2315     0.011  -0.00616     0.046    -0.133
   16    2.3365    2.3295     0.013   0.00700     0.045     0.154
   17    1.9395    1.9575     0.021   -0.0180     0.043    -0.422
   18    1.5315    1.6057     0.018   -0.0742     0.044    -1.700
   19    2.3324    2.3262     0.009   0.00620     0.046     0.134
   20    2.2355    2.2301     0.008   0.00545     0.047     0.117
   21    2.0374    2.0518     0.010   -0.0144     0.046    -0.312
   22    2.1335    1.9941     0.018    0.1394     0.044     3.176
   23    1.8451    1.8368     0.017   0.00834     0.044     0.188
   24    2.3424    2.3276     0.008    0.0148     0.047     0.318
   25    2.4409    2.4196     0.011    0.0213     0.046     0.464
   26    2.1584    2.1491     0.011   0.00935     0.046     0.203
   27    2.2577    2.1458     0.008    0.1119     0.047     2.402
   28    2.7589    2.8230     0.024   -0.0641     0.041    -1.579
   29    1.8573    1.8806     0.014   -0.0233     0.045    -0.513
   30    2.2504    2.1535     0.010    0.0969     0.046     2.094
   31    1.8513    1.9176     0.015   -0.0663     0.045    -1.480
   32    1.7634    1.7241     0.022    0.0393     0.042     0.941
   33    2.0645    2.0757     0.014   -0.0112     0.045    -0.249
   34    2.4698    2.4400     0.009    0.0298     0.047     0.642
   35    2.0607    2.0638     0.008  -0.00310     0.047    -0.067
   36    2.2648    2.2669     0.011  -0.00206     0.046    -0.045
   37    2.0719    2.1705     0.015   -0.0986     0.045    -2.202
   38    2.0792    1.9904     0.026    0.0888     0.039     2.264
   39    2.1790    2.1069     0.008    0.0721     0.047     1.544
   40    2.1703    2.1772     0.012  -0.00692     0.046    -0.151
   41    1.9777    1.9842     0.009  -0.00652     0.046    -0.141
   42    1.8751    1.9350     0.018   -0.0599     0.044    -1.372
   43    2.6840    2.7337     0.024   -0.0497     0.041    -1.220
   44    2.1847    2.1874     0.008  -0.00269     0.047    -0.058
   45    2.2810    2.3183     0.017   -0.0373     0.044    -0.845
   46    2.0899    2.1059     0.012   -0.0160     0.046    -0.351
   47    2.4928    2.4828     0.013   0.00998     0.046     0.219
   48    2.5999    2.5783     0.015    0.0216     0.045     0.481
   49    2.1987    2.1933     0.008   0.00542     0.047     0.116
   50    2.4914    2.4995     0.020  -0.00806     0.043    -0.188
   51    2.0934    2.0931     0.014  0.000261     0.045     0.006
   52    2.0969    2.0952     0.020   0.00170     0.043     0.040
   53    2.2967    2.2831     0.011    0.0136     0.046     0.295
   54    2.4955    2.5019     0.017  -0.00638     0.044    -0.144

The SAS System                             14:43 Thursday, December 23, 1999  31

                          Cook's
  Obs    -2-1-0 1 2            D

    1  |      |      |     0.000
    2  |      |      |     0.000
    3  |      |      |     0.000
    4  |      |      |     0.000
    5  |      |      |     0.004
    6  |      |      |     0.003
    7  |      |      |     0.000
    8  |     *|      |     0.010
    9  |  ****|      |     0.060
   10  |     *|      |     0.009
   11  |      |*     |     0.004
   12  |      |      |     0.003
   13  |      |**    |     0.064
   14  |      |      |     0.003
   15  |      |      |     0.000
   16  |      |      |     0.000
   17  |      |      |     0.008
   18  |   ***|      |     0.102
   19  |      |      |     0.000
   20  |      |      |     0.000
   21  |      |      |     0.001
   22  |      |******|     0.329
   23  |      |      |     0.001
   24  |      |      |     0.001
   25  |      |      |     0.003
   26  |      |      |     0.000
   27  |      |****  |     0.037
   28  |   ***|      |     0.180
   29  |     *|      |     0.005
   30  |      |****  |     0.039
   31  |    **|      |     0.052
   32  |      |*     |     0.050
   33  |      |      |     0.001
   34  |      |*     |     0.003
   35  |      |      |     0.000
   36  |      |      |     0.000
   37  |  ****|      |     0.115
   38  |      |****  |     0.468
   39  |      |***   |     0.013
   40  |      |      |     0.000
   41  |      |      |     0.000
   42  |    **|      |     0.066
   43  |    **|      |     0.105
   44  |      |      |     0.000
   45  |     *|      |     0.022
   46  |      |      |     0.002
   47  |      |      |     0.001
   48  |      |      |     0.005
   49  |      |      |     0.000
   50  |      |      |     0.002
   51  |      |      |     0.000
   52  |      |      |     0.000
   53  |      |      |     0.001
   54  |      |      |     0.001


The SAS System                             14:43 Thursday, December 23, 1999  32

Sum of Residuals                      0
Sum of Squared Residuals         0.1098
Predicted Resid SS (Press)       0.1456


The SAS System                             14:43 Thursday, December 23, 1999  33

      -+-----+-----+-----+-----+-----+-       -+-----+-----+-----+-----+-----+-
      |                               |       |                               |
  3.0 +                               +   3.0 +                               +
      |           1                   |       |                             1 |
      |                               |       |                               |
      |                            1  |       |                       1       |
      |                 1  1          |       |                    1     1    |
      |                               |       |                               |
L     |        1                      | L     |                          1    |
O 2.5 +      1 1  2 1      1          + O 2.5 +                      21 3     +
G     |             1                 | G     |                  1            |
Y     |           1    2              | Y     |                    2 1        |
      |    11    21111 1              |       |               111111  3       |
      |        11 1  1  1             |       |                 2111          |
      |    1     11                   |       |                1 1      1     |
      |  1  1 1 12  12                |       |  1         1   111 1 11  1    |
  2.0 +         11   1                +   2.0 +               1  1   1        +
      |           21                  |       |           1  1           1    |
      |    11    1   1                |       |        2       1  1           |
      |              1     1          |       |              11               |
      |                               |       |                               |
      |                               |       |                               |
      |                               |       |                               |
  1.5 +     1                         +   1.5 +               1               +
      -+-----+-----+-----+-----+-----+-       -+-----+-----+-----+-----+-----+-
       2     4     6     8    10    12         0    20    40    60    80   100
 
                  X1                                      X2
 
      -+-----+-----+-----+-----+-----+-       --+---+---+---+---+---+---+---+--
      |                               |       |                               |
  3.0 +                               +   3.0 +                               +
      |                            1  |       |                 1             |
      |                               |       |                               |
      |                     1         |       |                       1       |
      |                    1        1 |       |                  1        1   |
      |                               |       |                               |
L     |                        1      | L     |                 1             |
O 2.5 +                1  11 1  11    + O 2.5 +             12  111           +
G     |                        1      | G     |             1                 |
Y     |              1 1   1          | Y     |           1   2               |
      |            1     112 3 1      |       |       1  26                   |
      |              1  3  1          |       |           121 1               |
      |          1     1   1          |       |     1  1      1               |
      |      1 1      111111         1|       |      1  2 131 1               |
  2.0 +      1       1 1              +   2.0 +        21                     +
      |  1          1  1              |       |       1 1   1                 |
      |           1  2         1      |       |    1 1  1  1                  |
      | 1     1                       |       |        1  1                   |
      |                               |       |                               |
      |                               |       |                               |
      |                               |       |                               |
  1.5 +      1                        +   1.5 +       1                       +
      -+-----+-----+-----+-----+-----+-       --+---+---+---+---+---+---+---+--
      20    40    60    80    100  120          0   1   2   3   4   5   6   7
 
                  X3                                      X4
 

The SAS System                             14:43 Thursday, December 23, 1999  34

       ---+----+----+----+----+----+---        ---+----+----+----+----+----+---
       |                              |        |                              |
   0.2 +                              +    0.2 +                              +
       |                              |        |                              |
       |                              |        |                              |
       |                              |        |                              |
       |      1                       |        |                       1      |
       |                              |        |                              |
R      |          1                   | R      |               1              |
E  0.1 +            1                 + E  0.1 +                     1        +
S      |        1                     | S      |    1                         |
I      |         1                    | I      |                 1            |
D      |            1                 | D      |                          1   |
U      |                   1          | U      |             1                |
A      |         1  21                | A      |                    1  21     |
L      |        1   221               | L      |         1       3 11         |
   0.0 +          34 3213  1          +    0.0 +              2231221211      +
       |       1  3 211  1            |        |            2  2 21    2      |
       |      1   1                   |        |                1    1        |
       |      2            1          |        |                   1 1  1     |
       |      1                  1    |        |         1           1        |
       |     11                       |        |               1  1           |
       |                              |        |                              |
  -0.1 +    1       1                 +   -0.1 +                   1 1        +
       ---+----+----+----+----+----+---        ---+----+----+----+----+----+---
          2    4    6    8   10   12              0   20   40   60   80   100
 
                   X1                                      X2
 
       ---+----+----+----+----+----+---        -+------+------+------+------+--
       |                              |        |                              |
   0.2 +                              +    0.2 +                              +
       |                              |        |                              |
       |                              |        |                              |
       |                              |        |                              |
       |          1                   |        |    1                         |
       |                              |        |                              |
R      |                   1          | R      |         1                    |
E  0.1 +            1                 + E  0.1 +         1                    +
S      |                           1  | S      |          1                   |
I      |                1             | I      |         1                    |
D      |                          1   | D      |              1               |
U      |   1                          | U      |         1                    |
A      |                  111 1       | A      |            1 3               |
L      |              11  11  1 1     | L      |       11 112                 |
   0.0 +       2 1   1233112  1       +    0.0 +    1 2323222                 +
       |    1   1     121 1    1  1   |        |     111  211  11             |
       |           1         1        |        |        11                    |
       |                 1 11         |        |     1   1            1       |
       |                    1 1       |        |     1              1         |
       |       1     1                |        |   1 1                        |
       |                              |        |                              |
  -0.1 +                   11         +   -0.1 +       1 1                    +
       ---+----+----+----+----+----+---        -+------+------+------+------+--
         20   40   60   80   100  120           0      2      4      6      8
 
                   X3                                      X4
 

The SAS System                             14:43 Thursday, December 23, 1999  35

       -----+------+------+------+-----
       |                              |
   0.2 +                              +
       |                              |
       |                              |
       |                              |
       |           1                  |
       |                              |
R      |             1                |
E  0.1 +             1                +
S      |           1                  |
I      |            1                 |
D      |                       1      |
U      |       1                      |
A      |                 121          |
L      |         1   1 1111           |
   0.0 +          1231432 1           +
       |         1213     1  1        |
       |         1      1             |
       |             1 1     1        |
       |          1            1      |
       |     1    1                   |
       |                              |
  -0.1 +             1   1            +
       -----+------+------+------+-----
           1.5    2.0    2.5    3.0
 
                   PRED
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

The SAS System                             14:43 Thursday, December 23, 1999  36

Frequency

   |                            *****                                           
   |                            *****                                           
   |                            *****                                           
   |                            *****                                           
30 +                            *****                                           
   |                            *****                                           
   |                            *****                                           
   |                            *****                                           
   |                            *****                                           
25 +                            *****                                           
   |                            *****                                           
   |                            *****                                           
   |                            *****                                           
   |                            *****                                           
20 +                            *****                                           
   |                            *****                                           
   |                            *****                                           
   |                            *****                                           
   |                            *****                                           
15 +                            *****                                           
   |                            *****                                           
   |                            *****                                           
   |                            *****                                           
   |                            *****                                           
10 +                            *****                                           
   |                            *****                                           
   |                            *****                                           
   |                 *****      *****                                           
   |                 *****      *****                                           
 5 +                 *****      *****                                           
   |      *****      *****      *****      *****      *****                     
   |      *****      *****      *****      *****      *****                     
   |      *****      *****      *****      *****      *****                     
   |      *****      *****      *****      *****      *****      *****          
   -------------------------------------------------------------------------
            -2         -1         0          1          2          3

                              Studentized Residual

The SAS System                             14:43 Thursday, December 23, 1999  37

Univariate Procedure

Variable=SRESID2       Studentized Residual

                 Moments

 N                54  Sum Wgts         54
 Mean       -0.00244  Sum        -0.13196
 Std Dev    1.029039  Variance   1.058921
 Skewness   0.627116  Kurtosis   1.794059
 USS        56.12312  CSS         56.1228
 CV         -42110.8  Std Mean   0.140034
 T:Mean=0   -0.01745  Pr>|T|       0.9861
 Num ^= 0         54  Num > 0          25
 M(Sign)          -2  Pr>=|M|      0.6835
 Sgn Rank      -49.5  Pr>=|S|      0.6740


            Quantiles(Def=5)

 100% Max  3.175723       99%  3.175723
  75% Q3   0.294823       95%   2.26434
  50% Med  -0.05574       90%  1.307878
  25% Q1   -0.39434       10%  -1.37195
   0% Min  -2.20248        5%  -1.70045
                           1%  -2.20248
 Range     5.378208                    
 Q3-Q1     0.689165                    
 Mode      -2.20248                    


                 Extremes

    Lowest    Obs     Highest    Obs
  -2.20248(      37)  1.54351(      39)
  -2.18732(       9) 2.093907(      30)
  -1.70045(      18)  2.26434(      38)
   -1.5787(      28) 2.402034(      27)
  -1.48006(      31) 3.175723(      22)


   Stem Leaf                     #  Boxplot
      3 2                        1     *   
      2                                    
      2 134                      3     0   
      1 5                        1     0   
      1 3                        1     |   
      0 555569                   6     |   
      0 0011112222233           13  +-----+
     -0 444443222211111110      18  *--+--*
     -0 9875                     4     |   
     -1 42                       2     |   
     -1 765                      3     0   
     -2 22                       2     0   
        ----+----+----+----+              



The SAS System                             14:43 Thursday, December 23, 1999  38

Univariate Procedure

Variable=SRESID2       Studentized Residual

                       Normal Probability Plot              
    3.25+                                                *  
        |                                                  +
        |                                        * * *+++++ 
        |                                       *+++++      
        |                                   +++*+           
        |                              +++++***             
        |                          *********                
        |                 **********                        
        |              ***++++                              
        |           ***++                                   
        |      ++*+*                                        
   -2.25+ +*+++*                                            
         +----+----+----+----+----+----+----+----+----+----+
             -2        -1         0        +1        +2     



The SAS System                             14:43 Thursday, December 23, 1999  39

Forward Selection Procedure for Dependent Variable LOGY    

Step 1   Variable X4 Entered        R-square = 0.52737486   C(p) =788.14813627

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       1             2.09514023       2.09514023      58.02   0.0001
Error           52             1.87763202       0.03610831
Total           53             3.97277225

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       1.69638489      0.07174324      20.18803240     559.10   0.0001
X4             0.18575488      0.02438581       2.09514023      58.02   0.0001

Bounds on condition number:            1,            1
--------------------------------------------------------------------------------

Step 2   Variable X3 Entered        R-square = 0.68653440   C(p) =507.89639740

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       2             2.72744481       1.36372240      55.85   0.0001
Error           51             1.24532745       0.02441819
Total           53             3.97277225

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       1.38877757      0.08446782       6.60079464     270.32   0.0001
X3             0.00565254      0.00111080       0.63230458      25.89   0.0001
X4             0.13901497      0.02205693       0.96994304      39.72   0.0001

Bounds on condition number:     1.209789,     4.839155
--------------------------------------------------------------------------------

Step 3   Variable X2 Entered        R-square = 0.88290076   C(p) =161.66248928

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       3             3.50756363       1.16918788     125.66   0.0001
Error           50             0.46520862       0.00930417
Total           53             3.97277225

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       0.94226338      0.07138961       1.62088545     174.21   0.0001
X2             0.00789866      0.00086260       0.78011882      83.85   0.0001
X3             0.00699974      0.00070128       0.92694429      99.63   0.0001
X4             0.08184608      0.01497852       0.27780226      29.86   0.0001

Bounds on condition number:     1.464174,     11.82183
--------------------------------------------------------------------------------

The SAS System                             14:43 Thursday, December 23, 1999  40

Step 4   Variable X1 Entered        R-square = 0.97236929   C(p) =  5.00000000

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       4             3.86300172       0.96575043     431.10   0.0001
Error           49             0.10977053       0.00224021
Total           53             3.97277225

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       0.48875592      0.05023319       0.21207636      94.67   0.0001
X1             0.06852018      0.00543978       0.35543809     158.66   0.0001
X2             0.00925411      0.00043673       1.00582746     448.99   0.0001
X3             0.00947455      0.00039625       1.28075323     571.71   0.0001
X4             0.00192542      0.00970961       0.00008809       0.04   0.8436

Bounds on condition number:     2.555329,     29.28635
--------------------------------------------------------------------------------

All variables have been entered into the model.

Summary of Forward Selection Procedure for Dependent Variable LOGY    

        Variable   Number   Partial     Model
Step    Entered        In      R**2      R**2        C(p)           F   Prob>F

   1    X4              1    0.5274    0.5274    788.1481     58.0238   0.0001
   2    X3              2    0.1592    0.6865    507.8964     25.8948   0.0001
   3    X2              3    0.1964    0.8829    161.6625     83.8461   0.0001
   4    X1              4    0.0895    0.9724      5.0000    158.6625   0.0001

The SAS System                             14:43 Thursday, December 23, 1999  41

Model: MODEL1  
Dependent Variable: LOGY                                               

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            4      3.86300      0.96575      431.097       0.0001
Error           49      0.10977      0.00224
C Total         53      3.97277

    Root MSE       0.04733     R-square       0.9724
    Dep Mean       2.20614     Adj R-sq       0.9701
    C.V.           2.14541

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1      0.488756    0.05023319         9.730        0.0001
X1         1      0.068520    0.00543978        12.596        0.0001
X2         1      0.009254    0.00043673        21.189        0.0001
X3         1      0.009475    0.00039625        23.910        0.0001
X4         1      0.001925    0.00970961         0.198        0.8436

              Standardized              
Variable  DF      Estimate     Tolerance

INTERCEP   1    0.00000000     .        
X1         1    0.40119198    0.55586050
X2         1    0.57131764    0.77566563
X3         1    0.73550521    0.59593691
X4         1    0.00752741    0.39133899


The SAS System                             14:43 Thursday, December 23, 1999  42

Backward Elimination Procedure for Dependent Variable LOGY    

Step 0    All Variables Entered     R-square = 0.97236929   C(p) =  5.00000000

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       4             3.86300172       0.96575043     431.10   0.0001
Error           49             0.10977053       0.00224021
Total           53             3.97277225

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       0.48875592      0.05023319       0.21207636      94.67   0.0001
X1             0.06852018      0.00543978       0.35543809     158.66   0.0001
X2             0.00925411      0.00043673       1.00582746     448.99   0.0001
X3             0.00947455      0.00039625       1.28075323     571.71   0.0001
X4             0.00192542      0.00970961       0.00008809       0.04   0.8436

Bounds on condition number:     2.555329,     29.28635
--------------------------------------------------------------------------------

Step 1   Variable X4 Removed        R-square = 0.97234711   C(p) =  3.03932316

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       3             3.86291363       1.28763788     586.04   0.0001
Error           50             0.10985863       0.00219717
Total           53             3.97277225

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       0.48362086      0.04262871       0.28279376     128.71   0.0001
X1             0.06922508      0.00407795       0.63315225     288.17   0.0001
X2             0.00929454      0.00038250       1.29732180     590.45   0.0001
X3             0.00952364      0.00030641       2.12262768     966.07   0.0001

Bounds on condition number:     1.030813,     9.186356
--------------------------------------------------------------------------------

All variables left in the model are significant at the 0.1000 level.

Summary of Backward Elimination Procedure for Dependent Variable LOGY    

        Variable   Number   Partial     Model
Step    Removed        In      R**2      R**2        C(p)           F   Prob>F

   1    X4              3    0.0000    0.9723      3.0393      0.0393   0.8436

The SAS System                             14:43 Thursday, December 23, 1999  43

Model: MODEL2  
Dependent Variable: LOGY                                               

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            3      3.86291      1.28764      586.043       0.0001
Error           50      0.10986      0.00220
C Total         53      3.97277

    Root MSE       0.04687     R-square       0.9723
    Dep Mean       2.20614     Adj R-sq       0.9707
    C.V.           2.12470

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1      0.483621    0.04262871        11.345        0.0001
X1         1      0.069225    0.00407795        16.975        0.0001
X2         1      0.009295    0.00038250        24.299        0.0001
X3         1      0.009524    0.00030641        31.082        0.0001

              Standardized              
Variable  DF      Estimate     Tolerance

INTERCEP   1    0.00000000     .        
X1         1    0.40531921    0.97010805
X2         1    0.57381347    0.99177367
X3         1    0.73931630    0.97750637


The SAS System                             14:43 Thursday, December 23, 1999  44

Stepwise Procedure for Dependent Variable LOGY    

Step 1   Variable X4 Entered        R-square = 0.52737486   C(p) =788.14813627

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       1             2.09514023       2.09514023      58.02   0.0001
Error           52             1.87763202       0.03610831
Total           53             3.97277225

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       1.69638489      0.07174324      20.18803240     559.10   0.0001
X4             0.18575488      0.02438581       2.09514023      58.02   0.0001

Bounds on condition number:            1,            1
--------------------------------------------------------------------------------

Step 2   Variable X3 Entered        R-square = 0.68653440   C(p) =507.89639740

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       2             2.72744481       1.36372240      55.85   0.0001
Error           51             1.24532745       0.02441819
Total           53             3.97277225

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       1.38877757      0.08446782       6.60079464     270.32   0.0001
X3             0.00565254      0.00111080       0.63230458      25.89   0.0001
X4             0.13901497      0.02205693       0.96994304      39.72   0.0001

Bounds on condition number:     1.209789,     4.839155
--------------------------------------------------------------------------------

Step 3   Variable X2 Entered        R-square = 0.88290076   C(p) =161.66248928

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       3             3.50756363       1.16918788     125.66   0.0001
Error           50             0.46520862       0.00930417
Total           53             3.97277225

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       0.94226338      0.07138961       1.62088545     174.21   0.0001
X2             0.00789866      0.00086260       0.78011882      83.85   0.0001
X3             0.00699974      0.00070128       0.92694429      99.63   0.0001
X4             0.08184608      0.01497852       0.27780226      29.86   0.0001

Bounds on condition number:     1.464174,     11.82183
--------------------------------------------------------------------------------

The SAS System                             14:43 Thursday, December 23, 1999  45

Step 4   Variable X1 Entered        R-square = 0.97236929   C(p) =  5.00000000

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       4             3.86300172       0.96575043     431.10   0.0001
Error           49             0.10977053       0.00224021
Total           53             3.97277225

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       0.48875592      0.05023319       0.21207636      94.67   0.0001
X1             0.06852018      0.00543978       0.35543809     158.66   0.0001
X2             0.00925411      0.00043673       1.00582746     448.99   0.0001
X3             0.00947455      0.00039625       1.28075323     571.71   0.0001
X4             0.00192542      0.00970961       0.00008809       0.04   0.8436

Bounds on condition number:     2.555329,     29.28635
--------------------------------------------------------------------------------

Step 5   Variable X4 Removed        R-square = 0.97234711   C(p) =  3.03932316

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       3             3.86291363       1.28763788     586.04   0.0001
Error           50             0.10985863       0.00219717
Total           53             3.97277225

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       0.48362086      0.04262871       0.28279376     128.71   0.0001
X1             0.06922508      0.00407795       0.63315225     288.17   0.0001
X2             0.00929454      0.00038250       1.29732180     590.45   0.0001
X3             0.00952364      0.00030641       2.12262768     966.07   0.0001

Bounds on condition number:     1.030813,     9.186356
--------------------------------------------------------------------------------

All variables left in the model are significant at the 0.1500 level.
No other variable met the 0.0500 significance level for entry into the model.

Summary of Stepwise Procedure for Dependent Variable LOGY    

       Variable        Number   Partial    Model
Step   Entered Removed     In      R**2     R**2      C(p)          F   Prob>F

   1   X4                   1    0.5274   0.5274  788.1481    58.0238   0.0001
   2   X3                   2    0.1592   0.6865  507.8964    25.8948   0.0001
   3   X2                   3    0.1964   0.8829  161.6625    83.8461   0.0001
   4   X1                   4    0.0895   0.9724    5.0000   158.6625   0.0001
   5           X4           3    0.0000   0.9723    3.0393     0.0393   0.8436

The SAS System                             14:43 Thursday, December 23, 1999  46

Model: MODEL3  
Dependent Variable: LOGY                                               

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            3      3.86291      1.28764      586.043       0.0001
Error           50      0.10986      0.00220
C Total         53      3.97277

    Root MSE       0.04687     R-square       0.9723
    Dep Mean       2.20614     Adj R-sq       0.9707
    C.V.           2.12470

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1      0.483621    0.04262871        11.345        0.0001
X1         1      0.069225    0.00407795        16.975        0.0001
X2         1      0.009295    0.00038250        24.299        0.0001
X3         1      0.009524    0.00030641        31.082        0.0001

              Standardized              
Variable  DF      Estimate     Tolerance

INTERCEP   1    0.00000000     .        
X1         1    0.40531921    0.97010805
X2         1    0.57381347    0.99177367
X3         1    0.73931630    0.97750637


The SAS System                             14:43 Thursday, December 23, 1999  47

Model: MODEL1  
Dependent Variable: X1                                                 

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            3     60.48958     20.16319       13.317       0.0001
Error           50     75.70542      1.51411
C Total         53    136.19500

    Root MSE       1.23049     R-square       0.4441
    Dep Mean       5.78333     Adj R-sq       0.4108
    C.V.          21.27650

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1      6.618597    0.91069854         7.268        0.0001
X2         1     -0.019782    0.01100402        -1.798        0.0783
X3         1     -0.036118    0.00894609        -4.037        0.0002
X4         1      1.166381    0.19107702         6.104        0.0001

              Standardized
Variable  DF      Estimate

INTERCEP   1    0.00000000
X2         1   -0.20858157
X3         1   -0.47886942
X4         1    0.77880058


The SAS System                             14:43 Thursday, December 23, 1999  48

Model: MODEL2  
Dependent Variable: X2                                                 

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            3   3396.84194   1132.28065        4.820       0.0050
Error           50  11745.02843    234.90057
C Total         53  15141.87037

    Root MSE      15.32647     R-square       0.2243
    Dep Mean      63.24074     Adj R-sq       0.1778
    C.V.          24.23512

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1     73.410773   12.52232622         5.862        0.0001
X1         1     -3.068979    1.70717633        -1.798        0.0783
X3         1     -0.271051    0.12245259        -2.214        0.0315
X4         1     10.377992    2.78054642         3.732        0.0005

              Standardized
Variable  DF      Estimate

INTERCEP   1    0.00000000
X1         1   -0.29106144
X3         1   -0.34082752
X4         1    0.65718839


The SAS System                             14:43 Thursday, December 23, 1999  49

Model: MODEL3  
Dependent Variable: X3                                                 

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            3   9673.80903   3224.60301       11.300       0.0001
Error           50  14267.52430    285.35049
C Total         53  23941.33333

    Root MSE      16.89232     R-square       0.4041
    Dep Mean      77.11111     Adj R-sq       0.3683
    C.V.          21.90647

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1     95.287238   11.82476250         8.058        0.0001
X1         1     -6.806834    1.68598977        -4.037        0.0002
X2         1     -0.329264    0.14875190        -2.214        0.0315
X4         1     15.309410    2.70574448         5.658        0.0001

              Standardized
Variable  DF      Estimate

INTERCEP   1    0.00000000
X1         1   -0.51339493
X2         1   -0.26185471
X4         1    0.77099327


The SAS System                             14:43 Thursday, December 23, 1999  50

Model: MODEL4  
Dependent Variable: X4                                                 

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F

Model            3     36.95797     12.31932       25.922       0.0001
Error           50     23.76215      0.47524
C Total         53     60.72012

    Root MSE       0.68938     R-square       0.6087
    Dep Mean       2.74426     Adj R-sq       0.5852
    C.V.          25.12076

Parameter Estimates

                 Parameter      Standard    T for H0:               
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

INTERCEP   1     -2.666977    0.62694289        -4.254        0.0001
X1         1      0.366100    0.05997458         6.104        0.0001
X2         1      0.020996    0.00562551         3.732        0.0005
X3         1      0.025497    0.00450634         5.658        0.0001

              Standardized
Variable  DF      Estimate

INTERCEP   1    0.00000000
X1         1    0.54829410
X2         1    0.33156483
X3         1    0.50629475