SAS Textbook Examples
Applied Linear Statistical Models by Neter, Kutner, et. al.
Chapter 14: Logistic Regression, Poisson Regression and Generalized Linear Models

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options nocenter nodate;
Inputting the Programming Task data, table 14.1, p. 576.
data ch14tab01;
  input x y ;
  label x = 'Experience'
        y = 'Success';
cards;
14  0  0.310262
29  0  0.835263
 6  0  0.109996
25  1  0.726602
18  1  0.461837
 4  0  0.082130
18  0  0.461837
12  0  0.245666
22  1  0.620812
 6  0  0.109996
30  1  0.856299
11  0  0.216980
30  1  0.856299
 5  0  0.095154
20  1  0.542404
13  0  0.276802
 9  0  0.167100
32  1  0.891664
24  0  0.693379
13  1  0.276802
19  0  0.502134
 4  0  0.082130
28  1  0.811825
22  1  0.620812
 8  1  0.145815
;
run;
Logistic Regression, table 14.1, p. 576.
proc logistic data = ch14tab01 descending;
  model y = x;
  output out = temp resdev=devresidual p = fittedp;
run;
proc print data = temp;
  var x y  fittedp devresidual;
run;
The LOGISTIC Procedure

                    Model Information

Data Set                      WORK.CH14TAB01
Response Variable             y                    Success
Number of Response Levels     2
Number of Observations        25
Link Function                 Logit
Optimization Technique        Fisher's scoring

          Response Profile

 Ordered                      Total
   Value            y     Frequency

       1            1            11
       2            0            14

                    Model Convergence Status

         Convergence criterion (GCONV=1E-8) satisfied.

         Model Fit Statistics

                              Intercept
               Intercept         and
Criterion        Only        Covariates

AIC               36.296         29.425
SC                37.515         31.862
-2 Log L          34.296         25.425

        Testing Global Null Hypothesis: BETA=0

Test                 Chi-Square       DF     Pr > ChiSq

Likelihood Ratio         8.8719        1         0.0029
Score                    7.9742        1         0.0047
Wald                     6.1760        1         0.0129

             Analysis of Maximum Likelihood Estimates

                               Standard
Parameter    DF    Estimate       Error    Chi-Square    Pr > ChiSq

Intercept     1     -3.0597      1.2594        5.9029        0.0151
x             1      0.1615      0.0650        6.1760        0.0129

The LOGISTIC Procedure

           Odds Ratio Estimates

             Point          95% Wald
Effect    Estimate      Confidence Limits

x            1.175       1.035       1.335

Association of Predicted Probabilities and Observed Responses

Percent Concordant     82.5    Somers' D    0.662
Percent Discordant     16.2    Gamma        0.671
Percent Tied            1.3    Tau-a        0.340
Pairs                   154    c            0.831
Obs     x    y    fittedp    devresidual

  1    14    0    0.31026      -0.86191
  2    29    0    0.83526      -1.89916
  3     6    0    0.11000      -0.48276
  4    25    1    0.72660       0.79922
  5    18    1    0.46184       1.24302
  6     4    0    0.08213      -0.41400
  7    18    0    0.46184      -1.11319
  8    12    0    0.24567      -0.75089
  9    22    1    0.62081       0.97645
 10     6    0    0.11000      -0.48276
 11    30    1    0.85630       0.55702
 12    11    0    0.21698      -0.69942
 13    30    1    0.85630       0.55702
 14     5    0    0.09515      -0.44719
 15    20    1    0.54240       1.10611
 16    13    0    0.27680      -0.80507
 17     9    0    0.16710      -0.60472
 18    32    1    0.89166       0.47889
 19    24    0    0.69338      -1.53762
 20    13    1    0.27680       1.60278
 21    19    0    0.50213      -1.18104
 22     4    0    0.08213      -0.41400
 23    28    1    0.81182       0.64571
 24    22    1    0.62081       0.97645
 25     8    1    0.14582       1.96235
Fig. 14.3, p. 576.
proc sort data = temp;
  by x;
run;
goptions reset = all; 
symbol1 c=red v=dot h = .8 ;
symbol2 c=blue v=dot h=.8 i=join;
proc gplot data = temp;
  plot y*x fittedp*x / overlay;
run;
quit;
goptions reset = all;
Inputting Coupon Effectiveness data, Table 14.2, p. 579.
data ch14tab02;
  input x n r p;
  label x = 'Reduction'
        n = 'no.  households'
	r = 'coupons redeemed'
	p = 'proportion of coupons redeemed';
cards;
   5  200   30  .150
  10  200   55  .275
  15  200   70  .350
  20  200  100  .500
  30  200  137  .685
;
run;
Fig. 14.4, p. 579.
In order to implement logistic regression using proportions it is necessary to use proc genmod and specify the distribution and the link function.  The parameter estimates in the output correspond to the fitted response function (14.28) at the bottom of p. 578.
proc genmod data=ch14tab02;
  model r/n = x / dist = bin link = logit lrci;
  output out=temp p=predicted;
run;
The GENMOD Procedure

                            Model Information

Data Set                      WORK.CH14TAB02
Distribution                        Binomial
Link Function                          Logit
Response Variable (Events)                 r    coupons redeemed
Response Variable (Trials)                 n    no.  households
Observations Used                          5
Number Of Events                         392
Number Of Trials                        1000

           Criteria For Assessing Goodness Of Fit

Criterion                 DF           Value        Value/DF

Deviance                   3          2.1668          0.7223
Scaled Deviance            3          2.1668          0.7223
Pearson Chi-Square         3          2.1486          0.7162
Scaled Pearson X2          3          2.1486          0.7162
Log Likelihood                     -595.9863

Algorithm converged.


                            Analysis Of Parameter Estimates

                               Standard    Likelihood Ratio 95%       Chi-
Parameter    DF    Estimate       Error      Confidence Limits      Square    Pr > ChiSq

Intercept     1     -2.0443      0.1610     -2.3655     -1.7340     161.28        <.0001
x             1      0.0968      0.0085      0.0803      0.1139     128.29        <.0001
Scale         0      1.0000      0.0000      1.0000      1.0000

NOTE: The scale parameter was held fixed.
Fig. 14.4, p. 579. Fitted values for X=0 and X=40 have been added in order for the fitted curve to extend beyond the range of the X variable in the data set.
data extra;
  if _n_ = 1 then do;
  predicted = exp(-2.04435) / (1+ exp(-2.04435) ); 
  x=0; output;
  predicted = exp(-2.04435 + 0.096834*40) / (1+ exp(-2.04435 + 0.096834*40) ); 
  x=40; output;
  end;
  set temp;
  output;
run;
 
proc sort data = extra;
 by x;
run; 
 
symbol1 v=dot c=blue;
symbol2 i=spline v=none c=blue;
axis1 label=(angle = 90 h = 1) order=(0 to 1.0 by .2);
axis2 order=(0 to 40 by 10); 
proc gplot data = extra;
  plot (p predicted)*x / overlay vaxis=axis1 haxis=axis2;
run;
quit;
goptions reset = all;
Inputting the Disease Outbreak data, table 14.3, p. 583.
data ch14tab03;
  input id x1 socio x4 y x5;
  label  id = 'case'
         x1 = 'age'
      socio = 'socioeconomic status' 
         x4 = 'sector'
          y = 'Disease status'
         x5 = 'savings';
cards;
      1     33      1      1      0      1
      2     35      1      1      0      1
      3      6      1      1      0      0
      4     60      1      1      0      1
      5     18      3      1      1      0
      6     26      3      1      0      0
      7      6      3      1      0      0
      8     31      2      1      1      1
      9     26      2      1      1      0
     10     37      2      1      0      0
     11     23      1      1      0      0
     12     23      1      1      0      0
     13     27      1      1      0      1
     14      9      1      1      1      1
     15     37      1      2      1      1
     16     22      1      2      1      1
     17     67      1      2      1      1
     18      8      1      2      0      1
     19      6      1      2      1      1
     20     15      1      2      1      1
     21     21      2      2      1      1
     22     32      2      2      1      1
     23     16      1      2      1      1
     24     11      2      2      0      0
     25     14      3      2      0      0
     26      9      2      2      0      0
     27     18      2      2      0      0
     28      2      3      1      0      0
     29     61      3      1      0      1
     30     20      3      1      0      0
     31     16      3      1      0      0
     32      9      2      1      0      0
     33     35      2      1      0      1
     34      4      1      1      0      1
     35     44      3      2      0      0
     36     11      3      2      1      0
     37      3      2      2      0      1
     38      6      3      2      0      0
     39     17      2      2      1      0
     40      1      3      2      0      1
     41     53      2      2      1      1
     42     13      1      2      1      0
     43     24      1      2      0      0
     44     70      1      2      1      1
     45     16      3      2      1      1
     46     12      2      2      0      1
     47     20      3      2      1      1
     48     65      3      2      0      1
     49     40      2      2      1      0
     50     38      2      2      1      1
     51     68      2      2      1      1
     52     74      1      2      1      1
     53     14      1      2      1      1
     54     27      1      2      1      1
     55     31      1      2      0      1
     56     18      1      2      0      1
     57     39      1      2      0      0
     58     50      1      2      0      1
     59     31      1      2      0      1
     60     61      1      2      0      1
     61     18      3      1      0      0
     62      5      3      1      0      0
     63      2      3      1      0      1
     64     16      3      1      0      0
     65     59      3      1      1      1
     66     22      3      1      0      0
     67     24      1      1      0      1
     68     30      1      1      0      1
     69     46      1      1      0      1
     70     28      1      1      0      0
     71     27      1      1      0      1
     72     27      1      1      1      0
     73     28      1      1      0      1
     74     52      1      1      1      1
     75     11      3      1      0      1
     76      6      2      1      0      1
     77     46      3      1      0      0
     78     20      2      1      1      1
     79      3      1      1      0      1
     80     18      2      1      0      0
     81     25      2      1      0      0
     82      6      3      1      0      1
     83     65      3      1      1      1
     84     51      3      1      0      1
     85     39      2      1      0      1
     86      8      1      1      0      1
     87      8      2      1      0      0
     88     14      3      1      0      0
     89      6      3      1      0      0
     90      6      3      1      0      1
     91      7      3      1      0      0
     92      4      3      1      0      0
     93      8      3      1      0      0
     94      9      2      1      0      0
     95     32      3      1      1      0
     96     19      3      1      0      0
     97     11      3      1      0      0
     98     35      3      1      0      0
;
run;
Creating the dummy variables for socioeconomic status.
data ch14tb03a;
  set ch14tab03;
  x2 = 0;
  if socio = 2 then x2 = 1;
  x3 = 0;
  if socio = 3 then x3 = 1;
run;
Table 14.4, p. 584.  It is the option covb in the model statement that gives us part b of the table. 
Note: The estimate for the intercept is different from the book perhaps because the authors used a slightly different algorithm. However, it is usually the odds ratio of the other parameters estimates that are of interest and they are the same as in the book.
proc logistic data = ch14tb03a descending;
  model y = x1 x2 x3 x4/ covb;
run;
The LOGISTIC Procedure

                        Model Information

Data Set                      WORK.CH14TB03A
Response Variable             y                    Disease status
Number of Response Levels     2
Number of Observations        98
Link Function                 Logit
Optimization Technique        Fisher's scoring

          Response Profile

 Ordered                      Total
   Value            y     Frequency
       1            1            31
       2            0            67

                    Model Convergence Status

         Convergence criterion (GCONV=1E-8) satisfied.

         Model Fit Statistics

                              Intercept
               Intercept         and
Criterion        Only        Covariates

AIC              124.318        111.054
SC               126.903        123.979
-2 Log L         122.318        101.054

        Testing Global Null Hypothesis: BETA=0

Test                 Chi-Square       DF     Pr > ChiSq

Likelihood Ratio        21.2635        4         0.0003
Score                   20.4067        4         0.0004
Wald                    16.6437        4         0.0023

The LOGISTIC Procedure

             Analysis of Maximum Likelihood Estimates

                               Standard
Parameter    DF    Estimate       Error    Chi-Square    Pr > ChiSq

Intercept     1     -3.8874      0.9955       15.2496        <.0001
x1            1      0.0297      0.0135        4.8535        0.0276
x2            1      0.4088      0.5990        0.4657        0.4950
x3            1     -0.3051      0.6041        0.2551        0.6135
x4            1      1.5746      0.5016        9.8543        0.0017

           Odds Ratio Estimates

             Point          95% Wald
Effect    Estimate      Confidence Limits

x1           1.030       1.003       1.058
x2           1.505       0.465       4.868
x3           0.737       0.226       2.408
x4           4.829       1.807      12.907

Association of Predicted Probabilities and Observed Responses

Percent Concordant     77.5    Somers' D    0.554
Percent Discordant     22.1    Gamma        0.556
Percent Tied            0.3    Tau-a        0.242
Pairs                  2077    c            0.777

                          Estimated Covariance Matrix

Variable       Intercept            x1            x2            x3            x4

Intercept       0.990945      -0.00605      -0.19645      -0.26324      -0.41483
x1              -0.00605      0.000182       0.00115      0.000732      0.000338
x2              -0.19645       0.00115      0.358793      0.148217      0.012887
x3              -0.26324      0.000732      0.148217      0.364944      0.062267
x4              -0.41483      0.000338      0.012887      0.062267      0.251609
Testing multiple parameters, p. 589.
In SAS testing linear hypotheses about the regression coefficients is done using a Wald test. To use the built in SAS option just add test statements for all the hypothesis that needs to be tested. The partial deviance can be used by running the full and reduced model for each hypothesis and then taking each model and comparing this difference to the appropriate chi-square distribution.
proc logistic data = ch14tb03a descending;
  model y = x1 x2 x3 x4;
  test: test x1=0;
run;
proc logistic data = ch14tb03a descending;
  model y = x2 x3 x4;
run;
The LOGISTIC Procedure

                        Model Information

Data Set                      WORK.CH14TB03A
Response Variable             y                    Disease status
Number of Response Levels     2
Number of Observations        98
Link Function                 Logit
Optimization Technique        Fisher's scoring

          Response Profile

 Ordered                      Total
   Value            y     Frequency

       1            1            31
       2            0            67

                    Model Convergence Status

         Convergence criterion (GCONV=1E-8) satisfied.

         Model Fit Statistics

                              Intercept
               Intercept         and
Criterion        Only        Covariates

AIC              124.318        111.054
SC               126.903        123.979
-2 Log L         122.318        101.054

        Testing Global Null Hypothesis: BETA=0

Test                 Chi-Square       DF     Pr > ChiSq

Likelihood Ratio        21.2635        4         0.0003
Score                   20.4067        4         0.0004
Wald                    16.6437        4         0.0023

The LOGISTIC Procedure

             Analysis of Maximum Likelihood Estimates

                               Standard
Parameter    DF    Estimate       Error    Chi-Square    Pr > ChiSq

Intercept     1     -3.8874      0.9955       15.2496        <.0001
x1            1      0.0297      0.0135        4.8535        0.0276
x2            1      0.4088      0.5990        0.4657        0.4950
x3            1     -0.3051      0.6041        0.2551        0.6135
x4            1      1.5746      0.5016        9.8543        0.0017

           Odds Ratio Estimates

             Point          95% Wald
Effect    Estimate      Confidence Limits

x1           1.030       1.003       1.058
x2           1.505       0.465       4.868
x3           0.737       0.226       2.408
x4           4.829       1.807      12.907

Association of Predicted Probabilities and Observed Responses

Percent Concordant     77.5    Somers' D    0.554
Percent Discordant     22.1    Gamma        0.556
Percent Tied            0.3    Tau-a        0.242
Pairs                  2077    c            0.777

    Linear Hypotheses Testing Results

                Wald
 Label    Chi-Square      DF    Pr > ChiSq

 test         4.8535       1        0.0276

The LOGISTIC Procedure

                        Model Information

Data Set                      WORK.CH14TB03A
Response Variable             y                    Disease status
Number of Response Levels     2
Number of Observations        98
Link Function                 Logit
Optimization Technique        Fisher's scoring

          Response Profile

 Ordered                      Total
   Value            y     Frequency

       1            1            31
       2            0            67

                    Model Convergence Status

         Convergence criterion (GCONV=1E-8) satisfied.

         Model Fit Statistics

                              Intercept
               Intercept         and
Criterion        Only        Covariates

AIC              124.318        114.204
SC               126.903        124.544
-2 Log L         122.318        106.204

        Testing Global Null Hypothesis: BETA=0

Test                 Chi-Square       DF     Pr > ChiSq

Likelihood Ratio        16.1139        3         0.0011
Score                   15.8641        3         0.0012
Wald                    14.2743        3         0.0026

The LOGISTIC Procedure

             Analysis of Maximum Likelihood Estimates

                               Standard
Parameter    DF    Estimate       Error    Chi-Square    Pr > ChiSq

Intercept     1     -3.0595      0.8639       12.5427        0.0004
x2            1      0.2351      0.5752        0.1670        0.6828
x3            1     -0.4779      0.5829        0.6721        0.4123
x4            1      1.6203      0.4857       11.1289        0.0008

           Odds Ratio Estimates

             Point          95% Wald
Effect    Estimate      Confidence Limits

x2           1.265       0.410       3.906
x3           0.620       0.198       1.944
x4           5.055       1.951      13.095

Association of Predicted Probabilities and Observed Responses

Percent Concordant     65.8    Somers' D    0.465
Percent Discordant     19.3    Gamma        0.546
Percent Tied           14.9    Tau-a        0.203
Pairs                  2077    c            0.733
Creating all the interactions to be tested.
data ch14tb03b;
  set ch14tb03a;
  x1x2 = x1*x2;
  x1x3 = x1*x3;
  x1x4 = x1*x4;
  x2x4 = x2*x4;
  x3x4 = x3*x4;
run;
Testing the interactions, p. 589.
proc logistic data = ch14tb03b descending;
  model y = x1-x4 x1x2 x1x3 x1x4 x2x4 x3x4;
  test: test x1x2=x1x3= x1x4= x2x4= x3x4=0;
run;
The LOGISTIC Procedure

                        Model Information

Data Set                      WORK.CH14TB03B
Response Variable             y                    Disease status
Number of Response Levels     2
Number of Observations        98
Link Function                 Logit
Optimization Technique        Fisher's scoring

          Response Profile

 Ordered                      Total
   Value            y     Frequency

       1            1            31
       2            0            67

                   Model Convergence Status
         Convergence criterion (GCONV=1E-8) satisfied.

         Model Fit Statistics

                              Intercept
               Intercept         and
Criterion        Only        Covariates

AIC              124.318        113.996
SC               126.903        139.846
-2 Log L         122.318         93.996

        Testing Global Null Hypothesis: BETA=0

Test                 Chi-Square       DF     Pr > ChiSq

Likelihood Ratio        28.3217        9         0.0008
Score                   25.6302        9         0.0023
Wald                    17.9067        9         0.0363

The LOGISTIC Procedure

             Analysis of Maximum Likelihood Estimates

                               Standard
Parameter    DF    Estimate       Error    Chi-Square    Pr > ChiSq

Intercept     1     -5.5161      2.2471        6.0260        0.0141
x1            1      0.0646      0.0583        1.2294        0.2675
x2            1     -1.7862      3.0841        0.3354        0.5625
x3            1      0.2955      2.2550        0.0172        0.8957
x4            1      2.9796      1.2481        5.6988        0.0170
x1x2          1      0.1054      0.0559        3.5514        0.0595
x1x3          1      0.0140      0.0316        0.1952        0.6586
x1x4          1     -0.0342      0.0309        1.2231        0.2688
x2x4          1     -0.3094      1.4409        0.0461        0.8300
x3x4          1     -0.7396      1.2489        0.3507        0.5537

           Odds Ratio Estimates

             Point          95% Wald
Effect    Estimate      Confidence Limits

x1           1.067       0.952       1.196
x2           0.168      <0.001      70.702
x3           1.344       0.016     111.632
x4          19.680       1.705     227.221
x1x2         1.111       0.996       1.240
x1x3         1.014       0.953       1.079
x1x4         0.966       0.910       1.027
x2x4         0.734       0.044      12.363
x3x4         0.477       0.041       5.519

Association of Predicted Probabilities and Observed Responses

Percent Concordant     80.4    Somers' D    0.610
Percent Discordant     19.4    Gamma        0.612
Percent Tied            0.3    Tau-a        0.267
Pairs                  2077    c            0.805

    Linear Hypotheses Testing Results

                Wald
 Label    Chi-Square      DF    Pr > ChiSq

 test         5.9413       5        0.3120
Example 1, p. 591 and Fig. 14.5, p. 592.
Invoking the macro diag_plot.
Note: The macro splits the observations into groups with an equal number of observations except for the last group therefore they may not match the groups in the book since they are not the same size as those in the book.  Also, the results from the logistic regression produced by the macro has been omitted.
%include "c:\neter\diag_plot.sas";
%diag_plot(ch14tab01, y, x, 4);
Obs    class       min         max      midpoint    n       pj

 1       1      -2.41375    -1.60632    -2.01004    7    0.14286
 2       2      -1.28335    -0.15295    -0.71815    6    0.33333
 3       3      -0.15295     0.81597     0.33151    6    0.50000
 4       4       0.97745     2.10785     1.54265    6    0.83333
Example 2, p. 591 and Fig. 14.6, p. 592.
Invoking the macro diag_plot again and again the results from the logistic regression produced by the macro has been omitted.

 %diag_plot(ch14tb03a, y, x1 x2 x3 x4, 5);
Obs    class       min         max      midpoint     n       pj

 1       1      -2.55835    -2.08241    -2.32038    20    0.05000
 2       2      -2.07476    -1.47983    -1.77729    20    0.15000
 3       3      -1.42033    -0.74386    -1.08210    19    0.26316
 4       4      -0.71601     0.06505    -0.32548    20    0.55000
 5       5       0.17633     1.69341     0.93487    19    0.57895
Table 14.5, p. 594.
Note: The numbers are not exactly the same as those in the book most probably due to rounding errors.  Only the output from the final print procedure has been included in the results.
proc logistic data = ch14tb03a descending;
  model y = x1 x2 x3 x4 ;
  output out=temp p = pi;
run;
data temp;
  set temp;
  pihat = log( pi / (1 - pi) );
run;
proc sort data = temp;
  by pihat;
run;
data temp;
  set temp nobs=total;
  class = .;
  class = int( ( _n_ - 1 )/( total/5 ) ) +1;
run;
proc sql;
  create table temp1 as
  select *, max(pihat) as max, min(pihat) as min, sum(pi) as Ej1, count(pi) as n,
            sum(y) as Oj1, count(pi) - sum(pi) as Ej0, count(pi) - sum(y) as Oj0
  from temp
  group by class;
quit;
proc sort data = temp1 (keep = class n min max  Oj0 Ej0 Oj1 Ej1);
  by class ;
run;
data temp1;
  set temp1;
  by class;
  if first.class;
run;
proc print data=temp1;
  var class min max n Oj0 Ej0 Oj1 Ej1;
run;
Obs    class       min         max       n    Oj0      Ej0      Oj1      Ej1

 1       1      -2.55835    -2.08241    20     19    18.1952      1     1.8048
 2       2      -2.07476    -1.47983    20     17    16.9072      3     3.0928
 3       3      -1.42033    -0.74386    19     14    14.0400      5     4.9600
 4       4      -0.71601     0.06505    20      9    11.5587     11     8.4413
 5       5       0.17633     1.69341    19      8     6.2976     11    12.7024
Index plots, including the RESDEV (Residual deviance) plot which is the same as Fig. 14.7, p. 596.
proc logistic data = ch14tab01 desc;
  model y = x / iplots;
run;
The LOGISTIC Procedure

                    Model Information

Data Set                      WORK.CH14TAB01
Response Variable             y                    Success
Number of Response Levels     2
Number of Observations        25
Link Function                 Logit
Optimization Technique        Fisher's scoring

          Response Profile

 Ordered                      Total
   Value            y     Frequency

       1            1            11
       2            0            14

                    Model Convergence Status

         Convergence criterion (GCONV=1E-8) satisfied.

         Model Fit Statistics

                              Intercept
               Intercept         and
Criterion        Only        Covariates

AIC               36.296         29.425
SC                37.515         31.862
-2 Log L          34.296         25.425

        Testing Global Null Hypothesis: BETA=0

Test                 Chi-Square       DF     Pr > ChiSq

Likelihood Ratio         8.8719        1         0.0029
Score                    7.9742        1         0.0047
Wald                     6.1760        1         0.0129

             Analysis of Maximum Likelihood Estimates

                               Standard
Parameter    DF    Estimate       Error    Chi-Square    Pr > ChiSq

Intercept     1     -3.0597      1.2594        5.9029        0.0151
x             1      0.1615      0.0650        6.1760        0.0129

The LOGISTIC Procedure

           Odds Ratio Estimates

             Point          95% Wald
Effect    Estimate      Confidence Limits

x            1.175       1.035       1.335

Association of Predicted Probabilities and Observed Responses

Percent Concordant     82.5    Somers' D    0.662
Percent Discordant     16.2    Gamma        0.671
Percent Tied            1.3    Tau-a        0.340
Pairs                   154    c            0.831

The LOGISTIC Procedure

         -----+--------------+--------------+--------------+--------------+--------------+------
  RESCHI |                                                                                     |
P      4 +                                                                                     +
e        |                                                                                     |
a        |                                                                                     |
r        |                                                                               *     |
s      2 +                                                                                     +
o        |                                                                *                    |
n        |                   *           *                 *                          *        |
         |                *                    *     *              *              *           |
R      0 +                                                                                     +
e        |       *     *        *     *     *     *     *     *  *              *              |
s        |                         *                                         *                 |
i        |                                                             *                       |
d     -2 +                                                                                     +
u        |          *                                                                          |
a        |                                                                                     |
l        |                                                                                     |
      -4 +                                                                                     +
         |                                                                                     |
         -----+--------------+--------------+--------------+--------------+--------------+------
              0              5             10             15             20             25

                                           Case Number   INDEX


         -----+--------------+--------------+--------------+--------------+--------------+------
       2 +                                                                               *     +
D        |                                                                                     |
e        |                                                                *                    |
v        |                   *                                                                 |
i RESDEV |                                                 *                                   |
a        |                *              *                                            *        |
n        |                                     *     *                             *           |
c        |                                                          *                          |
e        |                                                                                     |
       0 +                                                                                     +
R        |                                                                                     |
e        |             *        *           *           *                       *              |
s        |                            *           *              *                             |
i        |       *                                            *                                |
d        |                         *                                         *                 |
u        |                                                                                     |
a        |                                                             *                       |
l        |                                                                                     |
      -2 +          *                                                                          +
         -----+--------------+--------------+--------------+--------------+--------------+------
              0              5             10             15             20             25

                                           Case Number   INDEX

The LOGISTIC Procedure

       ------+--------------+--------------+--------------+--------------+--------------+-------
  0.12 +                                                                                       +
       |                                                                                       |
       |                                                                                       |
H      |                                                                                       |
a      |           *                          *     *                                          |
t      |                                                           *              *            |
  0.10 +                                                                                       +
D      |                                                                                       |
i      |                                                                                       |
a    H |                 *                                                                     |
g      |                                                                                       |
o      |                                                              *                        |
n 0.08 +              *        *           *           *        *              *        *      +
a      |                                                                                       |
l      |                                *        *                                   *         |
       |                             *                                                         |
       |                                                     *           *                     |
       |        *                                         *                                    |
  0.06 +                    *     *                                         *                  +
       ------+--------------+--------------+--------------+--------------+--------------+-------
             0              5             10             15             20             25

                                          Case Number   INDEX


          -----+--------------+--------------+--------------+--------------+--------------+-----
      1.0 +                                                                                    +
I         |                                                                                    |
n         |                                                                                    |
t         |                                                                               *    |
e         |                                                                                    |
r         |                                                                                    |
c     0.5 +                                                                                    +
e         |          *                                                                         |
p         |                                                                *                   |
t DFBETA0 |                                                                                    |
          |                                                             *                      |
D         |                   *                                                                |
f     0.0 +                               *                 *                          *       +
B         |             *  *     *  *        *  *     *  *           *        *  *  *          |
e         |       *                    *           *           *  *                            |
t         |                                                                                    |
a         |                                                                                    |
          |                                                                                    |
     -0.5 +                                                                                    +
          -----+--------------+--------------+--------------+--------------+--------------+-----
               0              5             10             15             20             25

                                           Case Number   INDEX

The LOGISTIC Procedure

          -----+--------------+--------------+--------------+--------------+--------------+-----
      0.5 +                                                                                    +
          |                                                                                    |
          |                                                                                    |
          |                                                                                    |
          |                *                    *     *                             *          |
x         |       *     *        *     *  *  *     *     *  *  *  *  *           *     *       |
      0.0 +                   *     *                                         *                +
D         |                                                                                    |
f         |                                                                                    |
B DFBETA1 |                                                                *                   |
e         |                                                             *                      |
t         |                                                                                    |
a    -0.5 +                                                                                    +
          |                                                                               *    |
          |          *                                                                         |
          |                                                                                    |
          |                                                                                    |
          |                                                                                    |
     -1.0 +                                                                                    +
          -----+--------------+--------------+--------------+--------------+--------------+-----
               0              5             10             15             20             25

                                           Case Number   INDEX


       ------+--------------+--------------+--------------+--------------+--------------+-------
C 0.75 +                                                                                       +
o      |                                                                                       |
n      |           *                                                                           |
f      |                                                                                       |
i      |                                                                                       |
d      |                                                                                *      |
e 0.50 +                                                                                       +
n      |                                                                                       |
c      |                                                                                       |
e    C |                                                                                       |
       |                                                                                       |
I      |                                                                                       |
n 0.25 +                                                                                       +
t      |                                                              *  *                     |
e      |                                                                                       |
r      |                                                                                       |
v      |                    *                                               *                  |
a      |        *        *        *  *  *     *  *  *     *  *                    *  *         |
l 0.00 +              *        *           *           *        *  *           *               +
       ------+--------------+--------------+--------------+--------------+--------------+-------
D            0              5             10             15             20             25
i
                                          Case Number   INDEX

The LOGISTIC Procedure

       ------+--------------+--------------+--------------+--------------+--------------+-------
C  0.6 +           *                                                                           +
o      |                                                                                       |
n      |                                                                                       |
f      |                                                                                *      |
i      |                                                                                       |
d      |                                                                                       |
e  0.4 +                                                                                       +
n      |                                                                                       |
c      |                                                                                       |
e CBAR |                                                                                       |
       |                                                                                       |
I      |                                                                                       |
n  0.2 +                                                              *  *                     +
t      |                                                                                       |
e      |                                                                                       |
r      |                                                                                       |
v      |                    *     *                       *                 *                  |
a      |        *        *           *  *     *  *  *        *  *                 *  *         |
l  0.0 +              *        *           *           *           *           *               +
       ------+--------------+--------------+--------------+--------------+--------------+-------
D            0              5             10             15             20             25
i
                                          Case Number   INDEX


         -----+--------------+--------------+--------------+--------------+--------------+------
       6 +                                                                                     +
         |                                                                                     |
D        |                                                                                     |
e        |                                                                                     |
l        |                                                                                     |
t        |          *                                                                    *     |
a      4 +                                                                                     +
         |                                                                                     |
D        |                                                                                     |
e DIFDEV |                                                                                     |
v        |                                                             *  *                    |
i        |                                                                                     |
a      2 +                                                                                     +
n        |                   *                                                                 |
c        |                         *                       *                 *                 |
e        |                               *                                            *        |
         |       *        *           *           *           *                                |
         |             *        *           *  *     *  *        *  *           *  *           |
       0 +                                                                                     +
         -----+--------------+--------------+--------------+--------------+--------------+------
              0              5             10             15             20             25

                                           Case Number   INDEX

The LOGISTIC Procedure

           ----+--------------+--------------+--------------+--------------+--------------+-----
  DIFCHISQ |                                                                                   |
         8 +                                                                                   +
D          |                                                                                   |
e          |                                                                                   |
l          |                                                                              *    |
t        6 +                                                                                   +
a          |         *                                                                         |
           |                                                                                   |
C          |                                                                                   |
h        4 +                                                                                   +
i          |                                                                                   |
S          |                                                               *                   |
q          |                                                            *                      |
u        2 +                                                                                   +
a          |                                                                                   |
r          |                  *     *                       *                 *                |
e          |      *        *           *  *        *           *                    *  *       |
         0 +            *        *           *  *     *  *        *  *           *             +
           |                                                                                   |
           ----+--------------+--------------+--------------+--------------+--------------+-----
               0              5             10             15             20             25

                                            Case Number   INDEX
Predicting mean responses with confidence interval, example p. 604-605. 
The output contains the point estimate of the logit mean response as phat, the confidence limits for the logit mean response as lower1 and upper1, the point estimate for the mean response as p, and finally, the confidence interval for the mean response as lower and upper.  The output from the proc logistic is not shown.
data ch14tb03b;
  if _n_ = 1 then do;
    id = 99; x1=10; x2=0; x3=1; x4=1;
    end;
  output;
  set ch14tb03a;
run;
proc logistic data = ch14tb03b desc;
  model y = x1 x2 x3 x4;
  output out=temp p=p upper=upper lower=lower;
run;
data temp;
  set temp;
  lower1 = log(lower/ (1-lower) ) ;
  upper1 = log(upper / (1-upper) );
  phat = log(p / (1-p) );
run;
proc print data = temp;
  where id = 99;
  var  phat lower1 upper1 p lower upper;
run;
Obs      phat       lower1      upper1         p         lower      upper

 1    -2.32038    -3.38397    -1.25679    0.089449    0.032800    0.22153
Table 14.7, p. 607.
The table produced by SAS is very different from the table in the book. The book uses the list of predicted fitted values and then compares them to a specified cutoff point. SAS does not use this method because when you classify binary data and the observations that are used to fit the model are also used to estimate the classification error then the resulting error-count estimate is biased. One way to reduce the bias is to remove the observation to be classified and re-estimate the parameters of the model and then classify the observation based on the parameter estimates based on the smaller dataset (without the observation to be classified). In order to increase efficiency SAS uses a one-step approximation of the parameter estimates based on the smaller dataset (without the observation to be classified). For the details of the one-step approximation please refer to the manual under Proc Logistic Classification Table.
proc logistic data = ch14tb03a desc;
  model y = x1 x2 x3 x4/ ctable;
  output out=temp p=p;
run;
The LOGISTIC Procedure

                        Model Information

Data Set                      WORK.CH14TB03A
Response Variable             y                    Disease status
Number of Response Levels     2
Number of Observations        98
Link Function                 Logit
Optimization Technique        Fisher's scoring

          Response Profile

 Ordered                      Total
   Value            y     Frequency

       1            1            31
       2            0            67

                    Model Convergence Status

         Convergence criterion (GCONV=1E-8) satisfied.

         Model Fit Statistics

                              Intercept
               Intercept         and
Criterion        Only        Covariates

AIC              124.318        111.054
SC               126.903        123.979
-2 Log L         122.318        101.054

        Testing Global Null Hypothesis: BETA=0

Test                 Chi-Square       DF     Pr > ChiSq

Likelihood Ratio        21.2635        4         0.0003
Score                   20.4067        4         0.0004
Wald                    16.6437        4         0.0023

The LOGISTIC Procedure

             Analysis of Maximum Likelihood Estimates

                               Standard
Parameter    DF    Estimate       Error    Chi-Square    Pr > ChiSq

Intercept     1     -3.8874      0.9955       15.2496        <.0001
x1            1      0.0297      0.0135        4.8535        0.0276
x2            1      0.4088      0.5990        0.4657        0.4950
x3            1     -0.3051      0.6041        0.2551        0.6135
x4            1      1.5746      0.5016        9.8543        0.0017

           Odds Ratio Estimates

             Point          95% Wald
Effect    Estimate      Confidence Limits

x1           1.030       1.003       1.058
x2           1.505       0.465       4.868
x3           0.737       0.226       2.408
x4           4.829       1.807      12.907

Association of Predicted Probabilities and Observed Responses

Percent Concordant     77.5    Somers' D    0.554
Percent Discordant     22.1    Gamma        0.556
Percent Tied            0.3    Tau-a        0.242
Pairs                  2077    c            0.777

                          Classification Table

          Correct      Incorrect                Percentages
 Prob          Non-          Non-           Sensi-  Speci-  False  False
Level  Event  Event  Event  Event  Correct  tivity  ficity   POS    NEG

0.060     31      0     67      0     31.6   100.0     0.0   68.4     .
0.080     31      4     63      0     35.7   100.0     6.0   67.0    0.0
0.100     29     12     55      2     41.8    93.5    17.9   65.5   14.3
0.120     29     22     45      2     52.0    93.5    32.8   60.8    8.3
0.140     28     23     44      3     52.0    90.3    34.3   61.1   11.5
0.160     27     25     42      4     53.1    87.1    37.3   60.9   13.8
0.180     26     32     35      5     59.2    83.9    47.8   57.4   13.5
0.200     26     36     31      5     63.3    83.9    53.7   54.4   12.2
0.220     25     39     28      6     65.3    80.6    58.2   52.8   13.3
0.240     23     41     26      8     65.3    74.2    61.2   53.1   16.3
0.260     22     42     25      9     65.3    71.0    62.7   53.2   17.6
0.280     20     43     24     11     64.3    64.5    64.2   54.5   20.4
0.300     20     45     22     11     66.3    64.5    67.2   52.4   19.6
0.320     19     46     21     12     66.3    61.3    68.7   52.5   20.7
0.340     18     48     19     13     67.3    58.1    71.6   51.4   21.3

\The LOGISTIC Procedure

                          Classification Table

          Correct      Incorrect                Percentages
 Prob          Non-          Non-           Sensi-  Speci-  False  False
Level  Event  Event  Event  Event  Correct  tivity  ficity   POS    NEG

0.360     17     50     17     14     68.4    54.8    74.6   50.0   21.9
0.380     16     51     16     15     68.4    51.6    76.1   50.0   22.7
0.400     14     51     16     17     66.3    45.2    76.1   53.3   25.0
0.420     13     53     14     18     67.3    41.9    79.1   51.9   25.4
0.440     13     53     14     18     67.3    41.9    79.1   51.9   25.4
0.460     12     53     14     19     66.3    38.7    79.1   53.8   26.4
0.480     12     55     12     19     68.4    38.7    82.1   50.0   25.7
0.500     11     55     12     20     67.3    35.5    82.1   52.2   26.7
0.520     10     56     11     21     67.3    32.3    83.6   52.4   27.3
0.540     10     58      9     21     69.4    32.3    86.6   47.4   26.6
0.560      9     59      8     22     69.4    29.0    88.1   47.1   27.2
0.580      8     61      6     23     70.4    25.8    91.0   42.9   27.4
0.600      8     62      5     23     71.4    25.8    92.5   38.5   27.1
0.620      8     62      5     23     71.4    25.8    92.5   38.5   27.1
0.640      7     64      3     24     72.4    22.6    95.5   30.0   27.3
0.660      7     64      3     24     72.4    22.6    95.5   30.0   27.3
0.680      6     64      3     25     71.4    19.4    95.5   33.3   28.1
0.700      5     64      3     26     70.4    16.1    95.5   37.5   28.9
0.720      5     65      2     26     71.4    16.1    97.0   28.6   28.6
0.740      5     65      2     26     71.4    16.1    97.0   28.6   28.6
0.760      3     65      2     28     69.4     9.7    97.0   40.0   30.1
0.780      2     65      2     29     68.4     6.5    97.0   50.0   30.9
0.800      1     67      0     30     69.4     3.2   100.0    0.0   30.9
0.820      1     67      0     30     69.4     3.2   100.0    0.0   30.9
0.840      0     67      0     31     68.4     0.0   100.0     .    31.6
Inputting the validation data set which is the remaining data from Data Set C.3, p. 1370.
data validation;
  input id x1 socio x4 y x5;
  label  id = 'case'
         x1 = 'age'
      socio = 'socioeconomic status' 
         x4 = 'sector'
          y = 'Disease status'
         x5 = 'savings';
cards;
     99     16      1      1      0      0
    100      1      1      1      0      1
    101      6      1      1      0      1
    102     27      1      1      0      1
    103     25      1      1      0      1
    104     18      1      1      0      0
    105     37      3      1      0      0
    106     33      3      1      1      0
    107     27      2      1      0      0
    108      2      1      1      0      0
    109      8      2      1      0      0
    110      5      1      1      0      0
    111      1      1      1      0      1
    112     32      1      1      0      0
    113     25      1      1      1      1
    114     15      1      2      0      0
    115     15      1      2      0      1
    116     26      1      2      0      1
    117     42      1      2      1      1
    118      7      1      2      0      1
    119      2      1      2      0      0
    120     65      1      2      1      1
    121     33      2      2      0      1
    122      8      2      2      1      0
    123     30      2      2      0      0
    124      5      3      2      0      0
    125     15      3      2      0      0
    126     60      3      2      1      1
    127     13      3      2      1      1
    128     70      3      1      0      1
    129      5      3      1      0      0
    130      3      3      1      0      1
    131     50      2      1      0      1
    132      6      2      1      0      0
    133     12      2      1      0      1
    134     39      3      2      1      0
    135     15      2      2      0      1
    136     35      2      2      1      0
    137      2      2      2      0      1
    138     17      3      2      0      0
    139     43      3      2      1      1
    140     30      2      2      0      1
    141     11      1      2      0      1
    142     39      1      2      1      1
    143     32      1      2      0      1
    144     17      1      2      0      1
    145      3      3      2      0      1
    146      7      3      2      0      0
    147      2      2      2      0      0
    148     64      2      2      1      1
    149     13      1      2      1      2
    150     15      2      2      1      1
    151     48      2      2      0      1
    152     23      1      2      0      1
    153     48      1      2      1      0
    154     25      1      2      0      1
    155     12      1      2      0      1
    156     46      1      2      1      1
    157     79      1      2      0      1
    158     56      1      2      0      1
    159      8      1      2      0      1
    160     29      3      1      1      0
    161     35      3      1      1      0
    162     11      3      1      1      0
    163     69      3      1      0      1
    164     21      3      1      1      0
    165     13      3      1      0      0
    166     21      1      1      0      1
    167     32      1      1      1      1
    168     24      1      1      1      0
    169     24      1      1      0      1
    170     73      1      1      0      1
    171     42      1      1      0      1
    172     34      1      1      1      1
    173     30      2      1      0      0
    174      7      2      1      0      0
    175     29      3      1      1      0
    176     22      3      1      1      0
    177     38      2      1      0      1
    178     13      2      1      0      1
    179     12      2      1      0      1
    180     42      3      1      0      0
    181     17      3      1      1      0
    182     21      3      1      0      1
    183     34      1      1      0      1
    184      1      3      1      0      0
    185     14      2      1      0      0
    186     16      2      1      0      0
    187      9      3      1      0      0
    188     53      3      1      0      0
    189     27      3      1      0      0
    190     15      3      1      0      0
    191      9      3      1      0      0
    192      4      2      1      0      1
    193     10      3      1      0      1
    194     31      3      1      0      0
    195     85      3      1      0      1
    196     24      2      1      0      0
;
run;
Creating the dummy variables for the socioeconomic variable.
data validation;
  set validation;
  x2 = 0;
  if socio = 2 then x2 = 1;
  x3 = 0;
  if socio = 3 then x3 = 1;
run;
Creating the fitted values of the validation dataset using parameter estimates from the Disease Outbreak dataset (table 14.3), p. 608.  In order to get the same classification table it was necessary to use 0.7 as the cutoff value. The percentages shown in the table in the book are the column percentages which are in the second row of each cell.
Note: The proc format is simply to create nice labels for our table.\
data validation1;
  set validation;
  e =  2.3129 - 0.0297*x1 - .4088*x2 + 0.3051*x3 - 1.5746*x4;
  ex = exp(e);
  p = 1/( 1+ ex);
  yes = 0;
  if p >= .7 then yes = 1;
run;
proc format;
  value y 1='with disease' 0='without disease';
  value yes 1='pihat >= .7' 0='piehat < .7';
run;
proc freq data = validation1;
  format y y. yes yes.;
  table yes*y / missing norow nopercent;
run; 
The FREQ Procedure

Table of yes by y

yes          y(Disease status)

Frequency   |
Col Pct     |without |with dis|  Total
            |disease |ease    |
------------+--------+--------+
piehat < .7 |     44 |     12 |     56
            |  61.11 |  46.15 |
------------+--------+--------+
pihat >= .7 |     28 |     14 |     42
            |  38.89 |  53.85 |
------------+--------+--------+
Total             72       26       98
Inputting the Miller Lumber Company Example, p. 613.
data ch14tab08;
  input y x1 x2 x3 x4 x5;
  label x1 = 'Housing'
        x2 = 'Income'
		x3 = 'Age'
		x4 = 'Competitor Distance'
		x5 = 'Store Distance'
		 y = 'Costumers';
cards;
 9   606   41393   3  3.04  6.32
 6   641   23635  18  1.95  8.89
28   505   55475  27  6.54  2.05
11   866   64646  31  1.67  5.81
 4   599   31972   7  0.72  8.11
 4   520   41755  23  2.24  6.81
 0   354   46014  26  0.77  9.27
14   483   34626   1  3.51  7.92
16  1034   85207  13  4.23  4.40
13   456   33021  32  3.07  6.03
 9    19   39198  22  2.96  6.09
14   530   38794   5  2.77  6.08
 5   337   30855   1  1.33  9.86
 9   586   28852   7  2.98  8.64
 9  1113  120065   9  3.58  5.26
 7   525   32229   3  1.27  7.56
 4   377   36828  15  1.92  8.91
26  1127   90302  26  5.83  1.74
32   877   51707  27  5.19  3.66
26  1007   89860  55  5.03  2.03
11   657   60513  32  4.38  8.30
12   302   42191  54  3.41  5.21
 3   603   28736  41  0.34  8.29
15   556   49129  33  4.78  3.89
12   635   29308  42  2.53  6.17
 9   386   26734  14  4.99  9.70
14  1011   57862  54  4.60  3.94
10   925   70030  36  4.58  8.66
22   898   46027  44  3.03  5.60
 8   731   32202  43  5.15  9.67
 3   584   32871  13  1.47  8.02
11   439   29564  18  3.67  5.10
 2   153   46806  21  0.84  9.18
 6  1069   59805  22  2.50  9.43
11   443   42555  53  2.62  5.75
10   392   36998   7  1.03  7.74
 0   828   85664   4  1.30  9.66
15   159   21238   4  2.98  8.66
 9   830   47972  40  2.28  9.26
16   234   33246  26  3.95  4.61
29  1004   45927  24  4.90  2.69
 6   643   58315   8  0.78  6.26
26   741   69177   9  6.61  0.87
13   306   40886  27  4.53  2.68
 0   180   44588  14  0.88  9.38
 8   644   47347  35  2.94  7.69
 8   109   31791   9  4.37  9.31
21   809   42740  17  4.10  4.75
12   722   59175  35  2.38  5.09
26  1006   48862  48  5.04  2.21
 3   786   54678  20  3.59  8.52
 7  1041   59835  40  1.68  7.59
 5   524   51756  39  0.57  9.10
 9   725   34817  18  1.88  7.96
13   482   29942  14  3.17  6.91
28   666   68684  25  5.78  2.55
10   450   64790   3  4.35  6.03
12   667   58535  25  2.78  5.59
 6   921   42919  13  2.48  7.69
11   412   40722  32  2.47  9.43
12   526   42120  30  4.29  6.15
11   523   28647  43  2.69  7.54
 9  1066   61464  40  1.15  8.25
 8  1001   70136  29  2.58  9.67
 9   669   34595  38  4.06  8.78
 8   582   30878  58  1.91  6.86
 6   872   39366  52  0.73  8.67
 6   758   61563  31  3.08  8.33
15   782   38412  26  2.72  6.71
15   551   41045   2  3.62  7.45
12   201   23864  43  4.80  8.74
10   730   38647   9  0.67  7.92
 8   738   58387  13  2.01  6.60
 3   469   37242  40  1.42  8.37
10   898   38337  32  2.63  9.56
10   780   68201   5  4.12  6.69
15   622   41066  46  4.48  4.10
 6   391   40873  19  1.67  6.90
 9   531   54655  40  2.32  5.69
21   566   49826   1  3.06  4.03
13   410   29013  50  2.68  7.58
 8   719   78082  31  2.70  4.89
 6   684   57506  51  2.13  8.31
 8   865   47118  46  2.17  9.06
21  1031   72373  48  6.27  1.75
 7   862   67787   1  2.10  8.63
19   758   40305  15  3.95  5.58
13  1141   50026  45  2.79  6.18
24  1289   98701   8  5.87  2.73
 7   674   58195  54  4.30  6.40
 3   683   47991  57  1.54  9.52
 8   650   63123  15  3.17  9.46
 9   406   39051  29  3.11  9.62
18   966  114633  38  6.33  2.22
12  1103   55773  44  4.58  8.68
 8   312   43393  41  2.25  6.43
16   787   61765  53  5.39  3.37
 5   416   33348  48  1.48  7.66
 8   528   44541  31  4.91  9.67
11   919   40795   8  2.97  7.79
12   482   55972   9  2.91  5.85
14   781   33140  30  1.42  5.71
17   120   19673  21  2.65  6.25
17   693   36190   6  4.70  9.54
 6   348   25768  42  1.43  7.11
15   780   53974  47  4.21  6.41
10   752   71814   1  3.13  5.47
 6   817   54429  47  1.90  9.90
 4   268   34022  54  1.20  9.51
 6   519   52850  43  2.92  8.62
;
run;
Table 14.9, p. 613.
Note: In SAS the estimate for beta2 -0.00001169 is rounded to -0.0000.
proc genmod data=ch14tab08;
  model y = x1-x5 / dist = poisson link   = log;
  output out=temp p=muhati resdev=devi;
run;
The GENMOD Procedure

                        Model Information

Data Set              WORK.CH14TAB08
Distribution                 Poisson
Link Function                    Log
Dependent Variable                 y    Costumers
Observations Used                110

           Criteria For Assessing Goodness Of Fit

Criterion                 DF           Value        Value/DF

Deviance                 104        114.9854          1.1056
Scaled Deviance          104        114.9854          1.1056
Pearson Chi-Square       104        101.8808          0.9796
Scaled Pearson X2        104        101.8808          0.9796
Log Likelihood                     1898.0224

Algorithm converged.

                            Analysis Of Parameter Estimates

                               Standard     Wald 95% Confidence       Chi-
Parameter    DF    Estimate       Error           Limits            Square    Pr > ChiSq

Intercept     1      2.9424      0.2072      2.5362      3.3486     201.57        <.0001
x1            1      0.0006      0.0001      0.0003      0.0009      18.17        <.0001
x2            1     -0.0000      0.0000     -0.0000     -0.0000      30.63        <.0001
x3            1     -0.0037      0.0018     -0.0072     -0.0002       4.37        0.0365
x4            1      0.1684      0.0258      0.1179      0.2189      42.70        <.0001
x5            1     -0.1288      0.0162     -0.1605     -0.0970      63.17        <.0001
Scale         0      1.0000      0.0000      1.0000      1.0000

NOTE: The scale parameter was held fixed.
Table 14.10, p. 614.
proc print data = temp (obs=10);
  var y muhati devi;
run;
Obs     y     muhati      devi

  1     9    12.3378    -0.99880
  2     6     8.7671    -0.99158
  3    28    28.1259    -0.02375
  4    11     8.4071     0.85335
  5     4     7.2606    -1.32357
  6     4     8.8818    -1.83900
  7     0     4.2982    -2.93195
  8    14    10.9989     0.86785
  9    16    14.4440     0.40238
 10    13    11.6344     0.39289
Fig. 14.9, p. 614.
Note: It is necessary to first create an index variable and graph the devi versus the index.
data temp;
  set temp;
  id = _n_;
run;
 
symbol1 v=dot i=join c=blue h = .8;
axis1 label=(angle = 90);
 
proc gplot data = temp;
  plot devi*id/ vaxis = axis1;
run;
quit;

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