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SAS Textbook Examples
Applied Linear Statistical Models by Neter, Kutner, et. al.
Chapter 9: Building the Regression Model II: Diagnostics

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Inputting the Life Insurance data, Table 9.1, p. 364.
data ch9tab01;
  input x1 x2 y;
  label x1 = 'Income'
        x2 = 'Risk Aversion'
	 y = 'Insurance';
cards;
45.010   6   91
57.204   4  162
26.852   5   11
66.290   7  240
40.964   5   73
72.996  10  311
79.380   1  316
52.766   8  154
55.916   6  164
38.122   4   54
35.840   6   53
75.796   9  326
37.408   5   55
54.376   2  130
46.186   7  112
46.130   4   91
30.366   3   14
39.060   5   63
;;;
run;
The equation 9.3, p. 364 and the plots in Fig. 9.3, p. 365.
proc reg data = ch9tab01 ;
  model y = x1 x2 / partial ;
  plot r.*x1;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: y Insurance

                             Analysis of Variance

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

Model                     2         173919          86960     542.33    <.0001
Error                    15     2405.14763      160.34318
Corrected Total          17         176324

Root MSE             12.66267    R-Square     0.9864
Dependent Mean      134.44444    Adj R-Sq     0.9845
Coeff Var             9.41851

                                 Parameter Estimates

                                      Parameter       Standard
Variable     Label            DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept         1     -205.71866       11.39268     -18.06      <.0001
x1           Income            1        6.28803        0.20415      30.80      <.0001
x2           Risk Aversion     1        4.73760        1.37808       3.44      0.0037

The REG Procedure
Model: MODEL1
Partial Regression Residual Plot

       ---------+------+------+------+------+------+------+------+------+------+------+---------
     y |                                                                                       |
       |                                                                                       |
       |                                                                                       |
   125 +                                                                                       +
       |                                                                                       |
       |                                                                                       |
       |          11                                                                           |
   100 +                                                                                       +
       |                                                                                       |
       |                                                                                       |
       |                                                                                       |
    75 +                                                                                       +
       |                                                                                       |
       |                                                                                       |
       |                                                                                       |
    50 +                                                                                       +
       |                           1                                                           |
I      |                                     1                                                 |
n      |                                                                                       |
s   25 +                                                                                       +
u      |                                                                                       |
r      |                                    1                                                  |
a      |                                                                                       |
n    0 +                                        1                                              +
c      |                                                                                       |
e      |                                              1                                        |
       |                                              1                                        |
   -25 +                                                                                       +
       |                                                                                       |
       |                                                  1                                    |
       |                                                          11                           |
   -50 +                                                        1  1 1                         +
       |                                                        1             1                |
       |                                                                1                      |
       |                                                                                       |
   -75 +                                                                          1            +
       |                                                                                       |
       |                                                                                       |
       |                                                                                       |
  -100 +                                                                                       +
       |                                                                                       |
       |                                                                                       |
       |                                                                                       |
       ---------+------+------+------+------+------+------+------+------+------+------+---------
              -0.5   -0.4   -0.3   -0.2   -0.1    0.0    0.1    0.2    0.3    0.4    0.5

                                               Intercept
The REG Procedure
Model: MODEL1
Partial Regression Residual Plot

       -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
     y |                                                                                       |
   250 +                                                                              1        +
       |                                                                                       |
       |                                                                                       |
       |                                                                                       |
       |                                                                                       |
   200 +                                                                                       +
       |                                                                                       |
       |                                                                                       |
       |                                                                                       |
       |                                                                                       |
   150 +                                                                                       +
       |                                                         1                             |
       |                                                                                       |
       |                                                                                       |
       |                                                                                       |
   100 +                                                    1                                  +
I      |                                                                                       |
n      |                                                  1                                    |
s      |                                                                                       |
u      |                                                                                       |
r   50 +                                             11                                        +
a      |                                                                                       |
n      |                                                                                       |
c      |                                        1                                              |
e      |                                                                                       |
     0 +                                                                                       +
       |                                                                                       |
       |                                2                                                      |
       |                                                                                       |
       |                                                                                       |
   -50 +                          11                                                           +
       |                       11                                                              |
       |                    1 1                                                                |
       |               1                                                                       |
       |                1                                                                      |
  -100 +                                                                                       +
       |                                                                                       |
       |       1                                                                               |
       |                                                                                       |
       |                                                                                       |
  -150 +                                                                                       +
       |                                                                                       |
       -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
           -25   -20   -15   -10   -5     0     5    10    15    20    25    30    35    40

                                              Income   x1
The REG Procedure
Model: MODEL1
Partial Regression Residual Plot

      ---------+------+------+------+------+------+------+------+------+------+------+----------
   30 +                                                                                        +
      |                                                                            1           |
      |                                                     1                                  |
      |                                                                    1                   |
      |                                                                                        |
      |                                                                                        |
   20 +                                                                                        +
      |                                                                                        |
      |                                                                                        |
      |                                                                                        |
      |                                                                                        |
      |                                                                                        |
   10 +                                                          1                             +
      |                                                                                        |
      |                                      1                                                 |
    y |                                                                                        |
      |                                                                                        |
I     |                                                   1          1     1                   |
n   0 +                                                  1      1                              +
s     |                                                                                        |
u     |                                           1      1                                     |
r     |                                                                                        |
a     |                                                                                        |
n     |            1                                        1                                  |
c -10 +                                                                                        +
e     |                                                        1                               |
      |                                                                                        |
      |                                                                                        |
      |                                                                                        |
      |                                      1  1                                              |
  -20 +                                                                                        +
      |                                                                                        |
      |                                                                                        |
      |                                                                                        |
      |                                                                                        |
      |                                                                                        |
  -30 +                                                                                        +
      |                                                                                        |
      |                         1                                                              |
      |                                                                                        |
      |                                                                                        |
      |                                                                                        |
  -40 +                                                                                        +
      ---------+------+------+------+------+------+------+------+------+------+------+----------
              -6     -5     -4     -3     -2     -1      0      1      2      3      4

                                          Risk Aversion   x2
If the size of the partial plots are a problem here is another way of creating the plots one by one starting with the intercept, then x1 (Fig. 9.3b, p. 365) and finally x2.
Partial Regression plot for the intercept.
data ch9tab01; 
  set ch9tab01;
  Int=1;
run;
proc reg data=ch9tab01 noprint;
  model y Int = x1 x2 / noint;
  output out=tempint r=ry rx;
run;
symbol1 c=blue;
proc gplot data=tempint;
   plot ry*rx;
   label ry='Insurance'
         rx='Intercept';
run;
quit;
Partial Regression plot against e(X1|X2), Fig. 9.3b, p. 365.
proc reg data=ch9tab01 noprint;
  model y x1 = x2 ;
  output out=tempx1 r=ry rx;
run;
symbol1 c=blue;
proc gplot data=tempx1;
   plot ry*rx;
   label ry='e(Y|X2)'
         rx='e(X1|X2)';
run;
quit;
Partial Regression plot against e(X2|X1).
proc reg data=ch9tab01 noprint;
  model y x2 = x1 ;
  output out=tempx2 r=ry rx;
run;
symbol1 c=blue;
proc gplot data=tempx2;
   plot ry*rx;
   label ry='e(Y|X1)'
         rx='e(X2|X1)';
run;
quit;
Inputting Body Fat data set from ch. 7, table 1, p. 261.
data ch7tab01;
  input X1 X2 X3 Y;
  label x1 = 'Triceps' 
        x2 = 'Thigh cir.'
	x3 = 'Midarm cir.'
         y = 'body fat';
  cards;
  19.5  43.1  29.1  11.9
  24.7  49.8  28.2  22.8
  30.7  51.9  37.0  18.7
  29.8  54.3  31.1  20.1
  19.1  42.2  30.9  12.9
  25.6  53.9  23.7  21.7
  31.4  58.5  27.6  27.1
  27.9  52.1  30.6  25.4
  22.1  49.9  23.2  21.3
  25.5  53.5  24.8  19.3
  31.1  56.6  30.0  25.4
  30.4  56.7  28.3  27.2
  18.7  46.5  23.0  11.7
  19.7  44.2  28.6  17.8
  14.6  42.7  21.3  12.8
  29.5  54.4  30.1  23.9
  27.7  55.3  25.7  22.6
  30.2  58.6  24.6  25.4
  22.7  48.2  27.1  14.8
  25.2  51.0  27.5  21.1
;
run;
Fig. 9.4a-9.4d, p. 366.
proc reg data = ch7tab01;
  model y = x1 x2/partial;
  plot r.*x1 r.*x2;
run;quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat

                             Analysis of Variance

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

Model                     2      385.43871      192.71935      29.80    <.0001
Error                    17      109.95079        6.46769
Corrected Total          19      495.38950

Root MSE              2.54317    R-Square     0.7781
Dependent Mean       20.19500    Adj R-Sq     0.7519
Coeff Var            12.59305

                               Parameter Estimates

                                   Parameter       Standard
Variable     Label         DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept      1      -19.17425        8.36064      -2.29      0.0348
X1           Triceps        1        0.22235        0.30344       0.73      0.4737
X2           Thigh cir.     1        0.65942        0.29119       2.26      0.0369

The REG Procedure
Model: MODEL1
Partial Regression Residual Plot

     ------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+------
   Y |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
   4 +                                                                                         +
     |                                                                                         |
     |                             1                                                           |
     |                             1                     1  1                                  |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
   2 +                   1                                                                     +
     |                                                                  1                      |
     |                                                                                         |
     |         1        1                                                                      |
     |                                           1                                             |
     |                                   1    1   1                                            |
b    |                     1                                                                   |
o  0 +                                                                                         +
d    |                                                                                         |
y    |                                                                                         |
     |                                                                                         |
f    |                     1                                                                   |
a    |                                                                                         |
t    |                                                                                         |
  -2 +                                                                                         +
     |                                                                                         |
     |                                                                                 1       |
     |                                                                                         |
     |                                                                                         |
     |                                                   1                                     |
     |                                    1          1                                         |
  -4 +                                                                           1             +
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                              1          |
     |                                                                                         |
  -6 +                                                                                         +
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     ------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+------
         -0.12 -0.10 -0.08 -0.06 -0.04 -0.02 0.00  0.02  0.04  0.06  0.08  0.10  0.12  0.14

                                              Intercept
The REG Procedure
Model: MODEL1
Partial Regression Residual Plot

     --+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+---
   6 +                                                                                         +
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                      1                                  |
   4 +                                                                                         +
     |                                          2                                              |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |               1                      1                                                  |
   2 +                                                                                         +
     |                                                                                         |
     |                                                                                         |
b  Y |                                    1                                                    |
o    |                                                 1                                       |
d    |                                1             1                                          |
y    |                                                     1                                   |
   0 +    1                                                                                    +
f    |                                                                                         |
a    |                                                                                         |
t    |               1                                                                         |
     |                   1   1                                                                 |
     |                                                 1                                       |
     |                                                                                         |
  -2 +                                                                                   1     +
     |                                                                                         |
     |                                                                                         |
     |                 1                  1                1                                   |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
  -4 +                                                                                         +
     |                                                                                         |
     |           1                                                                             |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
  -6 +                                                                                         +
     --+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+---
     -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5  0.0  0.5  1.0  1.5  2.0  2.5  3.0  3.5  4.0  4.5  5.0

                                            Triceps   X1
The REG Procedure
Model: MODEL1
Partial Regression Residual Plot

     -------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+--------
   4 +                                                                                         +
     |                                                                     1                   |
     |                                                                                         |
     |                                           1                                             |
     |                                   1                                                     |
     |                                                         1                               |
     |                                   1                                                     |
   2 +                                                                                         +
     |                                                                  1  1                   |
     |                                                                                         |
     |                                                                           1  1          |
     |                                                  1                                      |
     |                                                                                         |
     |                                                  1                  1                   |
   0 +                                           1                                             +
     |                                                                                         |
     |                                                                                         |
b  Y |                                                                                         |
o    |                                                                        1                |
d    |                                                                                         |
y    |                                                                                         |
  -2 +                     1                                                                   +
f    |                                                                                         |
a    |                                                                                         |
t    |                                                                    1                    |
     |                                              1                                          |
     |                          1                                                              |
     |                                                                                         |
  -4 +                                       1                                                 +
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
  -6 +      1                                                                                  +
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
     |                                                                                         |
  -8 +                                                                                         +
     -------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+--------
          -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5  0.0  0.5  1.0  1.5  2.0  2.5  3.0

                                           Thigh cir.   X2
Table 9.3, p. 375.
proc reg data = ch7tab01 noprint ;
  model y = x1 x2  ;
  output out=temp r=residual h=hat rstudent=rstudent;
run;
proc print data = temp;
 var residual hat rstudent;
run;
Obs    residual      hat      rstudent

  1    -1.68271    0.20101    -0.72999
  2     3.64293    0.05889     1.53425
  3    -3.17597    0.37193    -1.65433
  4    -3.15847    0.11094    -1.34848
  5    -0.00029    0.24801    -0.00013
  6    -0.36082    0.12862    -0.14755
  7     0.71620    0.15552     0.29813
  8     4.01473    0.09629     1.76009
  9     2.65511    0.11464     1.11765
 10    -2.47481    0.11024    -1.03373
 11     0.33581    0.12034     0.13666
 12     2.22551    0.10927     0.92318
 13    -3.94686    0.17838    -1.82590
 14     3.44746    0.14801     1.52476
 15     0.57059    0.33321     0.26715
 16     0.64230    0.09528     0.25813
 17    -0.85095    0.10559    -0.34451
 18    -0.78292    0.19679    -0.33441
 19    -2.85729    0.06695    -1.17617
 20     1.04045    0.05009     0.40936
Fig. 9.7, p. 378.
symbol1 v=square c=blue h = .8;
axis1 order=(42 to 60 by 4);
axis2 order=(14 to 32 by 2);
proc gplot data = ch7tab01;
  plot x2*x1/ vaxis=axis1 haxis= axis2;
run;
quit;
Table 9.4, p. 380.
ods listing close;
proc reg data = ch7tab01;
  model y = x1 x2/influence ;
  ods output  OutputStatistics=temp;
  output out=temp1 cookd = cooksd;
run;
quit;
ods listing;
data temp2;
  set temp;
  keep observation dffits dfb_intercept dfb_x1 dfb_x2 ;
run;
data temp1;
  set temp1;
  observation = _n_;
  keep observation cooksd;
run;
data combined ;
  merge temp1 temp2;
  by observation;
run;
proc print data = combined;
 var dffits cooksd dfb_intercept dfb_x1 dfb_x2;
run; 
                                DFB_
Obs      DFFITS     cooksd    Intercept      DFB_X1      DFB_X2

  1     -0.3661    0.04595     -0.3052      -0.1315      0.2320
  2      0.3838    0.04548      0.1726       0.1150     -0.1426
  3     -1.2731    0.49016     -0.8471      -1.1825      1.0669
  4     -0.4763    0.07216     -0.1016      -0.2935      0.1961
  5     -0.0001    0.00000     -0.0001      -0.0000      0.0001
  6     -0.0567    0.00114      0.0397       0.0401     -0.0443
  7      0.1279    0.00576     -0.0775      -0.0156      0.0543
  8      0.5745    0.09794      0.2614       0.3911     -0.3325
  9      0.4022    0.05313     -0.1514      -0.2947      0.2469
 10     -0.3639    0.04396      0.2377       0.2446     -0.2688
 11      0.0505    0.00090     -0.0090       0.0171     -0.0025
 12      0.3233    0.03515     -0.1305       0.0225      0.0700
 13     -0.8508    0.21215      0.1194       0.5924     -0.3895
 14      0.6355    0.12489      0.4517       0.1132     -0.2977
 15      0.1889    0.01258     -0.0030      -0.1248      0.0688
 16      0.0838    0.00247      0.0093       0.0431     -0.0251
 17     -0.1184    0.00493      0.0795       0.0550     -0.0761
 18     -0.1655    0.00964      0.1321       0.0753     -0.1161
 19     -0.3151    0.03236     -0.1296      -0.0041      0.0644
 20      0.0940    0.00310      0.0102       0.0023     -0.0033
SAS actually has an influence option in the model statement that will display most of the diagnostic statistics. It contains everything in Table 9.3 and Table 9.4 except Cook's D. So, unless it is absolutely critical to have Cook's D with the Dfbetas, Dffits and the various residuals then this might be a nice simple alternative.
proc reg data = ch7tab01;
 model y = x1 x2/ influence;
run;quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat

                             Analysis of Variance

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

Model                     2      385.43871      192.71935      29.80    <.0001
Error                    17      109.95079        6.46769
Corrected Total          19      495.38950

Root MSE              2.54317    R-Square     0.7781
Dependent Mean       20.19500    Adj R-Sq     0.7519
Coeff Var            12.59305

                               Parameter Estimates

                                   Parameter       Standard
Variable     Label         DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept      1      -19.17425        8.36064      -2.29      0.0348
X1           Triceps        1        0.22235        0.30344       0.73      0.4737
X2           Thigh cir.     1        0.65942        0.29119       2.26      0.0369

The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat

                                     Output Statistics

                                Hat Diag       Cov            -----------DFBETAS-----------
     Obs   Residual   RStudent         H     Ratio    DFFITS  Intercept        X1        X2

       1    -1.6827    -0.7300    0.2010    1.3607   -0.3661    -0.3052   -0.1315    0.2320
       2     3.6429     1.5343    0.0589    0.8443    0.3838     0.1726    0.1150   -0.1426
       3    -3.1760    -1.6543    0.3719    1.1892   -1.2731    -0.8471   -1.1825    1.0669
       4    -3.1585    -1.3485    0.1109    0.9768   -0.4763    -0.1016   -0.2935    0.1961
       5  -0.000289  -0.000127    0.2480    1.5951   -0.0001    -0.0001   -0.0000    0.0001
       6    -0.3608    -0.1475    0.1286    1.3709   -0.0567     0.0397    0.0401   -0.0443
       7     0.7162     0.2981    0.1555    1.3969    0.1279    -0.0775   -0.0156    0.0543
       8     4.0147     1.7601    0.0963    0.7805    0.5745     0.2614    0.3911   -0.3325
       9     2.6551     1.1176    0.1146    1.0812    0.4022    -0.1514   -0.2947    0.2469
      10    -2.4748    -1.0337    0.1102    1.1104   -0.3639     0.2377    0.2446   -0.2688
      11     0.3358     0.1367    0.1203    1.3588    0.0505    -0.0090    0.0171   -0.0025
      12     2.2255     0.9232    0.1093    1.1525    0.3233    -0.1305    0.0225    0.0700
      13    -3.9469    -1.8259    0.1784    0.8274   -0.8508     0.1194    0.5924   -0.3895
      14     3.4475     1.5248    0.1480    0.9371    0.6355     0.4517    0.1132   -0.2977
      15     0.5706     0.2672    0.3332    1.7750    0.1889    -0.0030   -0.1248    0.0688
      16     0.6423     0.2581    0.0953    1.3094    0.0838     0.0093    0.0431   -0.0251
      17    -0.8509    -0.3445    0.1056    1.3117   -0.1184     0.0795    0.0550   -0.0761
      18    -0.7829    -0.3344    0.1968    1.4625   -0.1655     0.1321    0.0753   -0.1161
      19    -2.8573    -1.1762    0.0670    1.0024   -0.3151    -0.1296   -0.0041    0.0644
      20     1.0404     0.4094    0.0501    1.2238    0.0940     0.0102    0.0023   -0.0033

Sum of Residuals                           0
Sum of Squared Residuals           109.95079
Predicted Residual SS (PRESS)      154.47356
Fig. 9.8a, p. 382. With an added bonus: a line through zero. To get rid of the line just delete the vref=0 option in the model statement.
proc reg data=ch7tab01 noprint;
  model y=x1 x2;
  output out=tempout cookd=ckd p=yhat r=resid;
run;
quit;
axis1 order=(10 to 30 by 5);
axis2 order=(-4.5 to 4.5 by 1.5) label = (angle=90 h=1 color=black 'Studentized Resid' );
proc gplot data=tempout;
  bubble resid*yhat=ckd /haxis=axis1 vaxis=axis2  bsize=10 hminor=0 vminor=0 vref=0 bsize=4;
  label resid='Studentized Residuals';
  label yhat='YHat';
run;
quit;
To see another example of a Proportional Influence plot using studentized residuals versus leverage where the size is also controlled by the Cook's D please see: http://www.ats.ucla.edu/stat/sas/examples/ara/arasas11.htm.
Fig. 9.8b, p. 382. The first data step is just to create the index to be used in the plot. The extra option line after the quit statement is to make sure that future plots do not have observations joined by a line.
data tempout;
  set tempout;
  id = _n_;
run;
symbol1 v=square i=join h = .8;
axis1 label = (angle=90 h=1 color=black 'Cooks D' ) order=(0 to 0.5 by 0.1);
axis2 order=(0 to 25 by 5);
proc gplot data=tempout;
  plot ckd*id / vaxis=axis1 haxis=axis2;
run;
quit;
symbol1 v=square i=none h=.8;
Table 9.5, p. 388.
proc reg data = ch7tab01;
  model y = x1 x2 x3/ vif tol stb;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat

                             Analysis of Variance

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

Model                     3      396.98461      132.32820      21.52    <.0001
Error                    16       98.40489        6.15031
Corrected Total          19      495.38950

Root MSE              2.47998    R-Square     0.8014
Dependent Mean       20.19500    Adj R-Sq     0.7641
Coeff Var            12.28017

                                    Parameter Estimates

                                 Parameter      Standard                        Standardized
Variable    Label         DF      Estimate         Error   t Value   Pr > |t|       Estimate

Intercept   Intercept      1     117.08469      99.78240      1.17     0.2578              0
X1          Triceps        1       4.33409       3.01551      1.44     0.1699        4.26370
X2          Thigh cir.     1      -2.85685       2.58202     -1.11     0.2849       -2.92870
X3          Midarm cir.    1      -2.18606       1.59550     -1.37     0.1896       -1.56142

                   Parameter Estimates

                                                 Variance
Variable    Label         DF     Tolerance      Inflation

Intercept   Intercept      1             .              0
X1          Triceps        1       0.00141      708.84291
X2          Thigh cir.     1       0.00177      564.34339
X3          Midarm cir.    1       0.00956      104.60601
Surgical Unit example--continued, p. 388-392. Creating the logy variable.
data ch8tab01;
  input x1 x2 x3 x4 y logy;
  label x1 = 'blood-clotting'
        x2 = 'prognostic'
        x3 = 'enzyme'
	x4 = 'liver function'
	 y = 'survival'
    logy = 'logSurvival';
cards;
   6.7  62   81  2.59  200  2.3010
   5.1  59   66  1.70  101  2.0043
   7.4  57   83  2.16  204  2.3096
   6.5  73   41  2.01  101  2.0043
   7.8  65  115  4.30  509  2.7067
   5.8  38   72  1.42   80  1.9031
   5.7  46   63  1.91   80  1.9031
   3.7  68   81  2.57  127  2.1038
   6.0  67   93  2.50  202  2.3054
   3.7  76   94  2.40  203  2.3075
   6.3  84   83  4.13  329  2.5172
   6.7  51   43  1.86   65  1.8129
   5.8  96  114  3.95  830  2.9191
   5.8  83   88  3.95  330  2.5185
   7.7  62   67  3.40  168  2.2253
   7.4  74   68  2.40  217  2.3365
   6.0  85   28  2.98   87  1.9395
   3.7  51   41  1.55   34  1.5315
   7.3  68   74  3.56  215  2.3324
   5.6  57   87  3.02  172  2.2355
   5.2  52   76  2.85  109  2.0374
   3.4  83   53  1.12  136  2.1335
   6.7  26   68  2.10   70  1.8451
   5.8  67   86  3.40  220  2.3424
   6.3  59  100  2.95  276  2.4409
   5.8  61   73  3.50  144  2.1584
   5.2  52   86  2.45  181  2.2577
  11.2  76   90  5.59  574  2.7589
   5.2  54   56  2.71   72  1.8573
   5.8  76   59  2.58  178  2.2504
   3.2  64   65  0.74   71  1.8513
   8.7  45   23  2.52   58  1.7634
   5.0  59   73  3.50  116  2.0645
   5.8  72   93  3.30  295  2.4698
   5.4  58   70  2.64  115  2.0607
   5.3  51   99  2.60  184  2.2648
   2.6  74   86  2.05  118  2.0719
   4.3   8  119  2.85  120  2.0792
   4.8  61   76  2.45  151  2.1790
   5.4  52   88  1.81  148  2.1703
   5.2  49   72  1.84   95  1.9777
   3.6  28   99  1.30   75  1.8751
   8.8  86   88  6.40  483  2.6840
   6.5  56   77  2.85  153  2.1847
   3.4  77   93  1.48  191  2.2810
   6.5  40   84  3.00  123  2.0899
   4.5  73  106  3.05  311  2.4928
   4.8  86  101  4.10  398  2.5999
   5.1  67   77  2.86  158  2.1987
   3.9  82  103  4.55  310  2.4914
   6.6  77   46  1.95  124  2.0934
   6.4  85   40  1.21  125  2.0969
   6.4  59   85  2.33  198  2.2967
   8.8  78   72  3.20  313  2.4955
;
run;
The VIF at the bottom of p. 389.
Fig. 9.9a, 9.9b and 9.9d, p. 390.
proc reg data = ch8tab01;
  var x4;
  model logy = x1-x3/ vif tol;
  plot r.*p. r.*x4 r.*nqq.;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: logy logSurvival

                             Analysis of Variance

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

Model                     3        3.86291        1.28764     586.04    <.0001
Error                    50        0.10986        0.00220
Corrected Total          53        3.97277

Root MSE              0.04687    R-Square     0.9723
Dependent Mean        2.20614    Adj R-Sq     0.9707
Coeff Var             2.12470

                                     Parameter Estimates

                                    Parameter      Standard
Variable    Label            DF      Estimate         Error   t Value   Pr > |t|     Tolerance

Intercept   Intercept         1       0.48362       0.04263     11.34     <.0001             .
x1          blood-clotting    1       0.06923       0.00408     16.98     <.0001       0.97011
x2          prognostic        1       0.00929    0.00038250     24.30     <.0001       0.99177
x3          enzyme            1       0.00952    0.00030641     31.08     <.0001       0.97751

             Parameter Estimates

                                     Variance
Variable    Label            DF     Inflation

Intercept   Intercept         1             0
x1          blood-clotting    1       1.03081
x2          prognostic        1       1.00829
x3          enzyme            1       1.02301
Fig. 9.9c, p. 390.
proc reg data=ch8tab01 noprint;
  model logy x1 = x2 x3;
  output out=tempx1 r=ry rx;
run;
symbol1 v=square c=blue i=none;
axis1 label = (angle=90 h=1 color=black 'e(Y|X2, X3)' );
 
proc gplot data=tempx1;
   plot ry*rx / vaxis = axis1;
   label rx='e(X1|X2, X3)';
run;
quit;
Table 9.6, p. 391
In order to get only a few of the variables and observations from the influence option it is necessary to use an ods output. But influence does not give us Cook's D so we have to that from a regular output statement. The result is that there are two datasets: an ods dataset containing residual, hatdiagonal,rstudent, dffits and another data set containing Cook's D, these two datasets are then merged and we can pick out the interesting observations.
ods listing close;
proc reg data = ch8tab01;
  model logy = x1-x3/influence ;
  ods output  OutputStatistics=temp;
  output out=temp1 cookd = cooksd;
run;
quit;
ods listing;
data temp2;
  set temp;
  keep observation residual hatdiagonal rstudent dffits;
run;
data temp1;
  set temp1;
  observation = _n_;
  keep observation cooksd;
run;
data combined ;
  merge temp1 temp2;
  by observation;
run;
proc print data = combined;
 where observation=13 or observation=17 or observation=22 or
       observation=27 or observation=28 or observation=32 or observation=38;
 var residual hatdiagonal rstudent dffits cooksd; 
run;
                      Hat
Obs     Residual    Diagonal     RStudent      DFFITS     cooksd

 13       0.0560      0.1495       1.3046      0.5469    0.07375
 17      -0.0162      0.1499      -0.3709     -0.1557    0.00617
 22       0.1383      0.1274       3.4952      1.3353    0.36409
 27       0.1118      0.0311       2.5523      0.4572    0.04706
 28      -0.0636      0.2619      -1.6027     -0.9546    0.22090
 32       0.0402      0.2113       0.9656      0.4998    0.06252
 38       0.0902      0.2902       2.3903      1.5282    0.53356

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