Output from fitness3.sas
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Various selection methods for Fitness data 1 R Square Analysis
N = 31 Regression Models for Dependent Variable: OXY
Number in R-square C(p) Variables in Model Model
1 0.74338010 13.69884 RUNTIME
1 0.15948531 106.30211 RSTPULSE
1 0.15838344 106.47686 RUNPULSE
1 0.09277653 116.88184 AGE
1 0.05604592 122.70716 MAXPULSE
1 0.02648849 127.39485 WEIGHT
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2 0.76424693 12.38945 AGE RUNTIME
2 0.76142381 12.83718 RUNTIME RUNPULSE
2 0.74522106 15.40687 RUNTIME MAXPULSE
2 0.74493479 15.45227 WEIGHT RUNTIME
2 0.74353296 15.67460 RUNTIME RSTPULSE
2 0.37599543 73.96451 AGE RUNPULSE
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3 0.81109446 6.95963 AGE RUNTIME RUNPULSE
3 0.80998844 7.13504 RUNTIME RUNPULSE MAXPULSE
3 0.78173017 11.61668 AGE RUNTIME MAXPULSE
3 0.77083060 13.34531 AGE WEIGHT RUNTIME
3 0.76734943 13.89741 AGE RUNTIME RSTPULSE
3 0.76189848 14.76190 RUNTIME RUNPULSE RSTPULSE
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4 0.83681815 4.87996 AGE RUNTIME RUNPULSE MAXPULSE
4 0.81649255 8.10351 AGE WEIGHT RUNTIME RUNPULSE
4 0.81584902 8.20557 WEIGHT RUNTIME RUNPULSE MAXPULSE
4 0.81167015 8.86832 AGE RUNTIME RUNPULSE RSTPULSE
4 0.81040041 9.06970 RUNTIME RUNPULSE MAXPULSE RSTPULSE
4 0.78622430 12.90393 AGE WEIGHT RUNTIME MAXPULSE
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5 0.84800181 5.10628 AGE WEIGHT RUNTIME RUNPULSE MAXPULSE
5 0.83703132 6.84615 AGE RUNTIME RUNPULSE MAXPULSE RSTPULSE
5 0.81755611 9.93484 AGE WEIGHT RUNTIME RUNPULSE RSTPULSE
5 0.81608280 10.16850 WEIGHT RUNTIME RUNPULSE MAXPULSE RSTPULSE
5 0.78870109 14.51112 AGE WEIGHT RUNTIME MAXPULSE RSTPULSE
5 0.55406593 51.72328 AGE WEIGHT RUNPULSE MAXPULSE RSTPULSE
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6 0.84867192 7.00000 AGE WEIGHT RUNTIME RUNPULSE MAXPULSE RSTPULSE
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Various selection methods for Fitness data 2 Forward Selection
Forward Selection Procedure for Dependent Variable OXY
Statistics for Entry: Step 1
DF = 1,29
Model
Variable Tolerance R**2 F Prob>F
AGE 1.000000 0.0928 2.9657 0.0957
WEIGHT 1.000000 0.0265 0.7891 0.3817
RUNTIME 1.000000 0.7434 84.0076 0.0001
RUNPULSE 1.000000 0.1584 5.4575 0.0266
MAXPULSE 1.000000 0.0560 1.7218 0.1997
RSTPULSE 1.000000 0.1595 5.5027 0.0260
Step 1 Variable RUNTIME Entered R-square = 0.74338010 C(p) = 13.69884048
DF Sum of Squares Mean Square F Prob>F
Regression 1 632.90009985 632.90009985 84.01 0.0001 Error 29 218.48144499 7.53384293 Total 30 851.38154484
Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 82.42177268 3.85530378 3443.36654076 457.05 0.0001
RUNTIME -3.31055536 0.36119485 632.90009985 84.01 0.0001
Bounds on condition number: 1, 1
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Statistics for Entry: Step 2
DF = 1,28
Model
Variable Tolerance R**2 F Prob>F
AGE 0.964375 0.7642 2.4783 0.1267
WEIGHT 0.979406 0.7449 0.1707 0.6827
RUNPULSE 0.901625 0.7614 2.1177 0.1567
MAXPULSE 0.948877 0.7452 0.2023 0.6563
RSTPULSE 0.797156 0.7435 0.0167 0.8981
Step 2 Variable AGE Entered R-square = 0.76424693 C(p) = 12.38944895
DF Sum of Squares Mean Square F Prob>F
Regression 2 650.66573237 325.33286618 45.38 0.0001 Error 28 200.71581247 7.16842187 Total 30 851.38154484
Various selection methods for Fitness data 3 Forward Selection
Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 88.46228749 5.37263885 1943.41070877 271.11 0.0001
AGE -0.15036567 0.09551468 17.76563252 2.48 0.1267
RUNTIME -3.20395056 0.35877488 571.67750579 79.75 0.0001
Bounds on condition number: 1.036941, 4.147763
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Statistics for Entry: Step 3
DF = 1,27
Model
Variable Tolerance R**2 F Prob>F
WEIGHT 0.908971 0.7708 0.7757 0.3862
RUNPULSE 0.738136 0.8111 6.6959 0.0154
MAXPULSE 0.714334 0.7817 2.1627 0.1530
RSTPULSE 0.732809 0.7673 0.3601 0.5535
Step 3 Variable RUNPULSE Entered R-square = 0.81109446 C(p) = 6.95962673
DF Sum of Squares Mean Square F Prob>F
Regression 3 690.55085627 230.18361876 38.64 0.0001 Error 27 160.83068857 5.95669217 Total 30 851.38154484
Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 111.71806443 10.23508836 709.69013814 119.14 0.0001
AGE -0.25639826 0.09622892 42.28867438 7.10 0.0129
RUNTIME -2.82537867 0.35828041 370.43528607 62.19 0.0001
RUNPULSE -0.13090870 0.05059011 39.88512390 6.70 0.0154
Bounds on condition number: 1.354763, 11.59745
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Statistics for Entry: Step 4
DF = 1,26
Model
Variable Tolerance R**2 F Prob>F
WEIGHT 0.907816 0.8165 0.7648 0.3898
MAXPULSE 0.118790 0.8368 4.0986 0.0533
RSTPULSE 0.716821 0.8117 0.0795 0.7802
Various selection methods for Fitness data 4 Forward Selection
Step 4 Variable MAXPULSE Entered R-square = 0.83681815 C(p) = 4.87995808
DF Sum of Squares Mean Square F Prob>F
Regression 4 712.45152692 178.11288173 33.33 0.0001 Error 26 138.93001792 5.34346223 Total 30 851.38154484
Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 98.14788797 11.78569002 370.57373243 69.35 0.0001
AGE -0.19773470 0.09563662 22.84231496 4.27 0.0488
RUNTIME -2.76757879 0.34053642 352.93569605 66.05 0.0001
RUNPULSE -0.34810795 0.11749917 46.90088674 8.78 0.0064
MAXPULSE 0.27051297 0.13361978 21.90067065 4.10 0.0533
Bounds on condition number: 8.4182, 76.85135
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Statistics for Entry: Step 5
DF = 1,25
Model
Variable Tolerance R**2 F Prob>F
WEIGHT 0.875270 0.8480 1.8394 0.1871
RSTPULSE 0.714349 0.8370 0.0327 0.8580
Step 5 Variable WEIGHT Entered R-square = 0.84800181 C(p) = 5.10627546
DF Sum of Squares Mean Square F Prob>F
Regression 5 721.97309402 144.39461880 27.90 0.0001 Error 25 129.40845082 5.17633803 Total 30 851.38154484
Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 102.20427520 11.97928972 376.78934930 72.79 0.0001 AGE -0.21962138 0.09550245 27.37429100 5.29 0.0301 WEIGHT -0.07230234 0.05331009 9.52156710 1.84 0.1871 RUNTIME -2.68252297 0.34098544 320.35967836 61.89 0.0001 RUNPULSE -0.37340085 0.11714109 52.59623720 10.16 0.0038 MAXPULSE 0.30490783 0.13393642 26.82640270 5.18 0.0316 Bounds on condition number: 8.731225, 104.8254 ------------------------------------------------------------------------------
Various selection methods for Fitness data 5 Forward Selection
Statistics for Entry: Step 6
DF = 1,24
Model
Variable Tolerance R**2 F Prob>F
RSTPULSE 0.706420 0.8487 0.1063 0.7473
No other variable met the 0.5000 significance level for entry into the model.
Summary of Forward Selection Procedure for Dependent Variable OXY
Variable Number Partial Model
Step Entered In R**2 R**2 C(p) F Prob>F
1 RUNTIME 1 0.7434 0.7434 13.6988 84.0076 0.0001 2 AGE 2 0.0209 0.7642 12.3894 2.4783 0.1267 3 RUNPULSE 3 0.0468 0.8111 6.9596 6.6959 0.0154 4 MAXPULSE 4 0.0257 0.8368 4.8800 4.0986 0.0533 5 WEIGHT 5 0.0112 0.8480 5.1063 1.8394 0.1871
Various selection methods for Fitness data 6 Stepwise Analysis
Stepwise Procedure for Dependent Variable OXY
The first 2 variables are forced into the model because of the INCLUDE= option. Step 0 The First 2 Vars Entered R-square = 0.15063534 C(p) =109.70567678
DF Sum of Squares Mean Square F Prob>F
Regression 2 128.24814438 64.12407219 2.48 0.1017 Error 28 723.13340046 25.82619287 Total 30 851.38154484
Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 77.29049413 13.85462884 803.75329459 31.12 0.0001 AGE -0.37041610 0.18310074 105.69633373 4.09 0.0527 WEIGHT -0.15823204 0.11457181 49.25991780 1.91 0.1782 Bounds on condition number: 1.057687, 4.230747 ------------------------------------------------------------------------------ Step 1 Variable RUNTIME Entered R-square = 0.77083060 C(p) = 13.34530613
DF Sum of Squares Mean Square F Prob>F
Regression 3 656.27094936 218.75698312 30.27 0.0001 Error 27 195.11059548 7.22631835 Total 30 851.38154484
Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 93.12615008 7.55915630 1096.76539223 151.77 0.0001 AGE -0.17387679 0.09954587 22.04722118 3.05 0.0921 WEIGHT -0.05443652 0.06180913 5.60521700 0.78 0.3862 RUNTIME -3.14038657 0.36737984 528.02280498 73.07 0.0001 Bounds on condition number: 1.117292, 9.888012 ------------------------------------------------------------------------------ Step 2 Variable RUNPULSE Entered R-square = 0.81649255 C(p) = 8.10351211
DF Sum of Squares Mean Square F Prob>F
Regression 4 695.14669132 173.78667283 28.92 0.0001 Error 26 156.23485352 6.00903283 Total 30 851.38154484
Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F
Various selection methods for Fitness data 7 Stepwise Analysis
INTERCEP 115.66229667 11.22578205 637.90350440 106.16 0.0001 AGE -0.27641726 0.09932454 46.53950756 7.74 0.0099 WEIGHT -0.04932333 0.05639914 4.59583505 0.76 0.3898 RUNTIME -2.77236856 0.36492045 346.82476452 57.72 0.0001 RUNPULSE -0.12932379 0.05084420 38.87574195 6.47 0.0173 Bounds on condition number: 1.356487, 20.30177 ------------------------------------------------------------------------------ Step 3 Variable MAXPULSE Entered R-square = 0.84800181 C(p) = 5.10627546
DF Sum of Squares Mean Square F Prob>F
Regression 5 721.97309402 144.39461880 27.90 0.0001 Error 25 129.40845082 5.17633803 Total 30 851.38154484
Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 102.20427520 11.97928972 376.78934930 72.79 0.0001 AGE -0.21962138 0.09550245 27.37429100 5.29 0.0301 WEIGHT -0.07230234 0.05331009 9.52156710 1.84 0.1871 RUNTIME -2.68252297 0.34098544 320.35967836 61.89 0.0001 RUNPULSE -0.37340085 0.11714109 52.59623720 10.16 0.0038 MAXPULSE 0.30490783 0.13393642 26.82640270 5.18 0.0316 Bounds on condition number: 8.731225, 104.8254 ------------------------------------------------------------------------------ All variables left in the model are required or significant at the 0.1500 level. No other variable met the 0.1500 significance level for entry into the model.
Summary of Stepwise Procedure for Dependent Variable OXY
Variable Number Partial Model
Step Entered Removed In R**2 R**2 C(p) F Prob>F
1 RUNTIME 3 0.6202 0.7708 13.3453 73.0694 0.0001 2 RUNPULSE 4 0.0457 0.8165 8.1035 6.4696 0.0173 3 MAXPULSE 5 0.0315 0.8480 5.1063 5.1825 0.0316