1          **************************************************************************;
2          *** Bootstrap Example                                                  ***;
3          *** Problem from Neter, Kutner, Nachtsheim & Wasserman 1996, Table 7.1 ***;
4          **************************************************************************;
5
6          OPTIONS LS=99 PS=256 NOCENTER NODATE NONUMBER;
7
8          DATA ONE; INFILE CARDS MISSOVER;
9               TITLE1 'EXST7034 - Bodyfat Example, NKNW Table 7.1';
10              LABEL X1 = 'Triceps skinfold thickness';
11              LABEL X2 = 'Thigh circumference';
12              LABEL X3 = 'Midarm circumference';
13              LABEL Y = 'Body Fat';
14            INPUT SUBJECT X1 X2 X3 Y;
15         CARDS;
NOTE: The data set WORK.ONE has 20 observations and 5 variables.
NOTE: DATA statement used:
      real time           0.11 seconds
15       !        RUN;
36         ;
37
38         *******************************************;
39         ***  Bootstrap section                 ***;
40         *******************************************;
41
42         DATA BOOTS;
43            DO Run = 1 TO 50 BY 1;
44            DO rep = 1 TO 20 BY 1;
45               get = INT(RANUNI(37746319)*20+1);
46            SET ONE POINT=get NOBS=subjects; OUTPUT;
47            END;
48            END;
49            stop;
50         RUN;
NOTE: The data set WORK.BOOTS has 1000 observations and 7 variables.
NOTE: DATA statement used:
      real time           0.05 seconds
51         proc print data=boots; run;
NOTE: There were 1000 observations read from the data set WORK.BOOTS.
NOTE: The PROCEDURE PRINT printed pages 1-4.
NOTE: PROCEDURE PRINT used:
      real time           0.04 seconds
 

 EXST7034 - Bodyfat Example, NKNW Table 7.1
 Obs    Run    rep     X1      X2      X3       Y   SUBJECT
   1      1      1    29.8    54.3    31.1    20.1        4
   2      1      2    30.7    51.9    37.0    18.7        3
   3      1      3    27.7    55.3    25.7    22.6       17
   4      1      4    19.5    43.1    29.1    11.9        1
   5      1      5    30.2    58.6    24.6    25.4       18
   6      1      6    19.5    43.1    29.1    11.9        1
   7      1      7    24.7    49.8    28.2    22.8        2
   8      1      8    27.9    52.1    30.6    25.4        8
   9      1      9    29.8    54.3    31.1    20.1        4
  10      1     10    25.6    53.9    23.7    21.7        6
  11      1     11    30.7    51.9    37.0    18.7        3
  12      1     12    27.7    55.3    25.7    22.6       17
  13      1     13    30.2    58.6    24.6    25.4       18
  14      1     14    25.5    53.5    24.8    19.3       10
  15      1     15    27.7    55.3    25.7    22.6       17
  16      1     16    29.8    54.3    31.1    20.1        4
  17      1     17    30.4    56.7    28.3    27.2       12
  18      1     18    22.7    48.2    27.1    14.8       19
  19      1     19    24.7    49.8    28.2    22.8        2
  20      1     20    24.7    49.8    28.2    22.8        2
  21      2      1    27.9    52.1    30.6    25.4        8
  22      2      2    30.4    56.7    28.3    27.2       12
  23      2      3    14.6    42.7    21.3    12.8       15
  24      2      4    31.1    56.6    30.0    25.4       11
  25      2      5    30.2    58.6    24.6    25.4       18
  26      2      6    25.2    51.0    27.5    21.1       20
  27      2      7    29.5    54.4    30.1    23.9       16
  28      2      8    30.7    51.9    37.0    18.7        3
  29      2      9    30.7    51.9    37.0    18.7        3
  30      2     10    22.7    48.2    27.1    14.8       19
  31      2     11    29.5    54.4    30.1    23.9       16
  32      2     12    22.1    49.9    23.2    21.3        9
  33      2     13    27.9    52.1    30.6    25.4        8
  34      2     14    29.5    54.4    30.1    23.9       16
  35      2     15    19.1    42.2    30.9    12.9        5
  36      2     16    27.9    52.1    30.6    25.4        8
  37      2     17    22.1    49.9    23.2    21.3        9
  38      2     18    27.9    52.1    30.6    25.4        8
  39      2     19    19.7    44.2    28.6    17.8       14
  40      2     20    31.1    56.6    30.0    25.4       11
 
 

 53         PROC SORT DATA=BOOTS; BY run rep; run;
NOTE: There were 1000 observations read from the data set WORK.BOOTS.
NOTE: The data set WORK.BOOTS has 1000 observations and 7 variables.
NOTE: PROCEDURE SORT used:
      real time           0.00 seconds
54
55         PROC REG DATA=one; TITLE2 'Ordinary Regression';
56               MODEL  Y = X1 X2 X3 / vif collin;
57         RUN;
NOTE: 20 observations read.
NOTE: 20 observations used in computations.
58
NOTE: The PROCEDURE REG printed page 5.
NOTE: PROCEDURE REG used:
      real time           0.10 seconds
 

EXST7034 - Bodyfat Example, NKNW Table 7.1
Ordinary Regression

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                        Variance
Variable   Label                       DF     Estimate        Error  t Value  Pr > |t|    Inflation
Intercept  Intercept                    1    117.08469     99.78240     1.17    0.2578            0
X1         Triceps skinfold thickness   1      4.33409      3.01551     1.44    0.1699    708.84291
X2         Thigh circumference          1     -2.85685      2.58202    -1.11    0.2849    564.34339
X3         Midarm circumference         1     -2.18606      1.59550    -1.37    0.1896    104.60601

Collinearity Diagnostics
                             Condition    -----------------Proportion of Variation----------------
  Number     Eigenvalue          Index      Intercept             X1             X2             X3
       1        3.96796        1.00000     0.00000195     0.00000320     0.00000110     0.00000980
       2        0.02052       13.90482     0.00037152        0.00132     0.00003262        0.00139
       3        0.01151       18.56570     0.00059915     0.00021875     0.00032550        0.00693
       4     0.00000865      677.37207        0.99903        0.99846        0.99964        0.99167
 
 

59         PROC REG DATA=boots outest=BVALUES NOPRINT; by run;
60               TITLE2 'Bootstrap regression';
61               MODEL  Y = X1 X2 X3;
62         RUN;
NOTE: 20 observations read.
NOTE: 20 observations used in computations.
NOTE: The above message was for the following by-group:
      Run=1
NOTE: 20 observations read.
NOTE: 20 observations used in computations.
NOTE: The above message was for the following by-group:
      Run=2
NOTE: 20 observations read.
NOTE: 20 observations used in computations.
NOTE: The above message was for the following by-group:
      Run=3
. . .
NOTE: 20 observations read.
NOTE: 20 observations used in computations.
NOTE: The above message was for the following by-group:
      Run=50
NOTE: Interactivity disabled with BY processing.
NOTE: PROCEDURE REG used:
      real time           0.04 seconds
NOTE: The data set WORK.BVALUES has 50 observations and 10 variables.
 63         proc sort data=BVALUES; by x1 x2 x3; run;
NOTE: There were 50 observations read from the data set WORK.BVALUES.
NOTE: The data set WORK.BVALUES has 50 observations and 10 variables.
NOTE: PROCEDURE SORT used:
      real time           0.00 seconds
64         proc print data=BVALUES; run;
NOTE: There were 50 observations read from the data set WORK.BVALUES.
NOTE: The PROCEDURE PRINT printed page 6.
NOTE: PROCEDURE PRINT used:
      real time           0.00 seconds
 
 

EXST7034 - Bodyfat Example, NKNW Table 7.1
Bootstrap regression

Obs   Run   _MODEL_   _TYPE_   _DEPVAR_    _RMSE_   Intercept         X1      X2         X3       Y
  1    45   MODEL1    PARMS       Y       2.02826     -86.069    -2.2746    2.69354    0.96798   -1
  2     3   MODEL1    PARMS       Y       2.57250     -93.869    -1.8845    2.47138    1.27658   -1
  3    11   MODEL1    PARMS       Y       2.55378     -83.508    -1.6238    2.18801    1.20208   -1
  4     6   MODEL1    PARMS       Y       2.58466     -68.778    -1.3964    2.00652    0.75932   -1
  5    50   MODEL1    PARMS       Y       2.47264     -69.455    -1.1752    1.73600    1.12700   -1
  6    38   MODEL1    PARMS       Y       2.29334     -37.944    -0.5274    1.30906    0.17175   -1
  7    49   MODEL1    PARMS       Y       2.17482     -54.870    -0.4746    1.36310    0.62290   -1
  8    29   MODEL1    PARMS       Y       1.71841     -10.626     0.2922    0.60947   -0.29663   -1
  9    44   MODEL1    PARMS       Y       2.40471       6.600     1.2401   -0.17689   -0.28207   -1
 10    35   MODEL1    PARMS       Y       1.84837      26.990     1.4657   -0.37080   -0.89895   -1
 11    32   MODEL1    PARMS       Y       2.70628      24.093     1.4936   -0.42727   -0.69926   -1
 12    16   MODEL1    PARMS       Y       2.42875      28.031     1.6422   -0.64958   -0.58204   -1
 13    40   MODEL1    PARMS       Y       2.10121      38.661     1.7080   -0.64762   -1.02238   -1
 14    17   MODEL1    PARMS       Y       2.84546      40.393     2.0076   -0.88047   -0.95489   -1
 15    15   MODEL1    PARMS       Y       2.31671      45.586     2.1730   -0.95736   -1.12663   -1
 16    27   MODEL1    PARMS       Y       1.88707      58.810     2.4313   -1.25808   -1.28893   -1
 17    47   MODEL1    PARMS       Y       2.10667      39.182     2.4336   -1.15205   -0.77021   -1
 18    46   MODEL1    PARMS       Y       2.19939      53.957     2.5141   -1.38110   -0.95129   -1
 19    28   MODEL1    PARMS       Y       1.93668      69.801     2.9387   -1.71871   -1.29085   -1
 20    23   MODEL1    PARMS       Y       2.42737      81.924     3.2264   -1.90584   -1.67519   -1
 21    48   MODEL1    PARMS       Y       2.41676      91.942     3.7038   -2.24583   -1.83223   -1
 22    18   MODEL1    PARMS       Y       2.10993     102.046     3.7187   -2.41609   -1.88916   -1
 23    25   MODEL1    PARMS       Y       2.15277      98.314     3.7342   -2.31042   -1.98330   -1
 24     7   MODEL1    PARMS       Y       1.85771      92.992     3.7852   -2.28726   -1.87444   -1
 25    13   MODEL1    PARMS       Y       2.32050     127.377     4.6226   -3.36044   -1.85601   -1
 26    26   MODEL1    PARMS       Y       2.37111     133.914     4.7175   -3.18471   -2.52731   -1
 27    22   MODEL1    PARMS       Y       1.94202     131.030     4.9349   -3.16099   -2.71435   -1
 28    14   MODEL1    PARMS       Y       1.95453     130.200     4.9617   -3.21599   -2.60675   -1
 29    36   MODEL1    PARMS       Y       2.29776     138.831     5.1255   -3.47801   -2.55601   -1
 30     8   MODEL1    PARMS       Y       1.98470     147.198     5.1976   -3.59410   -2.71967   -1
 31    39   MODEL1    PARMS       Y       2.58372     150.196     5.2636   -3.72834   -2.61851   -1
 32    33   MODEL1    PARMS       Y       2.20953     146.101     5.3011   -3.71116   -2.51520   -1
 33    19   MODEL1    PARMS       Y       1.77352     149.207     5.4396   -3.68593   -2.84126   -1
 34    42   MODEL1    PARMS       Y       2.30561     157.401     5.9257   -4.02984   -2.93899   -1
 35     9   MODEL1    PARMS       Y       1.85783     175.036     6.0075   -4.30338   -3.13580   -1
 36    31   MODEL1    PARMS       Y       2.41120     172.321     6.1022   -4.24178   -3.21940   -1
 37    21   MODEL1    PARMS       Y       2.11778     178.011     6.2960   -4.51068   -3.11575   -1
 38    41   MODEL1    PARMS       Y       2.28227     179.042     6.3081   -4.46844   -3.26730   -1
 39    37   MODEL1    PARMS       Y       2.10368     190.881     6.6623   -4.73044   -3.51688   -1
 40     4   MODEL1    PARMS       Y       1.84715     188.573     6.8525   -4.76859   -3.59560   -1
 41    34   MODEL1    PARMS       Y       1.24266     218.639     7.0207   -5.52998   -3.33280   -1
 42    43   MODEL1    PARMS       Y       2.32869     203.406     7.0778   -5.18465   -3.52981   -1
 43     2   MODEL1    PARMS       Y       2.14797     223.911     7.3580   -5.54262   -3.81904   -1
 44    30   MODEL1    PARMS       Y       1.67673     245.073     7.9449   -6.14498   -3.99649   -1
 45    12   MODEL1    PARMS       Y       2.29412     254.024     8.3006   -6.38929   -4.20551   -1
 46    24   MODEL1    PARMS       Y       2.08328     249.820     8.8414   -6.41505   -4.57029   -1
 47     1   MODEL1    PARMS       Y       2.25141     279.694     9.5525   -7.13374   -4.97738   -1
 48    20   MODEL1    PARMS       Y       2.52198     315.426     9.9770   -7.97082   -5.07632   -1
 49     5   MODEL1    PARMS       Y       1.97195     303.961    10.1455   -7.67782   -5.34358   -1
 50    10   MODEL1    PARMS       Y       1.83336     365.081    12.0749   -9.32553   -6.28819   -1
 

 65         proc univariate data=bvalues plot normal; var x1 x2 x3; run;
NOTE: The PROCEDURE UNIVARIATE printed pages 7-9.
NOTE: PROCEDURE UNIVARIATE used:
      real time           0.00 seconds
 

EXST7034 - Bodyfat Example, NKNW Table 7.1
Bootstrap regression

The UNIVARIATE Procedure
Variable:  X1  (Triceps skinfold thickness)

                            Moments
N                          50    Sum Weights                 50
Mean               4.18327267    Sum Observations    209.163634
Std Deviation      3.40267416    Variance            11.5781914
Skewness           0.01136057    Kurtosis             -0.437222
Uncorrected SS     1442.31989    Corrected SS        567.331379
Coeff Variation    81.3400039    Std Error Mean      0.48121079

              Basic Statistical Measures
    Location                    Variability
Mean     4.183273     Std Deviation            3.40267
Median   4.670047     Variance                11.57819
Mode      .           Range                   14.34952
                      Interquartile Range      4.60007

           Tests for Location: Mu0=0
Test           -Statistic-    -----p Value------
Student's t    t  8.693223    Pr > |t|    <.0001
Sign           M        18    Pr >= |M|   <.0001
Signed Rank    S     586.5    Pr >= |S|   <.0001

                   Tests for Normality
Test                  --Statistic---    -----p Value------
Shapiro-Wilk          W     0.984593    Pr < W      0.7540
Kolmogorov-Smirnov    D      0.07136    Pr > D     >0.1500
Cramer-von Mises      W-Sq  0.029461    Pr > W-Sq  >0.2500
Anderson-Darling      A-Sq  0.206462    Pr > A-Sq  >0.2500

Quantiles (Definition 5)
Quantile        Estimate
100% Max       12.074908
99%            12.074908
95%             9.977006  <== 95th percentile used in calculating confidence intervals
90%             8.571038
75% Q3          6.308094
50% Median      4.670047
25% Q1          1.708026
10%            -0.851315
5%             -1.623760  <== 5th percentile used in calculating confidence intervals
1%             -2.274612
0% Min         -2.274612

            Extreme Observations
------Lowest-----        ------Highest-----
   Value      Obs            Value      Obs
-2.27461        1          8.84144       46
-1.88453        2          9.55255       47
-1.62376        3          9.97701       48
-1.39637        4         10.14549       49
-1.17521        5         12.07491       50

    Stem Leaf                     #  Boxplot
     12 1                        1     |
     11                                |
     10 01                       2     |
      9 6                        1     |
      8 38                       2     |
      7 0149                     4     |
      6 013379                   6  +-----+
      5 0123349                  7  |     |
      4 679                      3  *--+--*
      3 27778                    5  |     |
      2 024459                   6  |     |
      1 25567                    5  +-----+
      0 3                        1     |
     -0 55                       2     |
     -1 9642                     4     |
     -2 3                        1     |
        ----+----+----+----+

                       Normal Probability Plot
    12.5+                                               *+++
        |                                              ++
        |                                           *++
     9.5+                                        **+
        |                                     **+
        |                                  ***
     6.5+                              ****
        |                           ***+
        |                         **+
     3.5+                      ***
        |                   ****
        |                ***
     0.5+             ++*
        |          +++**
        |       *+** *
    -2.5+   *+++
         +----+----+----+----+----+----+----+----+----+----+
             -2        -1         0        +1        +2
 
 
 
 
 

EXST7034 - Bodyfat Example, NKNW Table 7.1
Bootstrap regression

The UNIVARIATE Procedure
Variable:  X2  (Thigh circumference)

                            Moments
N                          50    Sum Weights                 50
Mean               -2.7179113    Sum Observations    -135.89557
Std Deviation       2.8926404    Variance            8.36736846
Skewness            -0.019163    Kurtosis            -0.4632498
Uncorrected SS     779.353152    Corrected SS        410.001054
Coeff Variation     -106.4288    Std Error Mean      0.40908113

              Basic Statistical Measures
    Location                    Variability
Mean     -2.71791     Std Deviation            2.89264
Median   -3.17285     Variance                 8.36737
Mode       .          Range                   12.01907
                      Interquartile Range      3.86110

            Tests for Location: Mu0=0
Test           -Statistic-    -----p Value------
Student's t    t  -6.64394    Pr > |t|    <.0001
Sign           M       -17    Pr >= |M|   <.0001
Signed Rank    S    -513.5    Pr >= |S|   <.0001

                   Tests for Normality
Test                  --Statistic---    -----p Value------
Shapiro-Wilk          W     0.984508    Pr < W      0.7503
Kolmogorov-Smirnov    D      0.08087    Pr > D     >0.1500
Cramer-von Mises      W-Sq  0.026751    Pr > W-Sq  >0.2500
Anderson-Darling      A-Sq  0.194131    Pr > A-Sq  >0.2500

Quantiles (Definition 5)
Quantile       Estimate
100% Max       2.693542
99%            2.693542
95%            2.188008  <== 95th percentile used in calculating confidence intervals
90%            1.549550
75% Q3        -0.649579
50% Median    -3.172851
25% Q1        -4.510678
10%           -6.402169
5%            -7.677820  <== 5th percentile used in calculating confidence intervals
1%            -9.325527
0% Min        -9.325527

           Extreme Observations
------Lowest-----        -----Highest-----
   Value      Obs           Value      Obs
-9.32553       50         1.73600        5
-7.97082       48         2.00652        4
-7.67782       49         2.18801        3
-7.13374       47         2.47138        2
-6.41505       46         2.69354        1

   Stem Leaf                     #  Boxplot
      2 0257                     4     |
      1 347                      3     |
      0 6                        1     |
     -0 966442                   6  +-----+
     -1 974320                   6  |     |
     -2 4332                     4  |  +  |
     -3 777654222                9  *-----*
     -4 8755320                  7  +-----+
     -5 552                      3     |
     -6 441                      3     |
     -7 71                       2     |
     -8 0                        1     |
     -9 3                        1     |
        ----+----+----+----+

                       Normal Probability Plot
     2.5+                                        **+*+  *
        |                                    ***+++
        |                                   *++
        |                               ****
        |                            ***
        |                         +**
    -3.5+                     *****
        |                 *****
        |              +**+
        |           +***
        |       *+**
        |    +++
    -9.5++++*
         +----+----+----+----+----+----+----+----+----+----+
             -2        -1         0        +1        +2
 EXST7034 - Bodyfat Example, NKNW Table 7.1
Bootstrap regression

The UNIVARIATE Procedure
Variable:  X3  (Midarm circumference)
                            Moments
N                          50    Sum Weights                 50
Mean               -2.0835004    Sum Observations    -104.17502
Std Deviation      1.81430845    Variance            3.29171514
Skewness           0.00238801    Kurtosis            -0.4188596
Uncorrected SS     378.342743    Corrected SS        161.294042
Coeff Variation    -87.079821    Std Error Mean      0.25658196

              Basic Statistical Measures
    Location                    Variability
Mean     -2.08350     Std Deviation            1.81431
Median   -2.24925     Variance                 3.29172
Mode       .          Range                    7.56477
                      Interquartile Range      2.36835

           Tests for Location: Mu0=0
Test           -Statistic-    -----p Value------
Student's t    t  -8.12021    Pr > |t|    <.0001
Sign           M       -18    Pr >= |M|   <.0001
Signed Rank    S    -564.5    Pr >= |S|   <.0001

                   Tests for Normality
Test                  --Statistic---    -----p Value------

Shapiro-Wilk          W     0.982552    Pr < W      0.6634
Kolmogorov-Smirnov    D     0.094037    Pr > D     >0.1500
Cramer-von Mises      W-Sq   0.03496    Pr > W-Sq  >0.2500
Anderson-Darling      A-Sq  0.235474    Pr > A-Sq  >0.2500

Quantiles (Definition 5)
Quantile       Estimate
100% Max       1.276578
99%            1.276578
95%            1.127003  <== 95th percentile used in calculating confidence intervals
90%            0.691110
75% Q3        -0.898947
50% Median    -2.249251
25% Q1        -3.267301
10%           -4.387901
5%            -5.076321  <== 5th percentile used in calculating confidence intervals
1%            -6.288195
0% Min        -6.288195

            Extreme Observations
------Lowest-----        ------Highest-----
   Value      Obs            Value      Obs
-6.28819       50         0.759323        4
-5.34358       49         0.967975        1
-5.07632       48         1.127003        5
-4.97738       47         1.202083        3
-4.57029       46         1.276578        2

    Stem Leaf                     #  Boxplot
      1 0123                     4     |
      0 68                       2     |
      0 2                        1     |
     -0 33                       2     |
     -0 9876                     4  +-----+
     -1 331000                   6  |     |
     -1 99987                    5  |     |
     -2 0                        1  *--+--*
     -2 987766655                9  |     |
     -3 33211                    5  +-----+
     -3 8655                     4     |
     -4 20                       2     |
     -4 6                        1     |
     -5 310                      3     |
     -5                                |
     -6 3                        1     |
        ----+----+----+----+
 

                       Normal Probability Plot
    1.25+                                         *+*+  *
        |                                     ** *+
        |                                    *+++
   -0.25+                                  **+
        |                               ****
        |                            ***
   -1.75+                         ****
        |                       +++
        |                    +*****
   -3.25+                  ***
        |              ****
        |            +*+
   -4.75+         +*+*
        |       *+*
        |    +++
   -6.25+ ++*
         +----+----+----+----+----+----+----+----+----+----+
             -2        -1         0        +1        +2
 
 
 

68         *******************************************;
69         ***  Ridge Regression section           ***;
70         *******************************************;
71
72         PROC REG DATA=ONE outest=ridge1 outvif; TITLE2 'Ridge Regression';
73               MODEL  Y = X1 X2 X3 / ridge= 0.00 to 0.10 by 0.005;
74               output out=next1 r=e p=yhat;
75         RUN;

NOTE: 20 observations read.
NOTE: 20 observations used in computations.
NOTE: The data set WORK.RIDGE1 has 43 observations and 11 variables.
NOTE: The data set WORK.NEXT1 has 20 observations and 7 variables.
NOTE: The PROCEDURE REG printed page 10.
NOTE: PROCEDURE REG used:
      real time           0.05 seconds
76         proc print data=ridge1; run;
NOTE: There were 43 observations read from the data set WORK.RIDGE1.
NOTE: The PROCEDURE PRINT printed page 11.
NOTE: PROCEDURE PRINT used:
      real time           0.00 seconds
 

 EXST7034 - Bodyfat Example, NKNW Table 7.1
Ridge Regression

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
Variable     Label                         DF       Estimate          Error    t Value    Pr > |t|
Intercept    Intercept                      1      117.08469       99.78240       1.17      0.2578
X1           Triceps skinfold thickness     1        4.33409        3.01551       1.44      0.1699
X2           Thigh circumference            1       -2.85685        2.58202      -1.11      0.2849
X3           Midarm circumference           1       -2.18606        1.59550      -1.37      0.1896
 
 

78         data ridgeK ridgeV; set ridge1;
79            if _type_ eq 'PARMS' then delete;
80            if _type_ eq 'RIDGE' then output ridgeK;
81            if _type_ eq 'RIDGEVIF' then output ridgeV;
82         run;
NOTE: There were 43 observations read from the data set WORK.RIDGE1.
NOTE: The data set WORK.RIDGEK has 21 observations and 11 variables.
NOTE: The data set WORK.RIDGEV has 21 observations and 11 variables.
NOTE: DATA statement used:
      real time           0.04 seconds
 

EXST7034 - Bodyfat Example, NKNW Table 7.1
Ridge Regression

Obs _MODEL_ _TYPE_   _DEPVAR_ _RIDGE_ _PCOMIT_  _RMSE_ Intercept      X1       X2       X3  Y
  1 MODEL1  PARMS       Y       .         .    2.47998   117.085   4.334   -2.857   -2.186 -1
  2 MODEL1  RIDGEVIF    Y      0.000      .     .           .    708.843  564.343  104.606 -1
  3 MODEL1  RIDGE       Y      0.000      .    2.47998   117.085   4.334   -2.857   -2.186 -1
  4 MODEL1  RIDGEVIF    Y      0.005      .     .           .     11.643    9.476    2.580 -1
  5 MODEL1  RIDGE       Y      0.005      .    2.57755     4.268   0.918    0.065   -0.385 -1
  6 MODEL1  RIDGEVIF    Y      0.010      .     .           .      3.486    2.981    1.377 -1
  7 MODEL1  RIDGE       Y      0.010      .    2.59104    -3.312   0.685    0.262   -0.262 -1
  8 MODEL1  RIDGEVIF    Y      0.015      .     .           .      1.745    1.594    1.113 -1
  9 MODEL1  RIDGE       Y      0.015      .    2.59630    -6.029   0.600    0.332   -0.216 -1
 10 MODEL1  RIDGEVIF    Y      0.020      .     .           .      1.103    1.081    1.011 -1
 11 MODEL1  RIDGE       Y      0.020      .    2.59924    -7.403   0.555    0.368   -0.192 -1
 12 MODEL1  RIDGEVIF    Y      0.025      .     .           .      0.796    0.834    0.957 -1
 13 MODEL1  RIDGE       Y      0.025      .    2.60122    -8.218   0.528    0.389   -0.176 -1
 14 MODEL1  RIDGEVIF    Y      0.030      .     .           .      0.626    0.697    0.923 -1
 15 MODEL1  RIDGE       Y      0.030      .    2.60276    -8.746   0.509    0.403   -0.165 -1
 16 MODEL1  RIDGEVIF    Y      0.035      .     .           .      0.521    0.612    0.900 -1
 17 MODEL1  RIDGE       Y      0.035      .    2.60405    -9.107   0.495    0.413   -0.157 -1
 18 MODEL1  RIDGEVIF    Y      0.040      .     .           .      0.453    0.555    0.881 -1
 19 MODEL1  RIDGE       Y      0.040      .    2.60522    -9.364   0.484    0.420   -0.151 -1
 20 MODEL1  RIDGEVIF    Y      0.045      .     .           .      0.405    0.515    0.866 -1
 21 MODEL1  RIDGE       Y      0.045      .    2.60632    -9.550   0.475    0.425   -0.145 -1
 22 MODEL1  RIDGEVIF    Y      0.050      .     .           .      0.370    0.486    0.853 -1
 23 MODEL1  RIDGE       Y      0.050      .    2.60740    -9.687   0.468    0.428   -0.141 -1
 24 MODEL1  RIDGEVIF    Y      0.055      .     .           .      0.344    0.463    0.841 -1
 25 MODEL1  RIDGE       Y      0.055      .    2.60847    -9.788   0.462    0.431   -0.137 -1
 26 MODEL1  RIDGEVIF    Y      0.060      .     .           .      0.324    0.445    0.831 -1
 27 MODEL1  RIDGE       Y      0.060      .    2.60956    -9.862   0.457    0.433   -0.133 -1
 28 MODEL1  RIDGEVIF    Y      0.065      .     .           .      0.308    0.431    0.821 -1
 29 MODEL1  RIDGE       Y      0.065      .    2.61066    -9.915   0.452    0.435   -0.130 -1
 30 MODEL1  RIDGEVIF    Y      0.070      .     .           .      0.296    0.419    0.811 -1
 31 MODEL1  RIDGE       Y      0.070      .    2.61180    -9.951   0.448    0.436   -0.127 -1
 32 MODEL1  RIDGEVIF    Y      0.075      .     .           .      0.285    0.409    0.802 -1
 33 MODEL1  RIDGE       Y      0.075      .    2.61297    -9.974   0.445    0.437   -0.125 -1
 34 MODEL1  RIDGEVIF    Y      0.080      .     .           .      0.276    0.400    0.793 -1
 35 MODEL1  RIDGE       Y      0.080      .    2.61418    -9.987   0.441    0.438   -0.122 -1
 36 MODEL1  RIDGEVIF    Y      0.085      .     .           .      0.269    0.392    0.785 -1
 37 MODEL1  RIDGE       Y      0.085      .    2.61542    -9.991   0.438    0.438   -0.120 -1
 38 MODEL1  RIDGEVIF    Y      0.090      .     .           .      0.262    0.385    0.777 -1
 39 MODEL1  RIDGE       Y      0.090      .    2.61671    -9.987   0.435    0.438   -0.118 -1
 40 MODEL1  RIDGEVIF    Y      0.095      .     .           .      0.257    0.379    0.769 -1
 41 MODEL1  RIDGE       Y      0.095      .    2.61804    -9.978   0.433    0.438   -0.116 -1
 42 MODEL1  RIDGEVIF    Y      0.100      .     .           .      0.252    0.373    0.761 -1
 43 MODEL1  RIDGE       Y      0.100      .    2.61942    -9.963   0.430    0.438   -0.114 -1

83         data ridgev; set ridgev; vx1=x1; vx2=x2; vx3=x3;
84             drop x1 x2 x3;
85         run;
NOTE: There were 21 observations read from the data set WORK.RIDGEV.
NOTE: The data set WORK.RIDGEV has 21 observations and 11 variables.
NOTE: DATA statement used:
      real time           0.05 seconds
86         data combo; merge ridgek ridgev; by _ridge_; run;
NOTE: There were 21 observations read from the data set WORK.RIDGEK.
NOTE: There were 21 observations read from the data set WORK.RIDGEV.
NOTE: The data set WORK.COMBO has 21 observations and 14 variables.
NOTE: DATA statement used:
      real time           0.00 seconds
87         proc print data=combo; run;
NOTE: There were 21 observations read from the data set WORK.COMBO.
NOTE: The PROCEDURE PRINT printed page 12.
NOTE: PROCEDURE PRINT used:
      real time           0.00 seconds

EXST7034 - Bodyfat Example, NKNW Table 7.1
Ridge Regression
                                      I
                      _         _     n
      _               D    _    P