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tests/testthat/_snaps/stepaic-f-output.md
In olsrr: Tools for Building OLS Regression Models
output from stepAIC forward regression is as expected
Code
ols_step_forward_aic(model)
Output
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_aic(model, progress = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Entered:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
No more variables to be added.
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_aic(model, details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Step => 0
Model => y ~ 1
AIC => 802.606
Initiating stepwise selection...
Table: Adding New Variables
-------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
liver_test 1 771.875 777.842 616.009 0.45454 0.44405
enzyme_test 1 782.629 788.596 626.220 0.33435 0.32154
pindex 1 794.100 800.067 637.196 0.17680 0.16097
alc_heavy 1 794.301 800.268 637.389 0.17373 0.15784
bcs 1 797.697 803.664 640.655 0.12010 0.10318
alc_mod 1 802.828 808.795 645.601 0.03239 0.01378
gender 1 802.956 808.923 645.725 0.03009 0.01143
age 1 803.834 809.801 646.572 0.01420 -0.00476
-------------------------------------------------------------------------
Step => 1
Added => liver_test
Model => y ~ liver_test
AIC => 771.8753
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_heavy 1 761.439 769.395 605.506 0.56674 0.54975
enzyme_test 1 762.077 770.033 606.090 0.56159 0.54440
pindex 1 770.387 778.343 613.737 0.48866 0.46861
alc_mod 1 771.141 779.097 614.435 0.48147 0.46113
gender 1 773.802 781.758 616.901 0.45528 0.43391
age 1 773.831 781.787 616.928 0.45498 0.43361
bcs 1 773.867 781.823 616.961 0.45462 0.43323
------------------------------------------------------------------------
Step => 2
Added => alc_heavy
Model => y ~ liver_test + alc_heavy
AIC => 761.4394
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 750.509 760.454 595.297 0.65900 0.63854
pindex 1 756.125 766.070 600.225 0.62163 0.59892
bcs 1 763.063 773.008 606.379 0.56975 0.54394
age 1 763.110 773.055 606.421 0.56938 0.54354
alc_mod 1 763.428 773.373 606.704 0.56683 0.54084
gender 1 763.433 773.378 606.709 0.56679 0.54080
------------------------------------------------------------------------
Step => 3
Added => enzyme_test
Model => y ~ liver_test + alc_heavy + enzyme_test
AIC => 750.5089
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
pindex 1 735.715 747.649 582.943 0.75015 0.72975
bcs 1 750.782 762.716 595.377 0.66973 0.64277
alc_mod 1 752.403 764.337 596.743 0.65967 0.63189
age 1 752.416 764.350 596.755 0.65959 0.63180
gender 1 752.509 764.443 596.833 0.65900 0.63116
----------------------------------------------------------------------
Step => 4
Added => pindex
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex
AIC => 735.7146
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
bcs 1 730.620 744.543 579.638 0.78091 0.75808
age 1 737.680 751.603 585.012 0.75030 0.72429
gender 1 737.712 751.635 585.036 0.75016 0.72413
alc_mod 1 737.713 751.636 585.037 0.75015 0.72413
----------------------------------------------------------------------
Step => 5
Added => bcs
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex + bcs
AIC => 730.6204
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
age 1 732.494 748.406 581.938 0.78142 0.75351
gender 1 732.551 748.463 581.978 0.78119 0.75325
alc_mod 1 732.614 748.526 582.023 0.78093 0.75297
----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_aic(model, include = "pindex", details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. enzyme_test
3. liver_test
4. age
5. gender
6. alc_mod
7. alc_heavy
Step => 0
Model => y ~ pindex
AIC => 794.0997
Initiating stepwise selection...
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 766.642 774.598 610.282 0.52292 0.50421
liver_test 1 770.387 778.343 613.737 0.48866 0.46861
alc_heavy 1 780.568 788.524 623.203 0.38256 0.35835
bcs 1 789.400 797.356 631.496 0.27285 0.24434
alc_mod 1 792.349 800.305 634.280 0.23204 0.20192
gender 1 795.111 803.067 636.895 0.19174 0.16004
age 1 795.450 803.406 637.216 0.18665 0.15476
------------------------------------------------------------------------
Step => 1
Added => enzyme_test
Model => y ~ pindex + enzyme_test
AIC => 766.6422
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
bcs 1 746.376 756.320 591.702 0.68413 0.66518
alc_heavy 1 748.167 758.112 593.257 0.67347 0.65388
liver_test 1 755.099 765.044 599.321 0.62875 0.60647
alc_mod 1 764.533 774.477 607.692 0.55788 0.53135
age 1 767.697 777.642 610.529 0.53120 0.50307
gender 1 768.479 778.424 611.232 0.52436 0.49582
-----------------------------------------------------------------------
Step => 2
Added => bcs
Model => y ~ pindex + enzyme_test + bcs
AIC => 746.3755
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
alc_heavy 1 730.924 742.858 579.087 0.77136 0.75269
alc_mod 1 744.985 756.919 590.537 0.70335 0.67913
age 1 747.171 759.105 592.354 0.69109 0.66588
liver_test 1 747.181 759.114 592.362 0.69104 0.66582
gender 1 748.330 760.264 593.322 0.68439 0.65863
-----------------------------------------------------------------------
Step => 3
Added => alc_heavy
Model => y ~ pindex + enzyme_test + bcs + alc_heavy
AIC => 730.9241
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
liver_test 1 730.620 744.543 579.638 0.78091 0.75808
age 1 732.339 746.262 580.934 0.77382 0.75026
gender 1 732.516 746.439 581.067 0.77308 0.74944
alc_mod 1 732.909 746.832 581.365 0.77142 0.74761
-----------------------------------------------------------------------
Step => 4
Added => liver_test
Model => y ~ pindex + enzyme_test + bcs + alc_heavy + liver_test
AIC => 730.6204
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
age 1 732.494 748.406 581.938 0.78142 0.75351
gender 1 732.551 748.463 581.978 0.78119 0.75325
alc_mod 1 732.614 748.526 582.023 0.78093 0.75297
----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> pindex
=> enzyme_test
=> bcs
=> alc_heavy
=> liver_test
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 794.100 800.067 637.196 0.17680 0.16097
1 enzyme_test 766.642 774.598 610.282 0.52292 0.50421
2 bcs 746.376 756.320 591.702 0.68413 0.66518
3 alc_heavy 730.924 742.858 579.087 0.77136 0.75269
4 liver_test 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
------------------------------------------------------------------------------------------------
output from stepSBC forward regression is as expected
Code
ols_step_forward_sbc(model)
Output
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbc(model, progress = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Entered:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
No more variables to be added.
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbc(model, details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Step => 0
Model => y ~ 1
SBC => 806.584
Initiating stepwise selection...
Table: Adding New Variables
-------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
liver_test 1 771.875 777.842 616.009 0.45454 0.44405
enzyme_test 1 782.629 788.596 626.220 0.33435 0.32154
pindex 1 794.100 800.067 637.196 0.17680 0.16097
alc_heavy 1 794.301 800.268 637.389 0.17373 0.15784
bcs 1 797.697 803.664 640.655 0.12010 0.10318
alc_mod 1 802.828 808.795 645.601 0.03239 0.01378
gender 1 802.956 808.923 645.725 0.03009 0.01143
age 1 803.834 809.801 646.572 0.01420 -0.00476
-------------------------------------------------------------------------
Step => 1
Added => liver_test
Model => y ~ liver_test
SBC => 777.8423
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_heavy 1 761.439 769.395 605.506 0.56674 0.54975
enzyme_test 1 762.077 770.033 606.090 0.56159 0.54440
pindex 1 770.387 778.343 613.737 0.48866 0.46861
alc_mod 1 771.141 779.097 614.435 0.48147 0.46113
gender 1 773.802 781.758 616.901 0.45528 0.43391
age 1 773.831 781.787 616.928 0.45498 0.43361
bcs 1 773.867 781.823 616.961 0.45462 0.43323
------------------------------------------------------------------------
Step => 2
Added => alc_heavy
Model => y ~ liver_test + alc_heavy
SBC => 769.3953
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 750.509 760.454 595.297 0.65900 0.63854
pindex 1 756.125 766.070 600.225 0.62163 0.59892
bcs 1 763.063 773.008 606.379 0.56975 0.54394
age 1 763.110 773.055 606.421 0.56938 0.54354
alc_mod 1 763.428 773.373 606.704 0.56683 0.54084
gender 1 763.433 773.378 606.709 0.56679 0.54080
------------------------------------------------------------------------
Step => 3
Added => enzyme_test
Model => y ~ liver_test + alc_heavy + enzyme_test
SBC => 760.4538
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
pindex 1 735.715 747.649 582.943 0.75015 0.72975
bcs 1 750.782 762.716 595.377 0.66973 0.64277
alc_mod 1 752.403 764.337 596.743 0.65967 0.63189
age 1 752.416 764.350 596.755 0.65959 0.63180
gender 1 752.509 764.443 596.833 0.65900 0.63116
----------------------------------------------------------------------
Step => 4
Added => pindex
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex
SBC => 747.6485
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
bcs 1 730.620 744.543 579.638 0.78091 0.75808
age 1 737.680 751.603 585.012 0.75030 0.72429
gender 1 737.712 751.635 585.036 0.75016 0.72413
alc_mod 1 737.713 751.636 585.037 0.75015 0.72413
----------------------------------------------------------------------
Step => 5
Added => bcs
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex + bcs
SBC => 744.5433
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
age 1 732.494 748.406 581.938 0.78142 0.75351
gender 1 732.551 748.463 581.978 0.78119 0.75325
alc_mod 1 732.614 748.526 582.023 0.78093 0.75297
----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbc(model, include = "pindex", details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. enzyme_test
3. liver_test
4. age
5. gender
6. alc_mod
7. alc_heavy
Step => 0
Model => y ~ pindex
SBC => 800.0667
Initiating stepwise selection...
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 766.642 774.598 610.282 0.52292 0.50421
liver_test 1 770.387 778.343 613.737 0.48866 0.46861
alc_heavy 1 780.568 788.524 623.203 0.38256 0.35835
bcs 1 789.400 797.356 631.496 0.27285 0.24434
alc_mod 1 792.349 800.305 634.280 0.23204 0.20192
gender 1 795.111 803.067 636.895 0.19174 0.16004
age 1 795.450 803.406 637.216 0.18665 0.15476
------------------------------------------------------------------------
Step => 1
Added => enzyme_test
Model => y ~ pindex + enzyme_test
SBC => 774.5982
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
bcs 1 746.376 756.320 591.702 0.68413 0.66518
alc_heavy 1 748.167 758.112 593.257 0.67347 0.65388
liver_test 1 755.099 765.044 599.321 0.62875 0.60647
alc_mod 1 764.533 774.477 607.692 0.55788 0.53135
age 1 767.697 777.642 610.529 0.53120 0.50307
gender 1 768.479 778.424 611.232 0.52436 0.49582
-----------------------------------------------------------------------
Step => 2
Added => bcs
Model => y ~ pindex + enzyme_test + bcs
SBC => 756.3204
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
alc_heavy 1 730.924 742.858 579.087 0.77136 0.75269
alc_mod 1 744.985 756.919 590.537 0.70335 0.67913
age 1 747.171 759.105 592.354 0.69109 0.66588
liver_test 1 747.181 759.114 592.362 0.69104 0.66582
gender 1 748.330 760.264 593.322 0.68439 0.65863
-----------------------------------------------------------------------
Step => 3
Added => alc_heavy
Model => y ~ pindex + enzyme_test + bcs + alc_heavy
SBC => 742.858
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
liver_test 1 730.620 744.543 579.638 0.78091 0.75808
age 1 732.339 746.262 580.934 0.77382 0.75026
gender 1 732.516 746.439 581.067 0.77308 0.74944
alc_mod 1 732.909 746.832 581.365 0.77142 0.74761
-----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> pindex
=> enzyme_test
=> bcs
=> alc_heavy
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 794.100 800.067 637.196 0.17680 0.16097
1 enzyme_test 766.642 774.598 610.282 0.52292 0.50421
2 bcs 746.376 756.320 591.702 0.68413 0.66518
3 alc_heavy 730.924 742.858 579.087 0.77136 0.75269
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.878 RMSE 188.249
R-Squared 0.771 MSE 39053.801
Adj. R-Squared 0.753 Coef. Var 28.147
Pred R-Squared 0.695 AIC 730.924
MAE 140.619 SBC 742.858
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6455884.265 4 1613971.066 41.327 0.0000
Residual 1913636.272 49 39053.801
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1334.424 180.589 -7.389 0.000 -1697.332 -971.516
pindex 10.131 1.622 0.431 6.246 0.000 6.871 13.390
enzyme_test 11.243 1.308 0.601 8.596 0.000 8.614 13.871
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
output from stepSBIC forward regression is as expected
Code
ols_step_forward_sbic(model)
Output
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbic(model, progress = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Entered:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
No more variables to be added.
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbic(model, details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Step => 0
Model => y ~ 1
SBIC => 649.3977
Initiating stepwise selection...
Table: Adding New Variables
-------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
liver_test 1 771.875 777.842 616.009 0.45454 0.44405
enzyme_test 1 782.629 788.596 626.220 0.33435 0.32154
pindex 1 794.100 800.067 637.196 0.17680 0.16097
alc_heavy 1 794.301 800.268 637.389 0.17373 0.15784
bcs 1 797.697 803.664 640.655 0.12010 0.10318
alc_mod 1 802.828 808.795 645.601 0.03239 0.01378
gender 1 802.956 808.923 645.725 0.03009 0.01143
age 1 803.834 809.801 646.572 0.01420 -0.00476
-------------------------------------------------------------------------
Step => 1
Added => liver_test
Model => y ~ liver_test
SBIC => 618.7808
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_heavy 1 761.439 769.395 605.506 0.56674 0.54975
enzyme_test 1 762.077 770.033 606.090 0.56159 0.54440
pindex 1 770.387 778.343 613.737 0.48866 0.46861
alc_mod 1 771.141 779.097 614.435 0.48147 0.46113
gender 1 773.802 781.758 616.901 0.45528 0.43391
age 1 773.831 781.787 616.928 0.45498 0.43361
bcs 1 773.867 781.823 616.961 0.45462 0.43323
------------------------------------------------------------------------
Step => 2
Added => alc_heavy
Model => y ~ liver_test + alc_heavy
SBIC => 608.54
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 750.509 760.454 595.297 0.65900 0.63854
pindex 1 756.125 766.070 600.225 0.62163 0.59892
bcs 1 763.063 773.008 606.379 0.56975 0.54394
age 1 763.110 773.055 606.421 0.56938 0.54354
alc_mod 1 763.428 773.373 606.704 0.56683 0.54084
gender 1 763.433 773.378 606.709 0.56679 0.54080
------------------------------------------------------------------------
Step => 3
Added => enzyme_test
Model => y ~ liver_test + alc_heavy + enzyme_test
SBIC => 597.8907
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
pindex 1 735.715 747.649 582.943 0.75015 0.72975
bcs 1 750.782 762.716 595.377 0.66973 0.64277
alc_mod 1 752.403 764.337 596.743 0.65967 0.63189
age 1 752.416 764.350 596.755 0.65959 0.63180
gender 1 752.509 764.443 596.833 0.65900 0.63116
----------------------------------------------------------------------
Step => 4
Added => pindex
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex
SBIC => 583.4688
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
bcs 1 730.620 744.543 579.638 0.78091 0.75808
age 1 737.680 751.603 585.012 0.75030 0.72429
gender 1 737.712 751.635 585.036 0.75016 0.72413
alc_mod 1 737.713 751.636 585.037 0.75015 0.72413
----------------------------------------------------------------------
Step => 5
Added => bcs
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex + bcs
SBIC => 578.8438
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
age 1 732.494 748.406 581.938 0.78142 0.75351
gender 1 732.551 748.463 581.978 0.78119 0.75325
alc_mod 1 732.614 748.526 582.023 0.78093 0.75297
----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbic(model, include = "pindex", details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. enzyme_test
3. liver_test
4. age
5. gender
6. alc_mod
7. alc_heavy
Step => 0
Model => y ~ pindex
SBIC => 641.0052
Initiating stepwise selection...
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 766.642 774.598 610.282 0.52292 0.50421
liver_test 1 770.387 778.343 613.737 0.48866 0.46861
alc_heavy 1 780.568 788.524 623.203 0.38256 0.35835
bcs 1 789.400 797.356 631.496 0.27285 0.24434
alc_mod 1 792.349 800.305 634.280 0.23204 0.20192
gender 1 795.111 803.067 636.895 0.19174 0.16004
age 1 795.450 803.406 637.216 0.18665 0.15476
------------------------------------------------------------------------
Step => 1
Added => enzyme_test
Model => y ~ pindex + enzyme_test
SBIC => 613.7429
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
bcs 1 746.376 756.320 591.702 0.68413 0.66518
alc_heavy 1 748.167 758.112 593.257 0.67347 0.65388
liver_test 1 755.099 765.044 599.321 0.62875 0.60647
alc_mod 1 764.533 774.477 607.692 0.55788 0.53135
age 1 767.697 777.642 610.529 0.53120 0.50307
gender 1 768.479 778.424 611.232 0.52436 0.49582
-----------------------------------------------------------------------
Step => 2
Added => bcs
Model => y ~ pindex + enzyme_test + bcs
SBIC => 593.7573
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
alc_heavy 1 730.924 742.858 579.087 0.77136 0.75269
alc_mod 1 744.985 756.919 590.537 0.70335 0.67913
age 1 747.171 759.105 592.354 0.69109 0.66588
liver_test 1 747.181 759.114 592.362 0.69104 0.66582
gender 1 748.330 760.264 593.322 0.68439 0.65863
-----------------------------------------------------------------------
Step => 3
Added => alc_heavy
Model => y ~ pindex + enzyme_test + bcs + alc_heavy
SBIC => 578.6783
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
liver_test 1 730.620 744.543 579.638 0.78091 0.75808
age 1 732.339 746.262 580.934 0.77382 0.75026
gender 1 732.516 746.439 581.067 0.77308 0.74944
alc_mod 1 732.909 746.832 581.365 0.77142 0.74761
-----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> pindex
=> enzyme_test
=> bcs
=> alc_heavy
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 794.100 800.067 637.196 0.17680 0.16097
1 enzyme_test 766.642 774.598 610.282 0.52292 0.50421
2 bcs 746.376 756.320 591.702 0.68413 0.66518
3 alc_heavy 730.924 742.858 579.087 0.77136 0.75269
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.878 RMSE 188.249
R-Squared 0.771 MSE 39053.801
Adj. R-Squared 0.753 Coef. Var 28.147
Pred R-Squared 0.695 AIC 730.924
MAE 140.619 SBC 742.858
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6455884.265 4 1613971.066 41.327 0.0000
Residual 1913636.272 49 39053.801
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1334.424 180.589 -7.389 0.000 -1697.332 -971.516
pindex 10.131 1.622 0.431 6.246 0.000 6.871 13.390
enzyme_test 11.243 1.308 0.601 8.596 0.000 8.614 13.871
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
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output from stepAIC forward regression is as expected
Code
ols_step_forward_aic(model)
Output
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_aic(model, progress = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Entered:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
No more variables to be added.
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_aic(model, details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Step => 0
Model => y ~ 1
AIC => 802.606
Initiating stepwise selection...
Table: Adding New Variables
-------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
liver_test 1 771.875 777.842 616.009 0.45454 0.44405
enzyme_test 1 782.629 788.596 626.220 0.33435 0.32154
pindex 1 794.100 800.067 637.196 0.17680 0.16097
alc_heavy 1 794.301 800.268 637.389 0.17373 0.15784
bcs 1 797.697 803.664 640.655 0.12010 0.10318
alc_mod 1 802.828 808.795 645.601 0.03239 0.01378
gender 1 802.956 808.923 645.725 0.03009 0.01143
age 1 803.834 809.801 646.572 0.01420 -0.00476
-------------------------------------------------------------------------
Step => 1
Added => liver_test
Model => y ~ liver_test
AIC => 771.8753
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_heavy 1 761.439 769.395 605.506 0.56674 0.54975
enzyme_test 1 762.077 770.033 606.090 0.56159 0.54440
pindex 1 770.387 778.343 613.737 0.48866 0.46861
alc_mod 1 771.141 779.097 614.435 0.48147 0.46113
gender 1 773.802 781.758 616.901 0.45528 0.43391
age 1 773.831 781.787 616.928 0.45498 0.43361
bcs 1 773.867 781.823 616.961 0.45462 0.43323
------------------------------------------------------------------------
Step => 2
Added => alc_heavy
Model => y ~ liver_test + alc_heavy
AIC => 761.4394
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 750.509 760.454 595.297 0.65900 0.63854
pindex 1 756.125 766.070 600.225 0.62163 0.59892
bcs 1 763.063 773.008 606.379 0.56975 0.54394
age 1 763.110 773.055 606.421 0.56938 0.54354
alc_mod 1 763.428 773.373 606.704 0.56683 0.54084
gender 1 763.433 773.378 606.709 0.56679 0.54080
------------------------------------------------------------------------
Step => 3
Added => enzyme_test
Model => y ~ liver_test + alc_heavy + enzyme_test
AIC => 750.5089
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
pindex 1 735.715 747.649 582.943 0.75015 0.72975
bcs 1 750.782 762.716 595.377 0.66973 0.64277
alc_mod 1 752.403 764.337 596.743 0.65967 0.63189
age 1 752.416 764.350 596.755 0.65959 0.63180
gender 1 752.509 764.443 596.833 0.65900 0.63116
----------------------------------------------------------------------
Step => 4
Added => pindex
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex
AIC => 735.7146
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
bcs 1 730.620 744.543 579.638 0.78091 0.75808
age 1 737.680 751.603 585.012 0.75030 0.72429
gender 1 737.712 751.635 585.036 0.75016 0.72413
alc_mod 1 737.713 751.636 585.037 0.75015 0.72413
----------------------------------------------------------------------
Step => 5
Added => bcs
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex + bcs
AIC => 730.6204
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
age 1 732.494 748.406 581.938 0.78142 0.75351
gender 1 732.551 748.463 581.978 0.78119 0.75325
alc_mod 1 732.614 748.526 582.023 0.78093 0.75297
----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_aic(model, include = "pindex", details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. enzyme_test
3. liver_test
4. age
5. gender
6. alc_mod
7. alc_heavy
Step => 0
Model => y ~ pindex
AIC => 794.0997
Initiating stepwise selection...
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 766.642 774.598 610.282 0.52292 0.50421
liver_test 1 770.387 778.343 613.737 0.48866 0.46861
alc_heavy 1 780.568 788.524 623.203 0.38256 0.35835
bcs 1 789.400 797.356 631.496 0.27285 0.24434
alc_mod 1 792.349 800.305 634.280 0.23204 0.20192
gender 1 795.111 803.067 636.895 0.19174 0.16004
age 1 795.450 803.406 637.216 0.18665 0.15476
------------------------------------------------------------------------
Step => 1
Added => enzyme_test
Model => y ~ pindex + enzyme_test
AIC => 766.6422
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
bcs 1 746.376 756.320 591.702 0.68413 0.66518
alc_heavy 1 748.167 758.112 593.257 0.67347 0.65388
liver_test 1 755.099 765.044 599.321 0.62875 0.60647
alc_mod 1 764.533 774.477 607.692 0.55788 0.53135
age 1 767.697 777.642 610.529 0.53120 0.50307
gender 1 768.479 778.424 611.232 0.52436 0.49582
-----------------------------------------------------------------------
Step => 2
Added => bcs
Model => y ~ pindex + enzyme_test + bcs
AIC => 746.3755
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
alc_heavy 1 730.924 742.858 579.087 0.77136 0.75269
alc_mod 1 744.985 756.919 590.537 0.70335 0.67913
age 1 747.171 759.105 592.354 0.69109 0.66588
liver_test 1 747.181 759.114 592.362 0.69104 0.66582
gender 1 748.330 760.264 593.322 0.68439 0.65863
-----------------------------------------------------------------------
Step => 3
Added => alc_heavy
Model => y ~ pindex + enzyme_test + bcs + alc_heavy
AIC => 730.9241
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
liver_test 1 730.620 744.543 579.638 0.78091 0.75808
age 1 732.339 746.262 580.934 0.77382 0.75026
gender 1 732.516 746.439 581.067 0.77308 0.74944
alc_mod 1 732.909 746.832 581.365 0.77142 0.74761
-----------------------------------------------------------------------
Step => 4
Added => liver_test
Model => y ~ pindex + enzyme_test + bcs + alc_heavy + liver_test
AIC => 730.6204
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
age 1 732.494 748.406 581.938 0.78142 0.75351
gender 1 732.551 748.463 581.978 0.78119 0.75325
alc_mod 1 732.614 748.526 582.023 0.78093 0.75297
----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> pindex
=> enzyme_test
=> bcs
=> alc_heavy
=> liver_test
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 794.100 800.067 637.196 0.17680 0.16097
1 enzyme_test 766.642 774.598 610.282 0.52292 0.50421
2 bcs 746.376 756.320 591.702 0.68413 0.66518
3 alc_heavy 730.924 742.858 579.087 0.77136 0.75269
4 liver_test 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
------------------------------------------------------------------------------------------------
output from stepSBC forward regression is as expected
Code
ols_step_forward_sbc(model)
Output
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbc(model, progress = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Entered:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
No more variables to be added.
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbc(model, details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Step => 0
Model => y ~ 1
SBC => 806.584
Initiating stepwise selection...
Table: Adding New Variables
-------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
liver_test 1 771.875 777.842 616.009 0.45454 0.44405
enzyme_test 1 782.629 788.596 626.220 0.33435 0.32154
pindex 1 794.100 800.067 637.196 0.17680 0.16097
alc_heavy 1 794.301 800.268 637.389 0.17373 0.15784
bcs 1 797.697 803.664 640.655 0.12010 0.10318
alc_mod 1 802.828 808.795 645.601 0.03239 0.01378
gender 1 802.956 808.923 645.725 0.03009 0.01143
age 1 803.834 809.801 646.572 0.01420 -0.00476
-------------------------------------------------------------------------
Step => 1
Added => liver_test
Model => y ~ liver_test
SBC => 777.8423
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_heavy 1 761.439 769.395 605.506 0.56674 0.54975
enzyme_test 1 762.077 770.033 606.090 0.56159 0.54440
pindex 1 770.387 778.343 613.737 0.48866 0.46861
alc_mod 1 771.141 779.097 614.435 0.48147 0.46113
gender 1 773.802 781.758 616.901 0.45528 0.43391
age 1 773.831 781.787 616.928 0.45498 0.43361
bcs 1 773.867 781.823 616.961 0.45462 0.43323
------------------------------------------------------------------------
Step => 2
Added => alc_heavy
Model => y ~ liver_test + alc_heavy
SBC => 769.3953
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 750.509 760.454 595.297 0.65900 0.63854
pindex 1 756.125 766.070 600.225 0.62163 0.59892
bcs 1 763.063 773.008 606.379 0.56975 0.54394
age 1 763.110 773.055 606.421 0.56938 0.54354
alc_mod 1 763.428 773.373 606.704 0.56683 0.54084
gender 1 763.433 773.378 606.709 0.56679 0.54080
------------------------------------------------------------------------
Step => 3
Added => enzyme_test
Model => y ~ liver_test + alc_heavy + enzyme_test
SBC => 760.4538
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
pindex 1 735.715 747.649 582.943 0.75015 0.72975
bcs 1 750.782 762.716 595.377 0.66973 0.64277
alc_mod 1 752.403 764.337 596.743 0.65967 0.63189
age 1 752.416 764.350 596.755 0.65959 0.63180
gender 1 752.509 764.443 596.833 0.65900 0.63116
----------------------------------------------------------------------
Step => 4
Added => pindex
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex
SBC => 747.6485
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
bcs 1 730.620 744.543 579.638 0.78091 0.75808
age 1 737.680 751.603 585.012 0.75030 0.72429
gender 1 737.712 751.635 585.036 0.75016 0.72413
alc_mod 1 737.713 751.636 585.037 0.75015 0.72413
----------------------------------------------------------------------
Step => 5
Added => bcs
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex + bcs
SBC => 744.5433
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
age 1 732.494 748.406 581.938 0.78142 0.75351
gender 1 732.551 748.463 581.978 0.78119 0.75325
alc_mod 1 732.614 748.526 582.023 0.78093 0.75297
----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbc(model, include = "pindex", details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. enzyme_test
3. liver_test
4. age
5. gender
6. alc_mod
7. alc_heavy
Step => 0
Model => y ~ pindex
SBC => 800.0667
Initiating stepwise selection...
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 766.642 774.598 610.282 0.52292 0.50421
liver_test 1 770.387 778.343 613.737 0.48866 0.46861
alc_heavy 1 780.568 788.524 623.203 0.38256 0.35835
bcs 1 789.400 797.356 631.496 0.27285 0.24434
alc_mod 1 792.349 800.305 634.280 0.23204 0.20192
gender 1 795.111 803.067 636.895 0.19174 0.16004
age 1 795.450 803.406 637.216 0.18665 0.15476
------------------------------------------------------------------------
Step => 1
Added => enzyme_test
Model => y ~ pindex + enzyme_test
SBC => 774.5982
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
bcs 1 746.376 756.320 591.702 0.68413 0.66518
alc_heavy 1 748.167 758.112 593.257 0.67347 0.65388
liver_test 1 755.099 765.044 599.321 0.62875 0.60647
alc_mod 1 764.533 774.477 607.692 0.55788 0.53135
age 1 767.697 777.642 610.529 0.53120 0.50307
gender 1 768.479 778.424 611.232 0.52436 0.49582
-----------------------------------------------------------------------
Step => 2
Added => bcs
Model => y ~ pindex + enzyme_test + bcs
SBC => 756.3204
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
alc_heavy 1 730.924 742.858 579.087 0.77136 0.75269
alc_mod 1 744.985 756.919 590.537 0.70335 0.67913
age 1 747.171 759.105 592.354 0.69109 0.66588
liver_test 1 747.181 759.114 592.362 0.69104 0.66582
gender 1 748.330 760.264 593.322 0.68439 0.65863
-----------------------------------------------------------------------
Step => 3
Added => alc_heavy
Model => y ~ pindex + enzyme_test + bcs + alc_heavy
SBC => 742.858
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
liver_test 1 730.620 744.543 579.638 0.78091 0.75808
age 1 732.339 746.262 580.934 0.77382 0.75026
gender 1 732.516 746.439 581.067 0.77308 0.74944
alc_mod 1 732.909 746.832 581.365 0.77142 0.74761
-----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> pindex
=> enzyme_test
=> bcs
=> alc_heavy
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 794.100 800.067 637.196 0.17680 0.16097
1 enzyme_test 766.642 774.598 610.282 0.52292 0.50421
2 bcs 746.376 756.320 591.702 0.68413 0.66518
3 alc_heavy 730.924 742.858 579.087 0.77136 0.75269
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.878 RMSE 188.249
R-Squared 0.771 MSE 39053.801
Adj. R-Squared 0.753 Coef. Var 28.147
Pred R-Squared 0.695 AIC 730.924
MAE 140.619 SBC 742.858
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6455884.265 4 1613971.066 41.327 0.0000
Residual 1913636.272 49 39053.801
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1334.424 180.589 -7.389 0.000 -1697.332 -971.516
pindex 10.131 1.622 0.431 6.246 0.000 6.871 13.390
enzyme_test 11.243 1.308 0.601 8.596 0.000 8.614 13.871
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
output from stepSBIC forward regression is as expected
Code
ols_step_forward_sbic(model)
Output
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbic(model, progress = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Entered:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
No more variables to be added.
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbic(model, details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Step => 0
Model => y ~ 1
SBIC => 649.3977
Initiating stepwise selection...
Table: Adding New Variables
-------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
liver_test 1 771.875 777.842 616.009 0.45454 0.44405
enzyme_test 1 782.629 788.596 626.220 0.33435 0.32154
pindex 1 794.100 800.067 637.196 0.17680 0.16097
alc_heavy 1 794.301 800.268 637.389 0.17373 0.15784
bcs 1 797.697 803.664 640.655 0.12010 0.10318
alc_mod 1 802.828 808.795 645.601 0.03239 0.01378
gender 1 802.956 808.923 645.725 0.03009 0.01143
age 1 803.834 809.801 646.572 0.01420 -0.00476
-------------------------------------------------------------------------
Step => 1
Added => liver_test
Model => y ~ liver_test
SBIC => 618.7808
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_heavy 1 761.439 769.395 605.506 0.56674 0.54975
enzyme_test 1 762.077 770.033 606.090 0.56159 0.54440
pindex 1 770.387 778.343 613.737 0.48866 0.46861
alc_mod 1 771.141 779.097 614.435 0.48147 0.46113
gender 1 773.802 781.758 616.901 0.45528 0.43391
age 1 773.831 781.787 616.928 0.45498 0.43361
bcs 1 773.867 781.823 616.961 0.45462 0.43323
------------------------------------------------------------------------
Step => 2
Added => alc_heavy
Model => y ~ liver_test + alc_heavy
SBIC => 608.54
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 750.509 760.454 595.297 0.65900 0.63854
pindex 1 756.125 766.070 600.225 0.62163 0.59892
bcs 1 763.063 773.008 606.379 0.56975 0.54394
age 1 763.110 773.055 606.421 0.56938 0.54354
alc_mod 1 763.428 773.373 606.704 0.56683 0.54084
gender 1 763.433 773.378 606.709 0.56679 0.54080
------------------------------------------------------------------------
Step => 3
Added => enzyme_test
Model => y ~ liver_test + alc_heavy + enzyme_test
SBIC => 597.8907
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
pindex 1 735.715 747.649 582.943 0.75015 0.72975
bcs 1 750.782 762.716 595.377 0.66973 0.64277
alc_mod 1 752.403 764.337 596.743 0.65967 0.63189
age 1 752.416 764.350 596.755 0.65959 0.63180
gender 1 752.509 764.443 596.833 0.65900 0.63116
----------------------------------------------------------------------
Step => 4
Added => pindex
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex
SBIC => 583.4688
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
bcs 1 730.620 744.543 579.638 0.78091 0.75808
age 1 737.680 751.603 585.012 0.75030 0.72429
gender 1 737.712 751.635 585.036 0.75016 0.72413
alc_mod 1 737.713 751.636 585.037 0.75015 0.72413
----------------------------------------------------------------------
Step => 5
Added => bcs
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex + bcs
SBIC => 578.8438
Table: Adding New Variables
----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
----------------------------------------------------------------------
age 1 732.494 748.406 581.938 0.78142 0.75351
gender 1 732.551 748.463 581.978 0.78119 0.75325
alc_mod 1 732.614 748.526 582.023 0.78093 0.75297
----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> liver_test
=> alc_heavy
=> enzyme_test
=> pindex
=> bcs
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 liver_test 771.875 777.842 616.009 0.45454 0.44405
2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975
3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854
4 pindex 735.715 747.649 582.943 0.75015 0.72975
5 bcs 730.620 744.543 579.638 0.78091 0.75808
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
------------------------------------------------------------------------------------------------
Code
ols_step_forward_sbic(model, include = "pindex", details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. enzyme_test
3. liver_test
4. age
5. gender
6. alc_mod
7. alc_heavy
Step => 0
Model => y ~ pindex
SBIC => 641.0052
Initiating stepwise selection...
Table: Adding New Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
enzyme_test 1 766.642 774.598 610.282 0.52292 0.50421
liver_test 1 770.387 778.343 613.737 0.48866 0.46861
alc_heavy 1 780.568 788.524 623.203 0.38256 0.35835
bcs 1 789.400 797.356 631.496 0.27285 0.24434
alc_mod 1 792.349 800.305 634.280 0.23204 0.20192
gender 1 795.111 803.067 636.895 0.19174 0.16004
age 1 795.450 803.406 637.216 0.18665 0.15476
------------------------------------------------------------------------
Step => 1
Added => enzyme_test
Model => y ~ pindex + enzyme_test
SBIC => 613.7429
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
bcs 1 746.376 756.320 591.702 0.68413 0.66518
alc_heavy 1 748.167 758.112 593.257 0.67347 0.65388
liver_test 1 755.099 765.044 599.321 0.62875 0.60647
alc_mod 1 764.533 774.477 607.692 0.55788 0.53135
age 1 767.697 777.642 610.529 0.53120 0.50307
gender 1 768.479 778.424 611.232 0.52436 0.49582
-----------------------------------------------------------------------
Step => 2
Added => bcs
Model => y ~ pindex + enzyme_test + bcs
SBIC => 593.7573
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
alc_heavy 1 730.924 742.858 579.087 0.77136 0.75269
alc_mod 1 744.985 756.919 590.537 0.70335 0.67913
age 1 747.171 759.105 592.354 0.69109 0.66588
liver_test 1 747.181 759.114 592.362 0.69104 0.66582
gender 1 748.330 760.264 593.322 0.68439 0.65863
-----------------------------------------------------------------------
Step => 3
Added => alc_heavy
Model => y ~ pindex + enzyme_test + bcs + alc_heavy
SBIC => 578.6783
Table: Adding New Variables
-----------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------
liver_test 1 730.620 744.543 579.638 0.78091 0.75808
age 1 732.339 746.262 580.934 0.77382 0.75026
gender 1 732.516 746.439 581.067 0.77308 0.74944
alc_mod 1 732.909 746.832 581.365 0.77142 0.74761
-----------------------------------------------------------------------
No more variables to be added.
Variables Selected:
=> pindex
=> enzyme_test
=> bcs
=> alc_heavy
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 794.100 800.067 637.196 0.17680 0.16097
1 enzyme_test 766.642 774.598 610.282 0.52292 0.50421
2 bcs 746.376 756.320 591.702 0.68413 0.66518
3 alc_heavy 730.924 742.858 579.087 0.77136 0.75269
--------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.878 RMSE 188.249
R-Squared 0.771 MSE 39053.801
Adj. R-Squared 0.753 Coef. Var 28.147
Pred R-Squared 0.695 AIC 730.924
MAE 140.619 SBC 742.858
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6455884.265 4 1613971.066 41.327 0.0000
Residual 1913636.272 49 39053.801
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1334.424 180.589 -7.389 0.000 -1697.332 -971.516
pindex 10.131 1.622 0.431 6.246 0.000 6.871 13.390
enzyme_test 11.243 1.308 0.601 8.596 0.000 8.614 13.871
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
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