In this lab, you will learn how

  1. To perform forward and backward stepwise selection using different model selection criteria.
  2. To perform best subset selection.
  3. To fit a linear model by LASSO and to choose the tuning parameter by using a validation set.

In this lab, we will be using the following blood pressure dataset. This dataset contains measurements possibly related to blood pressure from 39 Peruvians who moved from rural high altitude areas to urban lower altitude areas. The dataset contains the following variables:

  • Y = systolic blood pressure
  • $X_1$ = age
  • $X_2$ = years in urban area
  • $X_3$ = $X_2/X_1$ = fraction of life in an urban area
  • $X_4$ = weight in kg
  • $X_5$ = height in mm
  • $X_6$ = chin skinfold
  • $X_7$ = forearm skinfold
  • $X_8$ = calf skinfold
  • $X_9$ = resting pulse rate

To perform forward and backward subset selection, we can use the selection and select options in the model statement of PROC GLMSELECT. For best subset selection, we can use PROC REG.

In [2]:
LIBNAME Survey "H:\BiostatCourses\PHC6937SurveryBiostat\Lectures\VariableSelection\Data";

PROC IMPORT datafile="H:\BiostatCourses\PHC6937SurveryBiostat\Lectures\VariableSelection\Data\peru.csv"
out=Survey.peru dbms=csv replace;
getnames=Yes;
RUN;

PROC PRINT DATA=SURVEY.peru (OBS=5);
RUN;
Out[2]:
SAS Output

SAS Output

The SAS System

The PRINT Procedure

Data Set SURVEY.PERU

Obs Age Years Weight Height Chin Forearm Calf Pulse Systol Diastol UrbanFrac
1 21 1 71 1629 8 7 12.7 88 170 76 0.047619048
2 22 6 56.5 1569 3.3 5 8 64 120 60 0.272727273
3 24 5 56 1561 3.3 1.3 4.3 68 125 75 0.208333333
4 24 1 61 1619 3.7 3 4.3 52 148 120 0.041666667
5 25 1 65 1566 9 12.7 20.7 72 140 78 0.04
In [54]:
PROC GLMSELECT DATA=Survey.peru;
MODEL Systol = Age Years Weight Height Chin Forearm Calf Pulse UrbanFrac / 
SELECTION=FORWARD(SELECT=ADJRSQ STOP=NONE);
RUN;
QUIT;
Out[54]:
SAS Output

SAS Output

The SAS System

The GLMSELECT Procedure

The GLMSELECT Procedure

Model Information

Data Set SURVEY.PERU
Dependent Variable Systol
Selection Method Forward
Select Criterion Adj R-Sq
Stop Criterion None
Effect Hierarchy Enforced None

Number of Observations

Number of Observations Read 39
Number of Observations Used 39

Dimensions

Dimensions
Number of Effects 10
Number of Parameters 10

The SAS System

The GLMSELECT Procedure

Model Building Summary

Forward Selection Summary

Forward Selection Summary
Step Effect
Entered		 Number
Effects In		 Adjusted
R-Square
* Optimal Value of Criterion
0 Intercept 1 0.0000
1 Weight 2 0.2521
2 UrbanFrac 3 0.4438
3 Chin 4 0.4608
4 Age 5 0.4676
5 Years 6 0.5839
6 Forearm 7 0.5830
7 Height 8 0.5840*
8 Pulse 9 0.5774
9 Calf 10 0.5641

Stop Reason

Selection stopped because all effects are in the final model.

Selected Model

The SAS System

The GLMSELECT Procedure

Selected Model

The selected model is the model at the last step (Step 9).

Selected Effects

Effects: Intercept Age Years Weight Height Chin Forearm Calf Pulse UrbanFrac

ANOVA

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value
Model 9 4358.85192 484.31688 6.46
Error 29 2172.58398 74.91669  
Corrected Total 38 6531.43590    

Fit Statistics

Root MSE 8.65544
Dependent Mean 127.41026
R-Square 0.6674
Adj R-Sq 0.5641
AIC 217.78432
AICC 227.56210
SBC 193.41994

Parameter Estimates

Parameter Estimates
Parameter DF Estimate Standard
Error		 t Value
Intercept 1 146.819067 48.970963 3.00
Age 1 -1.121435 0.327412 -3.43
Years 1 2.455381 0.814577 3.01
Weight 1 1.413934 0.430973 3.28
Height 1 -0.034636 0.036864 -0.94
Chin 1 -0.943689 0.740969 -1.27
Forearm 1 -1.170855 1.193294 -0.98
Calf 1 -0.158666 0.537164 -0.30
Pulse 1 0.114553 0.170432 0.67
UrbanFrac 1 -115.293950 30.169005 -3.82
In [26]:
PROC REG DATA=Survey.peru;
MODEL Systol = Age Years Weight Height Chin Forearm Calf Pulse UrbanFrac / 
SELECTION=BACKWARD SLS=0.15;
RUN;
QUIT;
Out[26]:
SAS Output

SAS Output

The SAS System

The REG Procedure

Model: MODEL1

Dependent Variable: Systol

The REG Procedure

MODEL1

Backward Elimination Method

Systol

Number of Observations

Number of Observations Read 39
Number of Observations Used 39

Step 0

Backward Elimination: Step 0

ANOVA

All Variables Entered: R-Square = 0.6674 and C(p) = 10.0000

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 9 4358.85192 484.31688 6.46 <.0001
Error 29 2172.58398 74.91669    
Corrected Total 38 6531.43590      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept 146.81907 48.97096 673.38928 8.99 0.0055
Age -1.12144 0.32741 878.89624 11.73 0.0019
Years 2.45538 0.81458 680.69500 9.09 0.0053
Weight 1.41393 0.43097 806.37458 10.76 0.0027
Height -0.03464 0.03686 66.13721 0.88 0.3552
Chin -0.94369 0.74097 121.51672 1.62 0.2129
Forearm -1.17085 1.19329 72.12561 0.96 0.3346
Calf -0.15867 0.53716 6.53630 0.09 0.7698
Pulse 0.11455 0.17043 33.84478 0.45 0.5068
UrbanFrac -115.29395 30.16900 1094.13182 14.60 0.0006

Bounds on condition number: 34.289, 703.46

Step 1

Backward Elimination: Step 1

ANOVA

Variable Calf Removed: R-Square = 0.6664 and C(p) = 8.0872

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 8 4352.31562 544.03945 7.49 <.0001
Error 30 2179.12028 72.63734    
Corrected Total 38 6531.43590      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept 147.05587 48.21377 675.74435 9.30 0.0048
Age -1.10995 0.32011 873.30449 12.02 0.0016
Years 2.41595 0.79124 677.19544 9.32 0.0047
Weight 1.42678 0.42220 829.54503 11.42 0.0020
Height -0.03594 0.03604 72.22686 0.99 0.3267
Chin -0.97163 0.72364 130.95396 1.80 0.1894
Forearm -1.37112 0.96691 146.06451 2.01 0.1665
Pulse 0.11966 0.16695 37.31447 0.51 0.4791
UrbanFrac -113.54307 29.12747 1103.76280 15.20 0.0005

Bounds on condition number: 33.368, 579.91

Step 2

Backward Elimination: Step 2

ANOVA

Variable Pulse Removed: R-Square = 0.6607 and C(p) = 6.5853

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 7 4315.00115 616.42874 8.62 <.0001
Error 31 2216.43475 71.49790    
Corrected Total 38 6531.43590      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept 153.68245 46.94640 766.19127 10.72 0.0026
Age -1.09745 0.31712 856.28661 11.98 0.0016
Years 2.35670 0.78072 651.49872 9.11 0.0050
Weight 1.46055 0.41626 880.23412 12.31 0.0014
Height -0.03713 0.03572 77.26344 1.08 0.3066
Chin -1.03844 0.71196 152.10576 2.13 0.1547
Forearm -1.14395 0.90629 113.91384 1.59 0.2163
UrbanFrac -110.45540 28.58029 1067.90797 14.94 0.0005

Bounds on condition number: 33.004, 489.4

Step 3

Backward Elimination: Step 3

ANOVA

Variable Height Removed: R-Square = 0.6488 and C(p) = 5.6167

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 6 4237.73771 706.28962 9.85 <.0001
Error 32 2293.69819 71.67807    
Corrected Total 38 6531.43590      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept 110.30001 21.52986 1881.28713 26.25 <.0001
Age -1.09260 0.31748 848.92933 11.84 0.0016
Years 2.55234 0.75865 811.29748 11.32 0.0020
Weight 1.16807 0.30717 1036.53033 14.46 0.0006
Chin -0.87758 0.69582 114.01850 1.59 0.2163
Forearm -0.82140 0.85259 66.53005 0.93 0.3426
UrbanFrac -116.68185 27.98080 1246.44345 17.39 0.0002

Bounds on condition number: 31.086, 375.73

Step 4

Backward Elimination: Step 4

ANOVA

Variable Forearm Removed: R-Square = 0.6386 and C(p) = 4.5047

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 5 4171.20766 834.24153 11.66 <.0001
Error 33 2360.22823 71.52207    
Corrected Total 38 6531.43590      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept 109.35901 21.48427 1853.13848 25.91 <.0001
Age -1.01203 0.30594 782.64826 10.94 0.0023
Years 2.40675 0.74264 751.18706 10.50 0.0027
Weight 1.09764 0.29801 970.25859 13.57 0.0008
Chin -1.19179 0.61398 269.47952 3.77 0.0608
UrbanFrac -110.81115 27.27948 1180.14327 16.50 0.0003

Bounds on condition number: 29.853, 287.7

All variables left in the model are significant at the 0.1500 level.

Selection Summary

Summary of Backward Elimination
Step Variable
Removed		 Number
Vars In		 Partial
R-Square		 Model
R-Square		 C(p) F Value Pr > F
1 Calf 8 0.0010 0.6664 8.0872 0.09 0.7698
2 Pulse 7 0.0057 0.6607 6.5853 0.51 0.4791
3 Height 6 0.0118 0.6488 5.6167 1.08 0.3066
4 Forearm 5 0.0102 0.6386 4.5047 0.93 0.3426

The SAS System

The REG Procedure

Model: MODEL1

Dependent Variable: Systol

Observation-wise Statistics

Systol

Diagnostic Plots

Fit Diagnostics

Panel of fit diagnostics for Systol.

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for Systol.

Best subset selection can return a lot of output if you have many variables as seen below. Here we only have 9 canditate predictors, but that is $2^9$ possible models. If we want to limit the number of models output, we can use the BEST=n option to limit it to the top n models based on the chosen criterion.

In [27]:
PROC REG DATA=Survey.peru outest=peru_sel;
MODEL Systol = Age Years Weight Height Chin Forearm Calf Pulse UrbanFrac / 
SELECTION=adjrsq AIC BIC CP adjrsq;
RUN;
QUIT;
Out[27]:
SAS Output

SAS Output

The SAS System

The REG Procedure

Model: MODEL1

Dependent Variable: Systol

Adjusted R-Square Selection Method

The REG Procedure

MODEL1

Adjusted R-Square Selection Method

Systol

Number of Observations

Number of Observations Read 39
Number of Observations Used 39

Results

Number in
Model		 Adjusted
R-Square		 R-Square C(p) AIC BIC Variables in Model
7 0.5840 0.6607 6.5853 173.5636 180.4527 Age Years Weight Height Chin Forearm UrbanFrac
5 0.5839 0.6386 4.5047 172.0151 176.7568 Age Years Weight Chin UrbanFrac
6 0.5830 0.6488 5.6167 172.9000 178.5835 Age Years Weight Chin Forearm UrbanFrac
6 0.5828 0.6487 5.6295 172.9164 178.5930 Age Years Weight Chin Calf UrbanFrac
7 0.5775 0.6553 7.0513 174.1732 180.7603 Age Years Weight Chin Forearm Pulse UrbanFrac
8 0.5774 0.6664 8.0872 174.9015 182.8035 Age Years Weight Height Chin Forearm Pulse UrbanFrac
7 0.5768 0.6547 7.1016 174.2383 180.7934 Age Years Weight Height Chin Calf UrbanFrac
6 0.5763 0.6432 6.1059 173.5182 178.9424 Age Years Weight Height Chin UrbanFrac
5 0.5755 0.6314 5.1386 172.7920 177.2628 Age Years Weight Forearm UrbanFrac
6 0.5732 0.6406 6.3349 173.8044 179.1094 Age Years Weight Forearm Pulse UrbanFrac
7 0.5729 0.6516 7.3784 174.5953 180.9751 Age Years Weight Chin Forearm Calf UrbanFrac
6 0.5727 0.6401 6.3734 173.8522 179.1373 Age Years Weight Chin Pulse UrbanFrac
7 0.5726 0.6513 7.3993 174.6222 180.9889 Age Years Weight Chin Calf Pulse UrbanFrac
8 0.5721 0.6622 8.4518 175.3872 183.0126 Age Years Weight Height Chin Forearm Calf UrbanFrac
5 0.5695 0.6262 5.5914 173.3377 177.6200 Age Years Weight Calf UrbanFrac
6 0.5694 0.6374 6.6157 174.1522 179.3131 Age Years Weight Height Forearm UrbanFrac
6 0.5676 0.6359 6.7437 174.3099 179.4056 Age Years Weight Forearm Calf UrbanFrac
7 0.5665 0.6463 7.8352 175.1775 181.2738 Age Years Weight Height Forearm Pulse UrbanFrac
8 0.5658 0.6572 8.8828 175.9538 183.2594 Age Years Weight Chin Forearm Calf Pulse UrbanFrac
8 0.5647 0.6563 8.9627 176.0580 183.3052 Age Years Weight Height Chin Calf Pulse UrbanFrac
9 0.5641 0.6674 10.0000 176.7843 185.4431 Age Years Weight Height Chin Forearm Calf Pulse UrbanFrac
7 0.5636 0.6440 8.0369 175.4317 181.4052 Age Years Weight Height Chin Pulse UrbanFrac
7 0.5633 0.6438 8.0588 175.4592 181.4194 Age Years Weight Forearm Calf Pulse UrbanFrac
7 0.5599 0.6410 8.2992 175.7599 181.5754 Age Years Weight Height Forearm Calf UrbanFrac
6 0.5590 0.6286 7.3754 175.0784 179.8593 Age Years Weight Calf Pulse UrbanFrac
6 0.5567 0.6267 7.5428 175.2794 179.9786 Age Years Weight Height Calf UrbanFrac
8 0.5551 0.6488 9.6220 176.9068 183.6818 Age Years Weight Height Forearm Calf Pulse UrbanFrac
4 0.5500 0.5974 6.1018 174.2316 177.3175 Age Years Weight UrbanFrac
7 0.5451 0.6289 9.3520 177.0501 182.2535 Age Years Weight Height Calf Pulse UrbanFrac
5 0.5372 0.5981 8.0415 176.1646 179.4947 Age Years Weight Pulse UrbanFrac
5 0.5367 0.5976 8.0794 176.2067 179.5229 Age Years Weight Height UrbanFrac
6 0.5232 0.5985 10.0033 178.1221 181.6945 Age Years Weight Height Pulse UrbanFrac
5 0.4826 0.5506 12.1756 180.5139 182.4601 Age Weight Height Chin UrbanFrac
6 0.4786 0.5609 13.2816 181.6136 183.8756 Age Weight Height Chin Forearm UrbanFrac
4 0.4694 0.5252 12.3932 180.6614 182.0765 Age Years Height UrbanFrac
6 0.4688 0.5526 14.0013 182.3400 184.3395 Age Weight Height Chin Calf UrbanFrac
4 0.4676 0.5236 12.5317 180.7916 182.1746 Age Weight Chin UrbanFrac
5 0.4666 0.5368 13.3845 181.6992 183.2854 Age Years Height Pulse UrbanFrac
6 0.4665 0.5507 14.1704 182.5088 184.4478 Age Weight Height Chin Pulse UrbanFrac
4 0.4643 0.5207 12.7854 181.0291 182.3536 Weight Height Chin UrbanFrac
7 0.4639 0.5627 15.1266 183.4553 185.8208 Age Weight Height Chin Forearm Pulse UrbanFrac
4 0.4622 0.5188 12.9516 181.1840 182.4705 Years Weight Chin UrbanFrac
7 0.4621 0.5612 15.2580 183.5896 185.8991 Age Weight Height Chin Forearm Calf UrbanFrac
3 0.4608 0.5033 12.3013 180.4189 181.6045 Weight Chin UrbanFrac
6 0.4582 0.5437 14.7776 183.1087 184.8342 Age Years Height Calf Pulse UrbanFrac
5 0.4575 0.5289 14.0721 182.3576 183.7471 Age Years Height Calf UrbanFrac
5 0.4562 0.5278 14.1689 182.4495 183.8117 Years Weight Height Chin UrbanFrac
5 0.4546 0.5263 14.2957 182.5694 183.8961 Age Weight Height Forearm UrbanFrac
5 0.4538 0.5257 14.3534 182.6238 183.9344 Age Years Height Chin UrbanFrac
5 0.4533 0.5252 14.3932 182.6614 183.9609 Age Years Height Forearm UrbanFrac
6 0.4527 0.5391 15.1789 183.5001 185.0876 Age Years Height Forearm Pulse UrbanFrac
5 0.4527 0.5247 14.4401 182.7055 183.9920 Age Weight Chin Pulse UrbanFrac
5 0.4526 0.5246 14.4460 182.7110 183.9959 Age Weight Chin Forearm UrbanFrac
5 0.4518 0.5239 14.5039 182.7655 184.0343 Age Weight Chin Calf UrbanFrac
7 0.4518 0.5528 15.9890 184.3277 186.3322 Age Weight Height Chin Calf Pulse UrbanFrac
6 0.4518 0.5383 15.2486 183.5677 185.1315 Age Years Height Chin Pulse UrbanFrac
5 0.4512 0.5234 14.5481 182.8070 184.0635 Weight Height Chin Forearm UrbanFrac
5 0.4493 0.5218 14.6946 182.9443 184.1604 Years Weight Chin Pulse UrbanFrac
5 0.4490 0.5215 14.7181 182.9663 184.1759 Weight Height Chin Pulse UrbanFrac
5 0.4485 0.5210 14.7570 183.0026 184.2016 Weight Height Chin Calf UrbanFrac
4 0.4471 0.5053 14.1278 182.2623 183.2869 Weight Chin Pulse UrbanFrac
3 0.4468 0.4905 13.4197 181.4134 182.4075 Years Weight UrbanFrac
8 0.4467 0.5631 17.0860 185.4138 187.8446 Age Weight Height Chin Forearm Calf Pulse UrbanFrac
5 0.4460 0.5189 14.9442 183.1770 184.3249 Years Weight Chin Calf UrbanFrac
5 0.4459 0.5188 14.9483 183.1809 184.3276 Years Weight Chin Forearm UrbanFrac
3 0.4454 0.4892 13.5328 181.5126 182.4878 Age Years UrbanFrac
4 0.4449 0.5034 14.2984 182.4163 183.4038 Weight Chin Forearm UrbanFrac
4 0.4449 0.5033 14.3013 182.4189 183.4058 Weight Chin Calf UrbanFrac
3 0.4446 0.4885 13.5950 181.5671 182.5319 Age Weight UrbanFrac
6 0.4443 0.5320 15.8009 184.0992 185.4774 Age Years Height Forearm Calf UrbanFrac
2 0.4438 0.4731 12.9359 180.7224 181.7708 Weight UrbanFrac
4 0.4432 0.5018 14.4327 182.5370 183.4956 Age Weight Forearm UrbanFrac
6 0.4424 0.5304 15.9401 184.2321 185.5641 Age Weight Height Forearm Pulse UrbanFrac
4 0.4414 0.5002 14.5709 182.6610 183.5899 Age Years Pulse UrbanFrac
6 0.4413 0.5295 16.0152 184.3035 185.6108 Years Weight Height Chin Forearm UrbanFrac
6 0.4411 0.5293 16.0359 184.3233 185.6237 Years Weight Height Chin Pulse UrbanFrac
7 0.4408 0.5438 16.7692 185.1004 186.7902 Age Years Height Forearm Calf Pulse UrbanFrac
7 0.4407 0.5438 16.7767 185.1077 186.7946 Age Years Height Chin Calf Pulse UrbanFrac
6 0.4406 0.5289 16.0678 184.3535 185.6435 Age Years Height Chin Calf UrbanFrac
6 0.4397 0.5282 16.1333 184.4157 185.6842 Years Weight Height Chin Calf UrbanFrac
4 0.4387 0.4978 14.7809 182.8485 183.7326 Years Weight Forearm UrbanFrac
6 0.4380 0.5267 16.2596 184.5352 185.7625 Age Weight Chin Forearm Pulse UrbanFrac
6 0.4376 0.5264 16.2922 184.5661 185.7827 Age Weight Height Forearm Calf UrbanFrac
6 0.4370 0.5259 16.3348 184.6063 185.8091 Age Years Height Chin Forearm UrbanFrac
4 0.4369 0.4962 14.9268 182.9783 183.8315 Age Weight Calf UrbanFrac
6 0.4368 0.5258 16.3463 184.6171 185.8162 Weight Height Chin Forearm Pulse UrbanFrac
4 0.4367 0.4960 14.9388 182.9889 183.8396 Years Weight Calf UrbanFrac
3 0.4363 0.4808 14.2611 182.1453 183.0003 Weight Forearm UrbanFrac
6 0.4361 0.5251 16.3992 184.6670 185.8489 Age Weight Chin Calf Pulse UrbanFrac
4 0.4355 0.4949 15.0350 183.0742 183.9047 Age Weight Height UrbanFrac
6 0.4355 0.5246 16.4459 184.7110 185.8778 Age Weight Chin Forearm Calf UrbanFrac
7 0.4353 0.5394 17.1601 185.4819 187.0180 Age Years Height Chin Forearm Pulse UrbanFrac
6 0.4344 0.5237 16.5269 184.7871 185.9278 Weight Height Chin Forearm Calf UrbanFrac
4 0.4340 0.4936 15.1510 183.1768 183.9829 Age Years Calf UrbanFrac
5 0.4336 0.5081 15.8865 184.0435 184.9396 Age Weight Height Calf UrbanFrac
5 0.4335 0.5081 15.8873 184.0442 184.9401 Age Years Calf Pulse UrbanFrac
4 0.4334 0.4931 15.1950 183.2157 184.0125 Weight Height Forearm UrbanFrac
6 0.4330 0.5225 16.6288 184.8827 185.9906 Years Weight Chin Forearm Pulse UrbanFrac
3 0.4330 0.4777 14.5325 182.3784 183.1895 Weight Calf UrbanFrac
4 0.4326 0.4924 15.2582 183.2713 184.0550 Years Weight Pulse UrbanFrac
6 0.4324 0.5220 16.6712 184.9224 186.0167 Years Weight Chin Calf Pulse UrbanFrac
6 0.4323 0.5219 16.6791 184.9297 186.0216 Weight Height Chin Calf Pulse UrbanFrac
3 0.4319 0.4767 14.6190 182.4524 183.2496 Weight Height UrbanFrac
4 0.4310 0.4909 15.3814 183.3797 184.1378 Years Weight Height UrbanFrac
5 0.4310 0.5059 16.0805 184.2196 185.0650 Weight Chin Forearm Pulse UrbanFrac
5 0.4310 0.5059 16.0812 184.2201 185.0654 Age Weight Forearm Pulse UrbanFrac
5 0.4304 0.5054 16.1244 184.2593 185.0933 Weight Chin Calf Pulse UrbanFrac
5 0.4304 0.5053 16.1286 184.2630 185.0960 Age Years Forearm Pulse UrbanFrac
4 0.4301 0.4901 15.4559 183.4452 184.1878 Age Years Chin UrbanFrac
4 0.4297 0.4897 15.4898 183.4749 184.2105 Age Years Forearm UrbanFrac
3 0.4291 0.4742 14.8441 182.6444 183.4055 Weight Pulse UrbanFrac
4 0.4288 0.4889 15.5566 183.5334 184.2552 Age Weight Pulse UrbanFrac
6 0.4287 0.5189 16.9441 185.1770 186.1844 Years Weight Chin Forearm Calf UrbanFrac
5 0.4286 0.5038 16.2578 184.3797 185.1792 Years Weight Forearm Pulse UrbanFrac
5 0.4281 0.5034 16.2973 184.4153 185.2046 Weight Chin Forearm Calf UrbanFrac
5 0.4273 0.5026 16.3613 184.4729 185.2457 Years Weight Height Forearm UrbanFrac
7 0.4271 0.5327 17.7443 186.0451 187.3564 Years Weight Height Chin Forearm Pulse UrbanFrac
5 0.4271 0.5025 16.3738 184.4842 185.2538 Age Years Chin Pulse UrbanFrac
7 0.4267 0.5323 17.7755 186.0750 187.3745 Age Years Height Chin Forearm Calf UrbanFrac
5 0.4266 0.5021 16.4114 184.5180 185.2779 Age Weight Forearm Calf UrbanFrac
4 0.4248 0.4853 15.8688 183.8058 184.4636 Weight Forearm Pulse UrbanFrac
7 0.4244 0.5304 17.9397 186.2317 187.4692 Age Weight Height Forearm Calf Pulse UrbanFrac
7 0.4238 0.5299 17.9825 186.2724 187.4938 Years Weight Height Chin Calf Pulse UrbanFrac
4 0.4235 0.4841 15.9737 183.8969 184.5333 Weight Height Calf UrbanFrac
7 0.4234 0.5296 18.0121 186.3006 187.5108 Years Weight Height Chin Forearm Calf UrbanFrac
5 0.4231 0.4990 16.6815 184.7598 185.4508 Years Weight Calf Pulse UrbanFrac
5 0.4223 0.4984 16.7346 184.8073 185.4847 Years Weight Forearm Calf UrbanFrac
8 0.4223 0.5439 18.7636 187.0949 188.7485 Age Years Height Chin Forearm Calf Pulse UrbanFrac
5 0.4216 0.4977 16.7907 184.8572 185.5205 Weight Height Forearm Pulse UrbanFrac
5 0.4216 0.4977 16.7932 184.8594 185.5221 Years Weight Height Calf UrbanFrac
5 0.4210 0.4972 16.8348 184.8965 185.5486 Age Weight Calf Pulse UrbanFrac
4 0.4199 0.4810 16.2471 184.1332 184.7144 Weight Forearm Calf UrbanFrac
7 0.4199 0.5268 18.2562 186.5321 187.6511 Age Weight Chin Forearm Calf Pulse UrbanFrac
7 0.4192 0.5262 18.3064 186.5794 187.6798 Weight Height Chin Forearm Calf Pulse UrbanFrac
5 0.4185 0.4950 17.0293 185.0691 185.6723 Age Weight Height Pulse UrbanFrac
4 0.4183 0.4795 16.3758 184.2440 184.7994 Weight Calf Pulse UrbanFrac
5 0.4179 0.4945 17.0681 185.1035 185.6970 Age Years Forearm Calf UrbanFrac
4 0.4179 0.4792 16.4039 184.2681 184.8179 Years Weight Height Chin
5 0.4169 0.4936 17.1509 185.1767 185.7495 Age Years Chin Calf UrbanFrac
5 0.4163 0.4931 17.1921 185.2131 185.7756 Weight Height Forearm Calf UrbanFrac
6 0.4163 0.5084 17.8560 186.0158 186.7399 Years Weight Height Forearm Pulse UrbanFrac
6 0.4162 0.5084 17.8577 186.0173 186.7409 Age Weight Height Calf Pulse UrbanFrac
6 0.4162 0.5083 17.8643 186.0233 186.7449 Age Years Forearm Calf Pulse UrbanFrac
6 0.4160 0.5082 17.8790 186.0367 186.7538 Age Years Chin Calf Pulse UrbanFrac
4 0.4158 0.4773 16.5690 184.4097 184.9266 Weight Height Pulse UrbanFrac
5 0.4156 0.4925 17.2423 185.2574 185.8074 Years Weight Height Pulse UrbanFrac
7 0.4147 0.5225 18.6288 186.8827 187.8643 Years Weight Chin Forearm Calf Pulse UrbanFrac
5 0.4134 0.4906 17.4097 185.4047 185.9132 Age Years Weight Height Chin
6 0.4133 0.5059 18.0727 186.2125 186.8708 Weight Chin Forearm Calf Pulse UrbanFrac
6 0.4133 0.5059 18.0764 186.2158 186.8730 Age Weight Forearm Calf Pulse UrbanFrac
5 0.4129 0.4901 17.4524 185.4421 185.9402 Age Years Chin Forearm UrbanFrac
6 0.4126 0.5054 18.1217 186.2568 186.9004 Age Years Chin Forearm Pulse UrbanFrac
6 0.4110 0.5040 18.2418 186.3653 186.9727 Years Weight Forearm Calf Pulse UrbanFrac
6 0.4097 0.5029 18.3378 186.4518 187.0304 Years Weight Height Forearm Calf UrbanFrac
8 0.4082 0.5328 19.7316 188.0330 189.2641 Years Weight Height Chin Forearm Calf Pulse UrbanFrac
5 0.4074 0.4854 17.8674 185.8045 186.2011 Weight Forearm Calf Pulse UrbanFrac
5 0.4073 0.4853 17.8764 185.8124 186.2067 Weight Height Calf Pulse UrbanFrac
6 0.4063 0.5001 18.5857 186.6742 187.1791 Years Weight Height Calf Pulse UrbanFrac
3 0.4042 0.4512 16.8422 184.3082 184.7613 Years Weight Chin
5 0.4037 0.4822 18.1442 186.0444 186.3741 Years Weight Height Chin Forearm
6 0.4035 0.4977 18.7899 186.8565 187.3012 Weight Height Forearm Calf Pulse UrbanFrac
6 0.4029 0.4971 18.8399 186.9010 187.3311 Age Years Weight Height Chin Forearm
5 0.4003 0.4792 18.4026 186.2670 186.5350 Years Weight Height Chin Calf
5 0.4003 0.4792 18.4030 186.2673 186.5353 Years Weight Height Chin Pulse
6 0.4000 0.4947 19.0531 187.0902 187.4580 Age Years Chin Forearm Calf UrbanFrac
7 0.3975 0.5085 19.8516 188.0117 188.5575 Years Weight Height Forearm Calf Pulse UrbanFrac
7 0.3973 0.5084 19.8633 188.0224 188.5641 Age Years Chin Forearm Calf Pulse UrbanFrac
6 0.3952 0.4907 19.3994 187.3956 187.6635 Age Years Weight Height Chin Pulse
6 0.3952 0.4907 19.4040 187.3997 187.6662 Age Years Weight Height Chin Calf
4 0.3942 0.4579 18.2574 185.8286 186.0202 Age Years Weight Chin
2 0.3886 0.4208 17.4982 184.4154 184.9455 Years Weight
4 0.3876 0.4521 18.7685 186.2481 186.3451 Years Weight Chin Calf
6 0.3874 0.4841 19.9751 187.8980 188.0028 Years Weight Height Chin Forearm Calf
4 0.3873 0.4518 18.7926 186.2678 186.3603 Years Weight Chin Pulse
4 0.3867 0.4513 18.8376 186.3044 186.3888 Years Weight Chin Forearm
7 0.3864 0.4994 20.6441 188.7264 189.0012 Age Years Weight Height Chin Forearm Calf
6 0.3857 0.4827 20.1005 188.0066 188.0763 Years Weight Height Chin Forearm Pulse
7 0.3839 0.4974 20.8205 188.8837 189.0994 Age Years Weight Height Chin Forearm Pulse
6 0.3816 0.4792 20.4019 188.2664 188.2526 Years Weight Height Chin Calf Pulse
4 0.3816 0.4467 19.2400 186.6311 186.6423 Years Weight Height Forearm
3 0.3800 0.4289 18.7898 185.8644 186.0368 Years Weight Height
5 0.3775 0.4594 20.1276 187.7213 187.5923 Age Years Weight Height Forearm
3 0.3775 0.4266 18.9872 186.0187 186.1636 Years Weight Forearm
5 0.3764 0.4584 20.2151 187.7936 187.6452 Age Years Weight Chin Calf
5 0.3761 0.4582 20.2382 187.8127 187.6591 Age Years Weight Chin Pulse
5 0.3759 0.4580 20.2544 187.8261 187.6689 Age Years Weight Chin Forearm
7 0.3758 0.4908 21.3948 189.3915 189.4177 Age Years Weight Height Chin Calf Pulse
3 0.3758 0.4250 19.1258 186.1266 186.2525 Age Years Weight
3 0.3729 0.4224 19.3568 186.3060 186.4000 Years Weight Calf
3 0.3713 0.4209 19.4860 186.4059 186.4823 Years Weight Pulse
5 0.3696 0.4525 20.7309 188.2174 187.9554 Years Weight Chin Calf Pulse
5 0.3692 0.4522 20.7549 188.2370 187.9698 Years Weight Chin Forearm Calf
5 0.3688 0.4518 20.7925 188.2677 187.9923 Years Weight Chin Forearm Pulse
7 0.3686 0.4849 21.9048 189.8371 189.6985 Years Weight Height Chin Forearm Calf Pulse
4 0.3679 0.4344 20.3066 187.4841 187.3064 Age Years Weight Height
4 0.3668 0.4335 20.3931 187.5524 187.3597 Years Weight Height Calf
4 0.3665 0.4332 20.4170 187.5713 187.3744 Age Years Weight Forearm
8 0.3665 0.4998 22.6046 190.6912 190.7681 Age Years Weight Height Chin Forearm Calf Pulse
5 0.3650 0.4485 21.0783 188.5002 188.1630 Years Weight Height Forearm Pulse
5 0.3634 0.4472 21.1985 188.5976 188.2346 Years Weight Height Forearm Calf
4 0.3617 0.4289 20.7898 187.8644 187.6034 Years Weight Height Pulse
4 0.3610 0.4283 20.8462 187.9085 187.6379 Years Weight Forearm Pulse
4 0.3600 0.4274 20.9236 187.9691 187.6853 Age Years Weight Calf
6 0.3597 0.4608 22.0090 189.6230 189.1797 Age Years Weight Height Forearm Pulse
4 0.3594 0.4268 20.9692 188.0047 187.7131 Years Weight Forearm Calf
6 0.3588 0.4600 22.0764 189.6789 189.2182 Age Years Weight Height Forearm Calf
6 0.3575 0.4590 22.1670 189.7539 189.2698 Age Years Weight Chin Forearm Calf
4 0.3574 0.4251 21.1242 188.1254 187.8076 Age Years Weight Pulse
6 0.3571 0.4586 22.2010 189.7820 189.2892 Age Years Weight Chin Calf Pulse
6 0.3567 0.4583 22.2264 189.8029 189.3036 Age Years Weight Chin Forearm Pulse
5 0.3560 0.4407 21.7574 189.0472 188.5656 Age Years Weight Height Calf
4 0.3548 0.4227 21.3313 188.2862 187.9335 Years Weight Calf Pulse
6 0.3504 0.4530 22.6915 190.1851 189.5673 Years Weight Chin Forearm Calf Pulse
5 0.3489 0.4346 22.2966 189.4761 188.8824 Age Years Weight Height Pulse
5 0.3488 0.4344 22.3067 189.4842 188.8884 Age Years Weight Forearm Pulse
5 0.3476 0.4335 22.3905 189.5503 188.9373 Years Weight Height Calf Pulse
5 0.3476 0.4334 22.3970 189.5555 188.9411 Age Years Weight Forearm Calf
6 0.3461 0.4493 23.0089 190.4439 189.7463 Years Weight Height Forearm Calf Pulse
5 0.3421 0.4287 22.8106 189.8807 189.1821 Years Weight Forearm Calf Pulse
5 0.3407 0.4275 22.9151 189.9624 189.2427 Age Years Weight Calf Pulse
7 0.3401 0.4617 23.9319 191.5590 190.7977 Age Years Weight Height Forearm Calf Pulse
7 0.3374 0.4595 24.1239 191.7182 190.9005 Age Years Weight Chin Forearm Calf Pulse
6 0.3359 0.4408 23.7554 191.0456 190.1643 Age Years Weight Height Calf Pulse
6 0.3289 0.4349 24.2706 191.4556 190.4503 Age Years Weight Forearm Calf Pulse
4 0.3112 0.3837 24.7266 190.8322 189.9409 Years Height Pulse UrbanFrac
4 0.3085 0.3813 24.9435 190.9893 190.0657 Age Weight Height Chin
4 0.3084 0.3812 24.9504 190.9943 190.0696 Years Height Forearm UrbanFrac
3 0.3075 0.3622 24.6053 190.1727 189.6053 Age Weight Chin
3 0.3066 0.3614 24.6769 190.2228 189.6471 Years Height UrbanFrac
5 0.2989 0.3912 26.0802 192.3601 191.0362 Years Height Forearm Pulse UrbanFrac
2 0.2937 0.3309 25.3359 190.0423 189.8338 Age Weight
4 0.2928 0.3673 26.1647 191.8624 190.7604 Age Weight Chin Calf
5 0.2925 0.3856 26.5690 192.7177 191.3061 Years Height Calf Pulse UrbanFrac
4 0.2924 0.3669 26.1968 191.8851 190.7785 Years Height Calf UrbanFrac
5 0.2915 0.3847 26.6395 192.7689 191.3448 Years Height Chin Pulse UrbanFrac
5 0.2908 0.3842 26.6909 192.8063 191.3731 Age Weight Height Chin Pulse
5 0.2906 0.3840 26.7070 192.8180 191.3819 Age Weight Height Chin Calf
4 0.2900 0.3647 26.3836 192.0169 190.8836 Years Height Chin UrbanFrac
5 0.2896 0.3831 26.7826 192.8728 191.4234 Age Weight Height Chin Forearm
5 0.2891 0.3826 26.8248 192.9035 191.4466 Years Height Forearm Calf UrbanFrac
5 0.2886 0.3822 26.8600 192.9289 191.4659 Years Height Chin Forearm UrbanFrac
4 0.2883 0.3632 26.5203 192.1130 190.9604 Age Weight Chin Pulse
4 0.2873 0.3623 26.5946 192.1651 191.0020 Age Weight Chin Forearm
3 0.2873 0.3436 26.2298 191.2957 190.5445 Years Pulse UrbanFrac
2 0.2842 0.3218 26.1239 190.5656 190.2917 Years UrbanFrac
3 0.2793 0.3362 26.8684 191.7284 190.9074 Years Forearm UrbanFrac
3 0.2793 0.3362 26.8706 191.7300 190.9086 Age Weight Forearm
6 0.2782 0.3922 27.9905 194.2942 192.4585 Age Weight Height Chin Forearm Calf
6 0.2778 0.3918 28.0234 194.3184 192.4758 Years Height Forearm Calf Pulse UrbanFrac
6 0.2776 0.3917 28.0347 194.3267 192.4818 Years Height Chin Forearm Pulse UrbanFrac
3 0.2775 0.3345 27.0191 191.8299 190.9925 Age Weight Height
3 0.2754 0.3326 27.1892 191.9441 191.0884 Age Weight Pulse
3 0.2735 0.3309 27.3358 192.0422 191.1709 Age Weight Calf
5 0.2731 0.3687 28.0365 193.7717 192.1053 Age Weight Chin Forearm Calf
5 0.2729 0.3686 28.0475 193.7795 192.1112 Age Weight Chin Calf Pulse
6 0.2723 0.3872 28.4265 194.6138 192.6876 Age Weight Height Chin Calf Pulse
5 0.2717 0.3675 28.1418 193.8462 192.1620 Years Height Chin Calf UrbanFrac
4 0.2713 0.3480 27.8402 193.0293 191.6936 Age Weight Height Forearm
4 0.2710 0.3477 27.8677 193.0482 191.7088 Years Forearm Pulse UrbanFrac
6 0.2706 0.3857 28.5534 194.7063 192.7540 Years Height Chin Calf Pulse UrbanFrac
6 0.2697 0.3850 28.6200 194.7547 192.7888 Age Weight Height Chin Forearm Pulse
3 0.2691 0.3268 27.6946 192.2814 191.3718 Years Calf UrbanFrac
4 0.2680 0.3451 28.0983 193.2060 191.8353 Years Calf Pulse UrbanFrac
6 0.2678 0.3834 28.7548 194.8527 192.8592 Years Height Chin Forearm Calf UrbanFrac
5 0.2673 0.3637 28.4762 194.0820 192.3416 Age Weight Chin Forearm Pulse
4 0.2670 0.3441 28.1792 193.2612 191.8797 Years Chin Pulse UrbanFrac
3 0.2665 0.3244 27.9039 192.4202 191.4886 Years Chin UrbanFrac
4 0.2626 0.3402 28.5204 193.4932 192.0661 Age Weight Forearm Calf
4 0.2592 0.3372 28.7846 193.6720 192.2098 Age Weight Height Pulse
4 0.2589 0.3369 28.8068 193.6869 192.2219 Years Chin Forearm UrbanFrac
4 0.2587 0.3367 28.8256 193.6996 192.2321 Years Forearm Calf UrbanFrac
4 0.2585 0.3366 28.8389 193.7086 192.2393 Age Weight Forearm Pulse
4 0.2565 0.3348 28.9935 193.8127 192.3231 Age Weight Height Calf
7 0.2560 0.3930 29.9164 196.2396 193.8935 Age Weight Height Chin Forearm Calf Pulse
5 0.2553 0.3533 29.3845 194.7154 192.8254 Age Weight Height Forearm Calf
7 0.2550 0.3922 29.9867 196.2914 193.9286 Years Height Chin Forearm Calf Pulse UrbanFrac
2 0.2546 0.2938 28.5674 192.1450 191.6770 Weight Chin
4 0.2540 0.3326 29.1884 193.9435 192.4284 Age Weight Calf Pulse
1 0.2521 0.2718 28.4846 191.3409 191.5007 Weight
6 0.2511 0.3693 29.9829 195.7337 193.4950 Age Weight Chin Forearm Calf Pulse
5 0.2498 0.3485 29.8006 195.0021 193.0451 Age Weight Height Forearm Pulse
5 0.2492 0.3480 29.8437 195.0317 193.0677 Years Chin Forearm Pulse UrbanFrac
5 0.2490 0.3478 29.8607 195.0433 193.0767 Years Forearm Calf Pulse UrbanFrac
3 0.2482 0.3076 29.3657 193.3762 192.2942 Weight Chin Calf
4 0.2479 0.3271 29.6649 194.2616 192.6848 Years Chin Calf UrbanFrac
5 0.2459 0.3451 30.0942 195.2032 193.1993 Years Chin Calf Pulse UrbanFrac
5 0.2404 0.3403 30.5136 195.4887 193.4186 Age Weight Forearm Calf Pulse
3 0.2393 0.2994 30.0804 193.8352 192.6819 Weight Height Chin
3 0.2380 0.2981 30.1914 193.9061 192.7418 Weight Chin Forearm
5 0.2370 0.3374 30.7659 195.6594 193.5499 Age Weight Height Calf Pulse
5 0.2369 0.3373 30.7740 195.6648 193.5541 Years Chin Forearm Calf UrbanFrac
2 0.2341 0.2744 30.2620 193.2039 192.6087 Weight Calf
3 0.2337 0.2942 30.5343 194.1240 192.9261 Weight Chin Pulse
2 0.2322 0.2726 30.4138 193.2974 192.6910 Weight Pulse
6 0.2321 0.3534 31.3763 196.7097 194.2046 Age Weight Height Forearm Calf Pulse
2 0.2317 0.2721 30.4577 193.3244 192.7148 Weight Height
2 0.2316 0.2720 30.4691 193.3313 192.7209 Weight Forearm
4 0.2307 0.3117 31.0088 195.1449 193.3988 Weight Height Chin Calf
4 0.2271 0.3084 31.2914 195.3282 193.5473 Weight Chin Calf Pulse
4 0.2262 0.3076 31.3615 195.3735 193.5841 Weight Chin Forearm Calf
6 0.2258 0.3480 31.8389 197.0284 194.4375 Years Chin Forearm Calf Pulse UrbanFrac
4 0.2192 0.3014 31.9032 195.7219 193.8668 Weight Height Chin Forearm
4 0.2180 0.3003 31.9988 195.7831 193.9165 Weight Height Chin Pulse
4 0.2177 0.3000 32.0271 195.8012 193.9312 Weight Chin Forearm Pulse
3 0.2167 0.2785 31.8987 194.9793 193.6509 Weight Forearm Calf
3 0.2134 0.2755 32.1632 195.1429 193.7898 Weight Calf Pulse
3 0.2122 0.2744 32.2581 195.2015 193.8396 Weight Height Calf
3 0.2108 0.2731 32.3705 195.2707 193.8984 Weight Height Pulse
3 0.2103 0.2727 32.4120 195.2962 193.9200 Weight Forearm Pulse
3 0.2103 0.2726 32.4125 195.2965 193.9203 Weight Height Forearm
5 0.2091 0.3132 32.8804 197.0614 194.6338 Weight Height Chin Calf Pulse
5 0.2083 0.3125 32.9388 197.0994 194.6633 Weight Height Chin Forearm Calf
5 0.2037 0.3085 33.2903 197.3275 194.8405 Weight Chin Forearm Calf Pulse
5 0.1981 0.3036 33.7161 197.6019 195.0541 Weight Height Chin Forearm Pulse
4 0.1949 0.2797 33.8008 196.9185 194.8414 Weight Height Forearm Calf
4 0.1938 0.2787 33.8852 196.9709 194.8842 Weight Forearm Calf Pulse
4 0.1904 0.2756 34.1518 197.1359 195.0190 Weight Height Calf Pulse
4 0.1879 0.2733 34.3521 197.2594 195.1200 Weight Height Forearm Pulse
6 0.1847 0.3134 34.8561 199.0456 195.9246 Weight Height Chin Forearm Calf Pulse
5 0.1707 0.2798 35.7864 198.9096 196.0764 Weight Height Forearm Calf Pulse
3 0.1523 0.2192 37.0714 198.0615 196.2802 Height Forearm UrbanFrac
4 0.1364 0.2273 38.3653 199.6548 197.0896 Age Height Forearm UrbanFrac
4 0.1347 0.2257 38.5017 199.7338 197.1548 Height Forearm Pulse UrbanFrac
4 0.1280 0.2197 39.0243 200.0345 197.4037 Height Chin Forearm UrbanFrac
4 0.1274 0.2192 39.0710 200.0613 197.4258 Height Forearm Calf UrbanFrac
5 0.1179 0.2340 39.7843 201.3171 197.9785 Age Height Forearm Pulse UrbanFrac
5 0.1104 0.2275 40.3514 201.6468 198.2410 Age Height Chin Forearm UrbanFrac
5 0.1102 0.2273 40.3648 201.6546 198.2472 Age Height Forearm Calf UrbanFrac
5 0.1096 0.2267 40.4152 201.6837 198.2705 Height Chin Forearm Pulse UrbanFrac
3 0.1090 0.1793 40.5474 200.0038 197.9507 Height Calf UrbanFrac
5 0.1085 0.2258 40.4956 201.7302 198.3075 Height Forearm Calf Pulse UrbanFrac
4 0.1085 0.2023 40.5448 200.8967 198.1188 Height Calf Pulse UrbanFrac
2 0.1078 0.1547 40.6931 199.1563 197.8883 Forearm UrbanFrac
4 0.1060 0.2001 40.7408 201.0064 198.2100 Height Chin Pulse UrbanFrac
3 0.1034 0.1741 41.0008 200.2502 198.1633 Height Chin UrbanFrac
5 0.1016 0.2198 41.0222 202.0333 198.5494 Height Chin Forearm Calf UrbanFrac
3 0.0997 0.1708 41.2914 200.4073 198.2990 Height Pulse UrbanFrac
4 0.0955 0.1907 41.5580 201.4607 198.5880 Height Chin Calf UrbanFrac
3 0.0933 0.1649 41.8046 200.6832 198.5374 Age Forearm UrbanFrac
4 0.0932 0.1887 41.7322 201.5569 198.6681 Age Height Calf UrbanFrac
5 0.0921 0.2115 41.7419 202.4438 198.8775 Age Height Calf Pulse UrbanFrac
5 0.0914 0.2110 41.7891 202.4705 198.8989 Height Chin Calf Pulse UrbanFrac
6 0.0909 0.2344 41.7463 203.2948 199.1295 Age Height Chin Forearm Pulse UrbanFrac
3 0.0907 0.1625 42.0127 200.7945 198.6337 Forearm Pulse UrbanFrac
6 0.0904 0.2340 41.7781 203.3134 199.1437 Age Height Forearm Calf Pulse UrbanFrac
5 0.0866 0.2068 42.1575 202.6789 199.0657 Age Height Chin Pulse UrbanFrac
4 0.0850 0.1813 42.3780 201.9114 198.9637 Age Height Pulse UrbanFrac
4 0.0841 0.1805 42.4440 201.9474 198.9938 Age Height Chin UrbanFrac
3 0.0835 0.1558 42.5955 201.1046 198.9020 Chin Forearm UrbanFrac
2 0.0827 0.1310 42.7621 200.2361 198.8539 Height Forearm
3 0.0827 0.1551 42.6619 201.1397 198.9324 Forearm Calf UrbanFrac
6 0.0826 0.2275 42.3502 203.6461 199.3986 Age Height Chin Forearm Calf UrbanFrac
2 0.0825 0.1308 42.7787 200.2447 198.8615 Height UrbanFrac
6 0.0818 0.2268 42.4129 203.6824 199.4265 Height Chin Forearm Calf Pulse UrbanFrac
3 0.0803 0.1529 42.8482 201.2382 199.0178 Years Height Forearm
2 0.0765 0.1251 43.2765 200.5000 199.0901 Calf UrbanFrac
5 0.0762 0.1978 42.9388 203.1170 199.4172 Age Height Chin Calf UrbanFrac
4 0.0755 0.1729 43.1124 202.3106 199.2971 Age Forearm Pulse UrbanFrac
3 0.0747 0.1478 43.2988 201.4755 199.2233 Calf Pulse UrbanFrac
6 0.0717 0.2182 43.1564 204.1102 199.7552 Age Height Chin Calf Pulse UrbanFrac
3 0.0708 0.1441 43.6186 201.6430 199.3685 Chin Pulse UrbanFrac
2 0.0692 0.1182 43.8764 200.8055 199.3639 Chin UrbanFrac
3 0.0683 0.1419 43.8150 201.7455 199.4575 Age Height UrbanFrac
4 0.0672 0.1654 43.7645 202.6617 199.5908 Age Chin Forearm UrbanFrac
4 0.0671 0.1653 43.7747 202.6672 199.5954 Age Forearm Calf UrbanFrac
2 0.0668 0.1160 44.0732 200.9053 199.4533 Pulse UrbanFrac
4 0.0660 0.1643 43.8559 202.7106 199.6318 Chin Forearm Pulse UrbanFrac
4 0.0650 0.1635 43.9321 202.7514 199.6659 Forearm Calf Pulse UrbanFrac
3 0.0623 0.1363 44.2988 201.9969 199.6756 Age Calf UrbanFrac
2 0.0618 0.1112 44.4862 201.1137 199.6402 Height Calf
7 0.0616 0.2344 43.7428 205.2928 200.2966 Age Height Chin Forearm Calf Pulse UrbanFrac
3 0.0614 0.1355 44.3665 202.0320 199.7061 Chin Calf UrbanFrac
3 0.0601 0.1343 44.4706 202.0858 199.7528 Height Forearm Calf
4 0.0601 0.1590 44.3181 202.9573 199.8384 Age Years Height Forearm
4 0.0599 0.1588 44.3340 202.9657 199.8455 Age Calf Pulse UrbanFrac
3 0.0571 0.1315 44.7140 202.2113 199.8618 Age Height Forearm
4 0.0568 0.1561 44.5758 203.0941 199.9531 Chin Forearm Calf UrbanFrac
3 0.0568 0.1312 44.7405 202.2250 199.8737 Height Chin Forearm
3 0.0567 0.1312 44.7474 202.2286 199.8768 Height Forearm Pulse
4 0.0563 0.1557 44.6113 203.1129 199.9689 Chin Calf Pulse UrbanFrac
4 0.0553 0.1548 44.6901 203.1547 200.0039 Years Height Forearm Pulse
4 0.0546 0.1541 44.7459 203.1842 200.0286 Years Height Forearm Calf
3 0.0537 0.1284 44.9868 202.3516 199.9837 Age Pulse UrbanFrac
4 0.0534 0.1530 44.8407 203.2343 200.0707 Years Height Chin Forearm
4 0.0528 0.1525 44.8862 203.2583 200.0908 Age Chin Pulse UrbanFrac
3 0.0514 0.1263 45.1737 202.4474 200.0670 Age Chin UrbanFrac
1 0.0513 0.0763 45.5344 200.6185 200.0236 UrbanFrac
1 0.0491 0.0741 45.7192 200.7079 200.1063 Forearm
5 0.0486 0.1738 45.0319 204.2670 200.3436 Age Chin Forearm Pulse UrbanFrac
5 0.0486 0.1738 45.0336 204.2680 200.3443 Age Forearm Calf Pulse UrbanFrac
3 0.0468 0.1220 45.5434 202.6362 200.2312 Years Height Calf
4 0.0437 0.1444 45.5936 203.6299 200.4029 Age Chin Calf UrbanFrac
3 0.0425 0.1181 45.8839 202.8094 200.3818 Height Calf Pulse
2 0.0399 0.0905 46.2967 202.0145 200.4489 Years Forearm
5 0.0392 0.1656 45.7420 204.6496 200.6530 Age Chin Forearm Calf UrbanFrac
2 0.0387 0.0893 46.3939 202.0622 200.4918 Age UrbanFrac
5 0.0385 0.1650 45.7971 204.6792 200.6769 Chin Forearm Calf Pulse UrbanFrac
5 0.0381 0.1647 45.8231 204.6931 200.6882 Age Chin Calf Pulse UrbanFrac
3 0.0377 0.1136 46.2746 203.0070 200.5539 Height Chin Calf
1 0.0376 0.0629 46.6993 201.1785 200.5417 Calf
3 0.0351 0.1112 46.4839 203.1125 200.6458 Age Height Calf
5 0.0341 0.1612 46.1278 204.8559 200.8201 Age Years Height Forearm Pulse
4 0.0331 0.1349 46.4241 204.0617 200.7660 Height Forearm Calf Pulse
4 0.0330 0.1348 46.4327 204.0662 200.7698 Height Chin Forearm Calf
4 0.0329 0.1347 46.4379 204.0689 200.7721 Age Height Forearm Calf
5 0.0328 0.1601 46.2283 204.9095 200.8635 Age Years Height Forearm Calf
4 0.0327 0.1345 46.4576 204.0790 200.7806 Years Height Calf Pulse
5 0.0316 0.1590 46.3170 204.9567 200.9018 Age Years Height Chin Forearm
4 0.0296 0.1318 46.6950 204.2016 200.8838 Age Height Forearm Pulse
4 0.0295 0.1317 46.7010 204.2046 200.8864 Age Height Chin Forearm
4 0.0292 0.1314 46.7281 204.2186 200.8981 Height Chin Forearm Pulse
5 0.0286 0.1564 46.5456 205.0781 201.0002 Years Height Forearm Calf Pulse
2 0.0286 0.0797 47.2345 202.4730 200.8612 Forearm Calf
5 0.0269 0.1550 46.6735 205.1459 201.0552 Years Height Chin Forearm Pulse
2 0.0263 0.0776 47.4198 202.5630 200.9422 Height Chin
5 0.0260 0.1542 46.7434 205.1829 201.0852 Years Height Chin Forearm Calf
4 0.0257 0.1283 47.0001 204.3584 201.0160 Years Height Chin Calf
4 0.0241 0.1268 47.1276 204.4238 201.0711 Age Years Height Calf
2 0.0232 0.0747 47.6742 202.6861 201.0530 Forearm Pulse
2 0.0228 0.0742 47.7119 202.7043 201.0694 Age Forearm
2 0.0227 0.0742 47.7174 202.7070 201.0718 Chin Forearm
1 0.0223 0.0480 47.9969 201.7931 201.1107 Height
3 0.0215 0.0988 47.5706 203.6557 201.1194 Years Height Chin
6 0.0197 0.1745 46.9686 206.2328 201.3997 Age Chin Forearm Calf Pulse UrbanFrac
3 0.0197 0.0971 47.7203 203.7299 201.1842 Age Years Forearm
2 0.0190 0.0706 48.0279 202.8567 201.2065 Years Calf
2 0.0185 0.0701 48.0693 202.8767 201.2245 Calf Pulse
4 0.0160 0.1196 47.7569 204.7449 201.3419 Height Chin Calf Pulse
3 0.0158 0.0935 48.0290 203.8826 201.3174 Years Forearm Calf
3 0.0151 0.0928 48.0890 203.9122 201.3432 Years Forearm Pulse
4 0.0146 0.1183 47.8694 204.8020 201.3901 Age Height Calf Pulse
2 0.0140 0.0659 48.4369 203.0531 201.3834 Height Pulse
2 0.0132 0.0652 48.5016 203.0841 201.4113 Chin Calf
3 0.0128 0.0908 48.2697 204.0012 201.4210 Years Chin Forearm
4 0.0114 0.1154 48.1178 204.9278 201.4964 Years Height Chin Pulse
2 0.0109 0.0629 48.6948 203.1764 201.4945 Age Calf
5 0.0100 0.1403 47.9528 205.8173 201.6010 Age Years Height Calf Pulse
4 0.0096 0.1139 48.2560 204.9976 201.5554 Age Height Chin Calf
5 0.0090 0.1394 48.0276 205.8562 201.6327 Years Height Chin Calf Pulse
3 0.0089 0.0871 48.5849 204.1559 201.5562 Height Chin Pulse
3 0.0069 0.0853 48.7445 204.2341 201.6245 Years Height Pulse
2 0.0065 0.0588 49.0601 203.3504 201.6513 Years Height
6 0.0057 0.1627 47.9949 206.7850 201.8312 Age Years Height Forearm Calf Pulse
5 0.0043 0.1353 48.3863 206.0422 201.7843 Age Height Forearm Calf Pulse
5 0.0042 0.1353 48.3905 206.0444 201.7861 Height Chin Forearm Calf Pulse
6 0.0040 0.1613 48.1218 206.8527 201.8842 Age Years Height Chin Forearm Pulse
5 0.0040 0.1350 48.4100 206.0544 201.7943 Age Height Chin Forearm Calf
3 0.0040 0.0826 48.9826 204.3503 201.7261 Years Calf Pulse
1 0.0027 0.0290 49.6574 202.5657 201.8267 Chin
6 0.0026 0.1601 48.2283 206.9095 201.9287 Age Years Height Chin Forearm Calf
3 0.0022 0.0810 49.1243 204.4194 201.7865 Forearm Calf Pulse
5 0.0011 0.1326 48.6262 206.1661 201.8853 Age Years Height Chin Calf
3 0.0010 0.0798 49.2234 204.4676 201.8286 Chin Forearm Calf
3 0.0008 0.0797 49.2330 204.4722 201.8327 Age Forearm Calf
5 0.0004 0.1319 48.6844 206.1961 201.9098 Age Height Chin Forearm Pulse
3 -.0002 0.0787 49.3186 204.5138 201.8691 Age Height Chin
6 -.0016 0.1565 48.5375 207.0738 202.0574 Years Height Chin Forearm Calf Pulse
4 -.0032 0.1024 49.2549 205.4987 201.9791 Age Years Height Chin
3 -.0033 0.0759 49.5667 204.6341 201.9743 Years Chin Calf
3 -.0033 0.0759 49.5668 204.6341 201.9743 Age Years Calf
3 -.0045 0.0748 49.6638 204.6811 202.0154 Age Forearm Pulse
3 -.0047 0.0747 49.6734 204.6857 202.0195 Chin Forearm Pulse
2 -.0048 0.0481 49.9934 203.7914 202.0490 Age Height
3 -.0051 0.0742 49.7110 204.7039 202.0354 Age Chin Forearm
4 -.0060 0.0999 49.4746 205.6080 202.0717 Age Years Forearm Pulse
4 -.0060 0.0999 49.4748 205.6081 202.0718 Age Years Forearm Calf
2 -.0076 0.0455 50.2199 203.8977 202.1449 Years Chin
3 -.0082 0.0714 49.9547 204.8215 202.1383 Chin Calf Pulse
1 -.0082 0.0184 50.5825 202.9895 202.2198 Pulse
4 -.0090 0.0972 49.7086 205.7241 202.1701 Age Years Chin Forearm
4 -.0095 0.0968 49.7450 205.7421 202.1853 Years Forearm Calf Pulse
3 -.0096 0.0701 50.0692 204.8766 202.1866 Age Calf Pulse
4 -.0130 0.0936 50.0184 205.8773 202.2999 Years Chin Forearm Calf
5 -.0130 0.1202 49.6991 206.7155 202.3341 Age Years Height Chin Pulse
4 -.0133 0.0934 50.0439 205.8899 202.3106 Years Chin Forearm Pulse
5 -.0133 0.1200 49.7220 206.7271 202.3436 Age Height Chin Calf Pulse
3 -.0138 0.0662 50.4069 205.0387 202.3286 Age Height Pulse
2 -.0144 0.0390 50.7851 204.1617 202.3831 Chin Pulse
3 -.0150 0.0652 50.5014 205.0840 202.3682 Age Chin Calf
4 -.0156 0.0913 50.2219 205.9777 202.3850 Age Years Height Pulse
6 -.0157 0.1447 49.5683 207.6167 202.4838 Age Years Height Chin Calf Pulse
3 -.0170 0.0633 50.6664 205.1628 202.4374 Age Years Height
4 -.0183 0.0889 50.4295 206.0797 202.4716 Age Years Calf Pulse
4 -.0185 0.0887 50.4472 206.0884 202.4789 Age Height Chin Pulse
3 -.0186 0.0618 50.7946 205.2240 202.4910 Years Chin Pulse
1 -.0192 0.0077 51.5155 203.4124 202.6123 Years
2 -.0202 0.0335 51.2618 204.3830 202.5830 Years Pulse
4 -.0207 0.0867 50.6238 206.1750 202.5524 Years Chin Calf Pulse
2 -.0245 0.0294 51.6178 204.5474 202.7315 Age Chin
7 -.0263 0.1628 49.9932 208.7841 202.8991 Age Years Height Chin Forearm Calf Pulse
6 -.0265 0.1356 50.3630 208.0301 202.8094 Age Height Chin Forearm Calf Pulse
1 -.0270 0.0000 52.1797 203.7107 202.8892 Age
4 -.0271 0.0810 51.1165 206.4156 202.7567 Chin Forearm Calf Pulse
4 -.0271 0.0810 51.1207 206.4176 202.7585 Age Forearm Calf Pulse
4 -.0274 0.0807 51.1459 206.4299 202.7689 Age Years Chin Calf
4 -.0284 0.0798 51.2229 206.4674 202.8007 Age Chin Forearm Calf
3 -.0319 0.0496 51.8615 205.7294 202.9344 Age Years Chin
5 -.0322 0.1036 51.1503 207.4465 202.9331 Age Years Forearm Calf Pulse
4 -.0341 0.0748 51.6637 206.6810 202.9824 Age Chin Forearm Pulse
2 -.0361 0.0184 52.5789 204.9879 203.1297 Age Pulse
5 -.0362 0.1002 51.4494 207.5955 203.0554 Age Years Chin Forearm Pulse
5 -.0365 0.0999 51.4722 207.6068 203.0647 Age Years Chin Forearm Calf
4 -.0377 0.0715 51.9501 206.8193 203.0999 Age Chin Calf Pulse
5 -.0398 0.0970 51.7223 207.7309 203.1666 Years Chin Forearm Calf Pulse
2 -.0422 0.0127 53.0778 205.2146 203.3348 Age Years
3 -.0422 0.0401 52.6901 206.1175 203.2752 Age Years Pulse
4 -.0426 0.0672 52.3278 207.0008 203.2545 Age Years Chin Pulse
3 -.0426 0.0397 52.7210 206.1319 203.2879 Age Chin Pulse
5 -.0449 0.0925 52.1139 207.9244 203.3258 Age Years Chin Calf Pulse
5 -.0582 0.0811 53.1144 208.4146 203.7295 Age Chin Forearm Calf Pulse
6 -.0643 0.1037 53.1405 209.4416 203.9272 Age Years Chin Forearm Calf Pulse

The SAS System

The REG Procedure

Model: MODEL1

Dependent Variable: Systol

Observation-wise Statistics

Systol

Diagnostic Plots

Fit Diagnostics

Panel of fit diagnostics for Systol.

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for Systol.

Panel 2

Panel of scatterplots of residuals by regressors for Systol.
In [23]:
PROC SORT DATA=peru_sel;
BY _IN_ DESCENDING _ADJRSQ_;
RUN;

DATA peru_sel1;
SET peru_sel;
by _IN_;
IF first._IN_ THEN OUTPUT;
RUN;

PROC PRINT DATA=peru_sel1;
VAR Age Years Weight Height Chin Forearm Calf Pulse UrbanFrac _BIC_ _RSQ_ _ADJRSQ_ _CP_;
RUN;
Out[23]:
SAS Output

SAS Output

The SAS System

The PRINT Procedure

Data Set WORK.PERU_SEL1

Obs Age Years Weight Height Chin Forearm Calf Pulse UrbanFrac _BIC_ _RSQ_ _ADJRSQ_ _CP_
1 . . 0.96286 . . . . . . 191.501 0.27182 0.25214 28.4846
2 . . 1.21686 . . . . . -26.767 181.771 0.47311 0.44384 12.9359
3 . . 1.44074 . -1.01353 . . . -27.352 181.605 0.50333 0.46075 12.3013
4 -0.95067 2.33925 0.83241 . . . . . -108.073 177.317 0.59738 0.55001 6.1018
5 -1.01203 2.40675 1.09764 . -1.19179 . . . -110.811 176.757 0.63864 0.58388 4.5047
6 -1.09260 2.55234 1.16807 . -0.87758 -0.82140 . . -116.682 178.583 0.64882 0.58298 5.6167
7 -1.09745 2.35670 1.46055 -0.037129 -1.03844 -1.14395 . . -110.455 180.453 0.66065 0.58402 6.5853
8 -1.10995 2.41595 1.42678 -0.035937 -0.97163 -1.37112 . 0.11966 -113.543 182.803 0.66636 0.57739 8.0872
9 -1.12144 2.45538 1.41393 -0.034636 -0.94369 -1.17085 -0.15867 0.11455 -115.294 185.443 0.66737 0.56413 10.0000
In [18]:
PROC CONTENTS DATA=peru_sel;
RUN;
Out[18]:
SAS Output

SAS Output

The SAS System

The CONTENTS Procedure

The CONTENTS Procedure

WORK.PERU_SEL

Attributes

Data Set Name WORK.PERU_SEL Observations 511
Member Type DATA Variables 22
Engine V9 Indexes 0
Created 01/17/2018 12:38:34 Observation Length 208
Last Modified 01/17/2018 12:38:34 Deleted Observations 0
Protection   Compressed NO
Data Set Type EST Sorted YES
Label Parameter Estimates and Statistics    
Data Representation WINDOWS_64    
Encoding wlatin1 Western (Windows)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 65536
Number of Data Set Pages 2
First Data Page 1
Max Obs per Page 314
Obs in First Data Page 298
Number of Data Set Repairs 0
ExtendObsCounter YES
Filename C:\Users\rlp176\AppData\Local\Temp\SAS Temporary Files\_TD1548_PHHP-DDH4LH2_\Prc2\peru_sel.sas7bdat
Release Created 9.0401M3
Host Created X64_7PRO

Variables

Alphabetic List of Variables and Attributes
# Variable Type Len Label
6 Age Num 8  
12 Calf Num 8  
10 Chin Num 8  
11 Forearm Num 8  
9 Height Num 8  
5 Intercept Num 8 Intercept
13 Pulse Num 8  
15 Systol Num 8  
14 UrbanFrac Num 8  
8 Weight Num 8  
7 Years Num 8  
21 _AIC_ Num 8 Akaike's information criterion
22 _BIC_ Num 8 Sawa's Bayesian information criterion
20 _CP_ Num 8 Mallows C(p)
3 _DEPVAR_ Char 9 Dependent variable
18 _EDF_ Num 8 Error degrees of freedom
16 _IN_ Num 8 Number of regressors in model
1 _MODEL_ Char 32 Label of model
17 _P_ Num 8 Number of parameters in model
4 _RMSE_ Num 8 Root mean squared error
19 _RSQ_ Num 8 R-squared
2 _TYPE_ Char 8 Type of statistics

Sortedby

Sort Information
Sortedby _IN_
Validated YES
Character Set ANSI
In [51]:
PROC GLMSELECT DATA=Survey.peru plots=ALL SEED=750;
partition fraction(validate=.5);
MODEL Systol = Age Years Weight Height Chin Forearm Calf Pulse UrbanFrac / 
SELECTION=LASSO(stop=NONE choose=CV) CVMETHOD=BLOCK(39);
RUN;
Out[51]:
SAS Output

SAS Output

The SAS System

The GLMSELECT Procedure

The GLMSELECT Procedure

Model Information

Data Set SURVEY.PERU
Dependent Variable Systol
Selection Method LASSO
Stop Criterion None
Choose Criterion Cross Validation
Cross Validation Method Block
Cross Validation Fold 39
Effect Hierarchy Enforced None
Random Number Seed 750

Number of Observations

Number of Observations Read 39
Number of Observations Used 39
Number of Observations Used for Training 24
Number of Observations Used for Validation 15

Dimensions

Dimensions
Number of Effects 10
Number of Parameters 10

The SAS System

The GLMSELECT Procedure

Model Building Summary

LASSO Selection Summary

LASSO Selection Summary
Step Effect
Entered		 Effect
Removed		 Number
Effects In		 ASE Validation
ASE		 CV PRESS
* Optimal Value of Criterion
0 Intercept   1 212.9566 100.9295 5565.0510
1 Weight   2 202.2776 94.6299 4329.8790
2 UrbanFrac   3 92.1532 95.9979 2825.9177
3 Age   4 83.5154 101.0164 3025.7322
4 Calf   5 81.6070 102.5024 3014.3543
5 Height   6 67.3044 124.8341 2825.5403*
6 Forearm   7 65.4040 127.4228 3353.1537
7 Pulse   8 64.9887 127.4788 3768.1333
8 Years   9 63.6359 115.6915 4197.7836
9 Chin   10 61.0125 72.8024* 4523.4090

Stop Reason

Selection stopped because all effects are in the final model.

Coefficient Plot

Panel showing how the standardized coefficients and the CHOOSE= criterion change with the effect sequence.

Criterion Panel

Panel showing how selection criteria change with the effect sequence.

ASE Plot

Plot showing how the average squared error for the training, validation, and test data change with the effect sequence.

Selected Model

The SAS System

The GLMSELECT Procedure

Selected Model

The selected model, based on Cross Validation, is the model at Step 5.

Selected Effects

Effects: Intercept Age Weight Height Calf UrbanFrac

ANOVA

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value
Model 5 3495.65259 699.13052 7.79
Error 18 1615.30575 89.73921  
Corrected Total 23 5110.95833    

Fit Statistics

Root MSE 9.47308
Dependent Mean 128.95833
R-Square 0.6840
Adj R-Sq 0.5962
AIC 139.02142
AICC 146.02142
SBC 120.08974
ASE (Train) 67.30441
ASE (Validate) 124.83414
CV PRESS 2825.54032

Parameter Estimates

Parameter Estimates
Parameter DF Estimate
Intercept 1 119.652958
Age 1 -0.377555
Weight 1 1.646242
Height 1 -0.039524
Calf 1 -0.554491
UrbanFrac 1 -36.804072

In this case, we used leave one out cross validation to choose the tuning parameter. It looks like we could have stopped earlier and gotten a simpler model that does just as well in terms of cross-validation error. We can force the procedure to stop and get the simpler model.

In [52]:
PROC GLMSELECT DATA=Survey.peru plots=ALL SEED=750;
partition fraction(validate=.5);
MODEL Systol = Age Years Weight Height Chin Forearm Calf Pulse UrbanFrac / 
SELECTION=LASSO(stop=3 choose=CV) CVMETHOD=BLOCK(39);
RUN;
Out[52]:
SAS Output

SAS Output

The SAS System

The GLMSELECT Procedure

The GLMSELECT Procedure

Model Information

Data Set SURVEY.PERU
Dependent Variable Systol
Selection Method LASSO
Stop at Specified Number of Effects 3
Choose Criterion Cross Validation
Cross Validation Method Block
Cross Validation Fold 39
Effect Hierarchy Enforced None
Random Number Seed 750

Number of Observations

Number of Observations Read 39
Number of Observations Used 39
Number of Observations Used for Training 24
Number of Observations Used for Validation 15

Dimensions

Dimensions
Number of Effects 10
Number of Parameters 10

The SAS System

The GLMSELECT Procedure

Model Building Summary

LASSO Selection Summary

LASSO Selection Summary
Step Effect
Entered		 Effect
Removed		 Number
Effects In		 ASE Validation
ASE		 CV PRESS
* Optimal Value of Criterion
0 Intercept   1 212.9566 100.9295 5565.0510
1 Weight   2 202.2776 94.6299* 4329.8790
2 UrbanFrac   3 92.1532 95.9979 2825.9177*

Stop Reason

Selection stopped at the first model containing the specified number of effects (3).

Coefficient Plot

Panel showing how the standardized coefficients and the CHOOSE= criterion change with the effect sequence.

Criterion Panel

Panel showing how selection criteria change with the effect sequence.

ASE Plot

Plot showing how the average squared error for the training, validation, and test data change with the effect sequence.

Selected Model

The SAS System

The GLMSELECT Procedure

Selected Model

The selected model, based on Cross Validation, is the model at Step 2.

Selected Effects

Effects: Intercept Weight UrbanFrac

ANOVA

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value
Model 2 2899.28269 1449.64134 13.76
Error 21 2211.67565 105.31789  
Corrected Total 23 5110.95833    

Fit Statistics

Root MSE 10.26245
Dependent Mean 128.95833
R-Square 0.5673
Adj R-Sq 0.5261
AIC 140.56285
AICC 142.66811
SBC 118.09701
ASE (Train) 92.15315
ASE (Validate) 95.99791
CV PRESS 2825.91771

Parameter Estimates

Parameter Estimates
Parameter DF Estimate
Intercept 1 78.789527
Weight 1 0.961946
UrbanFrac 1 -27.861392
In [ ]: