tests/testthat/_snaps/step-forward-output.md
In rsquaredacademy/olsrr: Tools for Building OLS Regression Models
output from stepwise forward regression is as expected
Code
ols_step_forward_p(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 33957.712
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_p(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 33957.712
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_p(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
R2 => 0
Initiating stepwise selection...
Selection Metrics Table
-----------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
-----------------------------------------------------------------
liver_test 0.00000 0.455 0.444 771.875
enzyme_test 0.00000 0.334 0.322 782.629
pindex 0.00155 0.177 0.161 794.100
alc_heavy 0.00172 0.174 0.158 794.301
bcs 0.01025 0.120 0.103 797.697
alc_mod 0.19286 0.032 0.014 802.828
gender 0.20972 0.030 0.011 802.956
age 0.39073 0.014 -0.005 803.834
-----------------------------------------------------------------
Step => 1
Selected => liver_test
Model => y ~ liver_test
R2 => 0.455
Selection Metrics Table
-----------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
-----------------------------------------------------------------
alc_heavy 0.00065 0.567 0.550 761.439
enzyme_test 0.00089 0.562 0.544 762.077
pindex 0.07087 0.489 0.469 770.387
alc_mod 0.10979 0.481 0.461 771.141
gender 0.79395 0.455 0.434 773.802
age 0.83908 0.455 0.434 773.831
bcs 0.93062 0.455 0.433 773.867
-----------------------------------------------------------------
Step => 2
Selected => alc_heavy
Model => y ~ liver_test + alc_heavy
R2 => 0.567
Selection Metrics Table
-----------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
-----------------------------------------------------------------
enzyme_test 0.00057 0.659 0.639 750.509
pindex 0.00961 0.622 0.599 756.125
bcs 0.55687 0.570 0.544 763.063
age 0.58269 0.569 0.544 763.110
alc_mod 0.91757 0.567 0.541 763.428
gender 0.93799 0.567 0.541 763.433
-----------------------------------------------------------------
Step => 3
Selected => enzyme_test
Model => y ~ liver_test + alc_heavy + enzyme_test
R2 => 0.659
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
pindex 1e-04 0.750 0.730 735.715
bcs 0.21294 0.670 0.643 750.782
alc_mod 0.75743 0.660 0.632 752.403
age 0.77290 0.660 0.632 752.416
gender 0.99197 0.659 0.631 752.509
---------------------------------------------------------------
Step => 4
Selected => pindex
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex
R2 => 0.75
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
bcs 0.01248 0.781 0.758 730.620
age 0.86220 0.750 0.724 737.680
gender 0.96390 0.750 0.724 737.712
alc_mod 0.97040 0.750 0.724 737.713
---------------------------------------------------------------
Step => 5
Selected => bcs
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex + bcs
R2 => 0.781
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
age 0.74164 0.781 0.754 732.494
gender 0.80666 0.781 0.753 732.551
alc_mod 0.94086 0.781 0.753 732.614
---------------------------------------------------------------
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 33957.712
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
------------------------------------------------------------------------------------------------
output from stepwise forward hierarchical regression
Code
ols_step_forward_p(model, 0.1, hierarchical = TRUE)
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 bcs 797.697 803.664 640.655 0.12010 0.10318
2 alc_heavy 791.701 799.657 633.668 0.24119 0.21144
3 pindex 778.574 788.519 620.390 0.42659 0.39218
4 enzyme_test 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 35437.709
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
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
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
------------------------------------------------------------------------------------------------
Code
ols_step_forward_p(model, 0.1, hierarchical = TRUE, progress = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. alc_heavy
3. pindex
4. enzyme_test
5. liver_test
6. age
7. gender
8. alc_mod
Variables Entered:
=> bcs
=> alc_heavy
=> pindex
=> enzyme_test
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 bcs 797.697 803.664 640.655 0.12010 0.10318
2 alc_heavy 791.701 799.657 633.668 0.24119 0.21144
3 pindex 778.574 788.519 620.390 0.42659 0.39218
4 enzyme_test 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 35437.709
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
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
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
------------------------------------------------------------------------------------------------
Code
ols_step_forward_p(model, 0.1, hierarchical = TRUE, details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. alc_heavy
3. pindex
4. enzyme_test
5. liver_test
6. age
7. gender
8. alc_mod
Step => 0
Model => y ~ 1
R2 => 0
Initiating stepwise selection...
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
bcs 0.01025 0.120 0.103 797.697
---------------------------------------------------------------
Step => 1
Selected => bcs
Model => y ~ bcs
R2 => 0.12
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
alc_heavy 0.00624 0.241 0.211 791.701
bcs 0.01025 0.120 0.103 797.697
---------------------------------------------------------------
Step => 2
Selected => alc_heavy
Model => y ~ bcs + alc_heavy
R2 => 0.241
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
pindex 2e-04 0.427 0.392 778.574
alc_heavy 0.00624 0.241 0.211 791.701
bcs 0.01025 0.120 0.103 797.697
---------------------------------------------------------------
Step => 3
Selected => pindex
Model => y ~ bcs + alc_heavy + pindex
R2 => 0.427
Selection Metrics Table
-----------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
-----------------------------------------------------------------
enzyme_test 0.00000 0.771 0.753 730.924
pindex 2e-04 0.427 0.392 778.574
alc_heavy 0.00624 0.241 0.211 791.701
bcs 0.01025 0.120 0.103 797.697
-----------------------------------------------------------------
Step => 4
Selected => enzyme_test
Model => y ~ bcs + alc_heavy + pindex + enzyme_test
R2 => 0.771
Selection Metrics Table
-----------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
-----------------------------------------------------------------
enzyme_test 0.00000 0.771 0.753 730.924
pindex 2e-04 0.427 0.392 778.574
alc_heavy 0.00624 0.241 0.211 791.701
bcs 0.01025 0.120 0.103 797.697
liver_test 0.15457 0.781 0.758 730.620
-----------------------------------------------------------------
Variables Selected:
=> bcs
=> alc_heavy
=> pindex
=> enzyme_test
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 bcs 797.697 803.664 640.655 0.12010 0.10318
2 alc_heavy 791.701 799.657 633.668 0.24119 0.21144
3 pindex 778.574 788.519 620.390 0.42659 0.39218
4 enzyme_test 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 35437.709
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
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
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
------------------------------------------------------------------------------------------------
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output from stepwise forward regression is as expected
Code
ols_step_forward_p(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 33957.712
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_p(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 33957.712
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_p(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
R2 => 0
Initiating stepwise selection...
Selection Metrics Table
-----------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
-----------------------------------------------------------------
liver_test 0.00000 0.455 0.444 771.875
enzyme_test 0.00000 0.334 0.322 782.629
pindex 0.00155 0.177 0.161 794.100
alc_heavy 0.00172 0.174 0.158 794.301
bcs 0.01025 0.120 0.103 797.697
alc_mod 0.19286 0.032 0.014 802.828
gender 0.20972 0.030 0.011 802.956
age 0.39073 0.014 -0.005 803.834
-----------------------------------------------------------------
Step => 1
Selected => liver_test
Model => y ~ liver_test
R2 => 0.455
Selection Metrics Table
-----------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
-----------------------------------------------------------------
alc_heavy 0.00065 0.567 0.550 761.439
enzyme_test 0.00089 0.562 0.544 762.077
pindex 0.07087 0.489 0.469 770.387
alc_mod 0.10979 0.481 0.461 771.141
gender 0.79395 0.455 0.434 773.802
age 0.83908 0.455 0.434 773.831
bcs 0.93062 0.455 0.433 773.867
-----------------------------------------------------------------
Step => 2
Selected => alc_heavy
Model => y ~ liver_test + alc_heavy
R2 => 0.567
Selection Metrics Table
-----------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
-----------------------------------------------------------------
enzyme_test 0.00057 0.659 0.639 750.509
pindex 0.00961 0.622 0.599 756.125
bcs 0.55687 0.570 0.544 763.063
age 0.58269 0.569 0.544 763.110
alc_mod 0.91757 0.567 0.541 763.428
gender 0.93799 0.567 0.541 763.433
-----------------------------------------------------------------
Step => 3
Selected => enzyme_test
Model => y ~ liver_test + alc_heavy + enzyme_test
R2 => 0.659
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
pindex 1e-04 0.750 0.730 735.715
bcs 0.21294 0.670 0.643 750.782
alc_mod 0.75743 0.660 0.632 752.403
age 0.77290 0.660 0.632 752.416
gender 0.99197 0.659 0.631 752.509
---------------------------------------------------------------
Step => 4
Selected => pindex
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex
R2 => 0.75
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
bcs 0.01248 0.781 0.758 730.620
age 0.86220 0.750 0.724 737.680
gender 0.96390 0.750 0.724 737.712
alc_mod 0.97040 0.750 0.724 737.713
---------------------------------------------------------------
Step => 5
Selected => bcs
Model => y ~ liver_test + alc_heavy + enzyme_test + pindex + bcs
R2 => 0.781
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
age 0.74164 0.781 0.754 732.494
gender 0.80666 0.781 0.753 732.551
alc_mod 0.94086 0.781 0.753 732.614
---------------------------------------------------------------
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 33957.712
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
------------------------------------------------------------------------------------------------
output from stepwise forward hierarchical regression
Code
ols_step_forward_p(model, 0.1, hierarchical = TRUE)
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 bcs 797.697 803.664 640.655 0.12010 0.10318
2 alc_heavy 791.701 799.657 633.668 0.24119 0.21144
3 pindex 778.574 788.519 620.390 0.42659 0.39218
4 enzyme_test 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 35437.709
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
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
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
------------------------------------------------------------------------------------------------
Code
ols_step_forward_p(model, 0.1, hierarchical = TRUE, progress = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. alc_heavy
3. pindex
4. enzyme_test
5. liver_test
6. age
7. gender
8. alc_mod
Variables Entered:
=> bcs
=> alc_heavy
=> pindex
=> enzyme_test
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 bcs 797.697 803.664 640.655 0.12010 0.10318
2 alc_heavy 791.701 799.657 633.668 0.24119 0.21144
3 pindex 778.574 788.519 620.390 0.42659 0.39218
4 enzyme_test 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 35437.709
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
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
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
------------------------------------------------------------------------------------------------
Code
ols_step_forward_p(model, 0.1, hierarchical = TRUE, details = TRUE)
Output
Forward Selection Method
------------------------
Candidate Terms:
1. bcs
2. alc_heavy
3. pindex
4. enzyme_test
5. liver_test
6. age
7. gender
8. alc_mod
Step => 0
Model => y ~ 1
R2 => 0
Initiating stepwise selection...
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
bcs 0.01025 0.120 0.103 797.697
---------------------------------------------------------------
Step => 1
Selected => bcs
Model => y ~ bcs
R2 => 0.12
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
alc_heavy 0.00624 0.241 0.211 791.701
bcs 0.01025 0.120 0.103 797.697
---------------------------------------------------------------
Step => 2
Selected => alc_heavy
Model => y ~ bcs + alc_heavy
R2 => 0.241
Selection Metrics Table
---------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
---------------------------------------------------------------
pindex 2e-04 0.427 0.392 778.574
alc_heavy 0.00624 0.241 0.211 791.701
bcs 0.01025 0.120 0.103 797.697
---------------------------------------------------------------
Step => 3
Selected => pindex
Model => y ~ bcs + alc_heavy + pindex
R2 => 0.427
Selection Metrics Table
-----------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
-----------------------------------------------------------------
enzyme_test 0.00000 0.771 0.753 730.924
pindex 2e-04 0.427 0.392 778.574
alc_heavy 0.00624 0.241 0.211 791.701
bcs 0.01025 0.120 0.103 797.697
-----------------------------------------------------------------
Step => 4
Selected => enzyme_test
Model => y ~ bcs + alc_heavy + pindex + enzyme_test
R2 => 0.771
Selection Metrics Table
-----------------------------------------------------------------
Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC
-----------------------------------------------------------------
enzyme_test 0.00000 0.771 0.753 730.924
pindex 2e-04 0.427 0.392 778.574
alc_heavy 0.00624 0.241 0.211 791.701
bcs 0.01025 0.120 0.103 797.697
liver_test 0.15457 0.781 0.758 730.620
-----------------------------------------------------------------
Variables Selected:
=> bcs
=> alc_heavy
=> pindex
=> enzyme_test
Stepwise Summary
--------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
--------------------------------------------------------------------------
0 Base Model 802.606 806.584 646.794 0.00000 0.00000
1 bcs 797.697 803.664 640.655 0.12010 0.10318
2 alc_heavy 791.701 799.657 633.668 0.24119 0.21144
3 pindex 778.574 788.519 620.390 0.42659 0.39218
4 enzyme_test 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 35437.709
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
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
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
------------------------------------------------------------------------------------------------
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