Nothing
tests/testthat/_snaps/stepaic-b-output.md
In olsrr: Tools for Building OLS Regression Models
output from stepAIC backward regression is as expected
Code
ols_step_backward_aic(model)
Output
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 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
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
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
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
------------------------------------------------------------------------------------------------
Code
ols_step_backward_aic(model, progress = TRUE)
Output
Backward Elimination Method
---------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Removed:
=> alc_mod
=> gender
=> age
No more variables to be removed.
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 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
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
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
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
------------------------------------------------------------------------------------------------
Code
ols_step_backward_aic(model, details = TRUE)
Output
Backward Elimination 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 ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_mod + alc_heavy
AIC => 736.3899
Initiating stepwise selection...
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_mod 1 734.407 752.308 584.276 0.78177 0.74856
gender 1 734.478 752.379 584.323 0.78148 0.74823
age 1 734.544 752.445 584.367 0.78121 0.74792
liver_test 1 735.878 753.779 585.255 0.77574 0.74162
bcs 1 741.677 759.577 589.203 0.75032 0.71233
alc_heavy 1 749.210 767.111 594.541 0.71294 0.66926
pindex 1 756.624 774.525 600.014 0.67070 0.62059
enzyme_test 1 763.557 781.458 605.318 0.62559 0.56861
------------------------------------------------------------------------
Step => 1
Removed => alc_mod
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_heavy
AIC => 734.4068
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
gender 1 732.494 748.406 581.938 0.78142 0.75351
age 1 732.551 748.463 581.978 0.78119 0.75325
liver_test 1 733.921 749.833 582.951 0.77556 0.74691
bcs 1 739.677 755.589 587.106 0.75032 0.71845
alc_heavy 1 750.486 766.398 595.217 0.69499 0.65605
pindex 1 754.759 770.671 598.530 0.66987 0.62773
enzyme_test 1 761.595 777.507 603.950 0.62532 0.57749
------------------------------------------------------------------------
Step => 2
Removed => gender
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + alc_heavy
AIC => 732.4942
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
age 1 730.620 744.543 579.638 0.78091 0.75808
liver_test 1 732.339 746.262 580.934 0.77382 0.75026
bcs 1 737.680 751.603 585.012 0.75030 0.72429
alc_heavy 1 748.486 762.409 593.500 0.69499 0.66322
pindex 1 752.777 766.700 596.959 0.66976 0.63536
enzyme_test 1 759.596 773.518 602.553 0.62532 0.58629
------------------------------------------------------------------------
Step => 3
Removed => age
Model => y ~ bcs + pindex + enzyme_test + liver_test + alc_heavy
AIC => 730.6204
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
liver_test 1 730.924 742.858 579.087 0.77136 0.75269
bcs 1 735.715 747.649 582.943 0.75015 0.72975
alc_heavy 1 747.181 759.114 592.362 0.69104 0.66582
pindex 1 750.782 762.716 595.377 0.66973 0.64277
enzyme_test 1 757.971 769.905 601.477 0.62270 0.59190
------------------------------------------------------------------------
No more variables to be removed.
Variables Removed:
=> alc_mod
=> gender
=> age
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 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
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
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
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
------------------------------------------------------------------------------------------------
output from stepSBC backward regression is as expected
Code
ols_step_backward_sbc(model)
Output
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
Code
ols_step_backward_sbc(model, progress = TRUE)
Output
Backward Elimination Method
---------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Removed:
=> alc_mod
=> gender
=> age
=> liver_test
No more variables to be removed.
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
Code
ols_step_backward_sbc(model, details = TRUE)
Output
Backward Elimination 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 ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_mod + alc_heavy
SBC => 756.2797
Initiating stepwise selection...
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_mod 1 734.407 752.308 584.276 0.78177 0.74856
gender 1 734.478 752.379 584.323 0.78148 0.74823
age 1 734.544 752.445 584.367 0.78121 0.74792
liver_test 1 735.878 753.779 585.255 0.77574 0.74162
bcs 1 741.677 759.577 589.203 0.75032 0.71233
alc_heavy 1 749.210 767.111 594.541 0.71294 0.66926
pindex 1 756.624 774.525 600.014 0.67070 0.62059
enzyme_test 1 763.557 781.458 605.318 0.62559 0.56861
------------------------------------------------------------------------
Step => 1
Removed => alc_mod
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_heavy
SBC => 752.3077
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
gender 1 732.494 748.406 581.938 0.78142 0.75351
age 1 732.551 748.463 581.978 0.78119 0.75325
liver_test 1 733.921 749.833 582.951 0.77556 0.74691
bcs 1 739.677 755.589 587.106 0.75032 0.71845
alc_heavy 1 750.486 766.398 595.217 0.69499 0.65605
pindex 1 754.759 770.671 598.530 0.66987 0.62773
enzyme_test 1 761.595 777.507 603.950 0.62532 0.57749
------------------------------------------------------------------------
Step => 2
Removed => gender
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + alc_heavy
SBC => 748.4061
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
age 1 730.620 744.543 579.638 0.78091 0.75808
liver_test 1 732.339 746.262 580.934 0.77382 0.75026
bcs 1 737.680 751.603 585.012 0.75030 0.72429
alc_heavy 1 748.486 762.409 593.500 0.69499 0.66322
pindex 1 752.777 766.700 596.959 0.66976 0.63536
enzyme_test 1 759.596 773.518 602.553 0.62532 0.58629
------------------------------------------------------------------------
Step => 3
Removed => age
Model => y ~ bcs + pindex + enzyme_test + liver_test + alc_heavy
SBC => 744.5433
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
liver_test 1 730.924 742.858 579.087 0.77136 0.75269
bcs 1 735.715 747.649 582.943 0.75015 0.72975
alc_heavy 1 747.181 759.114 592.362 0.69104 0.66582
pindex 1 750.782 762.716 595.377 0.66973 0.64277
enzyme_test 1 757.971 769.905 601.477 0.62270 0.59190
------------------------------------------------------------------------
Step => 4
Removed => liver_test
Model => y ~ bcs + pindex + enzyme_test + alc_heavy
SBC => 742.858
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_heavy 1 746.376 756.320 591.702 0.68413 0.66518
bcs 1 748.167 758.112 593.257 0.67347 0.65388
pindex 1 760.551 770.496 604.143 0.58930 0.56466
enzyme_test 1 778.574 788.519 620.390 0.42659 0.39218
------------------------------------------------------------------------
No more variables to be removed.
Variables Removed:
=> alc_mod
=> gender
=> age
=> liver_test
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
output from stepSBIC backward regression is as expected
Code
ols_step_backward_sbic(model)
Output
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
Code
ols_step_backward_sbic(model, progress = TRUE)
Output
Backward Elimination Method
---------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Removed:
=> alc_mod
=> gender
=> age
=> liver_test
No more variables to be removed.
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
Code
ols_step_backward_sbic(model, details = TRUE)
Output
Backward Elimination 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 ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_mod + alc_heavy
SBIC => 586.6645
Initiating stepwise selection...
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_mod 1 734.407 752.308 584.276 0.78177 0.74856
gender 1 734.478 752.379 584.323 0.78148 0.74823
age 1 734.544 752.445 584.367 0.78121 0.74792
liver_test 1 735.878 753.779 585.255 0.77574 0.74162
bcs 1 741.677 759.577 589.203 0.75032 0.71233
alc_heavy 1 749.210 767.111 594.541 0.71294 0.66926
pindex 1 756.624 774.525 600.014 0.67070 0.62059
enzyme_test 1 763.557 781.458 605.318 0.62559 0.56861
------------------------------------------------------------------------
Step => 1
Removed => alc_mod
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_heavy
SBIC => 584.2758
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
gender 1 732.494 748.406 581.938 0.78142 0.75351
age 1 732.551 748.463 581.978 0.78119 0.75325
liver_test 1 733.921 749.833 582.951 0.77556 0.74691
bcs 1 739.677 755.589 587.106 0.75032 0.71845
alc_heavy 1 750.486 766.398 595.217 0.69499 0.65605
pindex 1 754.759 770.671 598.530 0.66987 0.62773
enzyme_test 1 761.595 777.507 603.950 0.62532 0.57749
------------------------------------------------------------------------
Step => 2
Removed => gender
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + alc_heavy
SBIC => 581.9383
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
age 1 730.620 744.543 579.638 0.78091 0.75808
liver_test 1 732.339 746.262 580.934 0.77382 0.75026
bcs 1 737.680 751.603 585.012 0.75030 0.72429
alc_heavy 1 748.486 762.409 593.500 0.69499 0.66322
pindex 1 752.777 766.700 596.959 0.66976 0.63536
enzyme_test 1 759.596 773.518 602.553 0.62532 0.58629
------------------------------------------------------------------------
Step => 3
Removed => age
Model => y ~ bcs + pindex + enzyme_test + liver_test + alc_heavy
SBIC => 579.6377
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
liver_test 1 730.924 742.858 579.087 0.77136 0.75269
bcs 1 735.715 747.649 582.943 0.75015 0.72975
alc_heavy 1 747.181 759.114 592.362 0.69104 0.66582
pindex 1 750.782 762.716 595.377 0.66973 0.64277
enzyme_test 1 757.971 769.905 601.477 0.62270 0.59190
------------------------------------------------------------------------
Step => 4
Removed => liver_test
Model => y ~ bcs + pindex + enzyme_test + alc_heavy
SBIC => 579.0865
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_heavy 1 746.376 756.320 591.702 0.68413 0.66518
bcs 1 748.167 758.112 593.257 0.67347 0.65388
pindex 1 760.551 770.496 604.143 0.58930 0.56466
enzyme_test 1 778.574 788.519 620.390 0.42659 0.39218
------------------------------------------------------------------------
No more variables to be removed.
Variables Removed:
=> alc_mod
=> gender
=> age
=> liver_test
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
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output from stepAIC backward regression is as expected
Code
ols_step_backward_aic(model)
Output
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 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
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
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
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
------------------------------------------------------------------------------------------------
Code
ols_step_backward_aic(model, progress = TRUE)
Output
Backward Elimination Method
---------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Removed:
=> alc_mod
=> gender
=> age
No more variables to be removed.
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 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
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
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
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
------------------------------------------------------------------------------------------------
Code
ols_step_backward_aic(model, details = TRUE)
Output
Backward Elimination 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 ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_mod + alc_heavy
AIC => 736.3899
Initiating stepwise selection...
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_mod 1 734.407 752.308 584.276 0.78177 0.74856
gender 1 734.478 752.379 584.323 0.78148 0.74823
age 1 734.544 752.445 584.367 0.78121 0.74792
liver_test 1 735.878 753.779 585.255 0.77574 0.74162
bcs 1 741.677 759.577 589.203 0.75032 0.71233
alc_heavy 1 749.210 767.111 594.541 0.71294 0.66926
pindex 1 756.624 774.525 600.014 0.67070 0.62059
enzyme_test 1 763.557 781.458 605.318 0.62559 0.56861
------------------------------------------------------------------------
Step => 1
Removed => alc_mod
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_heavy
AIC => 734.4068
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
gender 1 732.494 748.406 581.938 0.78142 0.75351
age 1 732.551 748.463 581.978 0.78119 0.75325
liver_test 1 733.921 749.833 582.951 0.77556 0.74691
bcs 1 739.677 755.589 587.106 0.75032 0.71845
alc_heavy 1 750.486 766.398 595.217 0.69499 0.65605
pindex 1 754.759 770.671 598.530 0.66987 0.62773
enzyme_test 1 761.595 777.507 603.950 0.62532 0.57749
------------------------------------------------------------------------
Step => 2
Removed => gender
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + alc_heavy
AIC => 732.4942
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
age 1 730.620 744.543 579.638 0.78091 0.75808
liver_test 1 732.339 746.262 580.934 0.77382 0.75026
bcs 1 737.680 751.603 585.012 0.75030 0.72429
alc_heavy 1 748.486 762.409 593.500 0.69499 0.66322
pindex 1 752.777 766.700 596.959 0.66976 0.63536
enzyme_test 1 759.596 773.518 602.553 0.62532 0.58629
------------------------------------------------------------------------
Step => 3
Removed => age
Model => y ~ bcs + pindex + enzyme_test + liver_test + alc_heavy
AIC => 730.6204
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
liver_test 1 730.924 742.858 579.087 0.77136 0.75269
bcs 1 735.715 747.649 582.943 0.75015 0.72975
alc_heavy 1 747.181 759.114 592.362 0.69104 0.66582
pindex 1 750.782 762.716 595.377 0.66973 0.64277
enzyme_test 1 757.971 769.905 601.477 0.62270 0.59190
------------------------------------------------------------------------
No more variables to be removed.
Variables Removed:
=> alc_mod
=> gender
=> age
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 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
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
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
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
------------------------------------------------------------------------------------------------
output from stepSBC backward regression is as expected
Code
ols_step_backward_sbc(model)
Output
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
Code
ols_step_backward_sbc(model, progress = TRUE)
Output
Backward Elimination Method
---------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Removed:
=> alc_mod
=> gender
=> age
=> liver_test
No more variables to be removed.
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
Code
ols_step_backward_sbc(model, details = TRUE)
Output
Backward Elimination 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 ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_mod + alc_heavy
SBC => 756.2797
Initiating stepwise selection...
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_mod 1 734.407 752.308 584.276 0.78177 0.74856
gender 1 734.478 752.379 584.323 0.78148 0.74823
age 1 734.544 752.445 584.367 0.78121 0.74792
liver_test 1 735.878 753.779 585.255 0.77574 0.74162
bcs 1 741.677 759.577 589.203 0.75032 0.71233
alc_heavy 1 749.210 767.111 594.541 0.71294 0.66926
pindex 1 756.624 774.525 600.014 0.67070 0.62059
enzyme_test 1 763.557 781.458 605.318 0.62559 0.56861
------------------------------------------------------------------------
Step => 1
Removed => alc_mod
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_heavy
SBC => 752.3077
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
gender 1 732.494 748.406 581.938 0.78142 0.75351
age 1 732.551 748.463 581.978 0.78119 0.75325
liver_test 1 733.921 749.833 582.951 0.77556 0.74691
bcs 1 739.677 755.589 587.106 0.75032 0.71845
alc_heavy 1 750.486 766.398 595.217 0.69499 0.65605
pindex 1 754.759 770.671 598.530 0.66987 0.62773
enzyme_test 1 761.595 777.507 603.950 0.62532 0.57749
------------------------------------------------------------------------
Step => 2
Removed => gender
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + alc_heavy
SBC => 748.4061
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
age 1 730.620 744.543 579.638 0.78091 0.75808
liver_test 1 732.339 746.262 580.934 0.77382 0.75026
bcs 1 737.680 751.603 585.012 0.75030 0.72429
alc_heavy 1 748.486 762.409 593.500 0.69499 0.66322
pindex 1 752.777 766.700 596.959 0.66976 0.63536
enzyme_test 1 759.596 773.518 602.553 0.62532 0.58629
------------------------------------------------------------------------
Step => 3
Removed => age
Model => y ~ bcs + pindex + enzyme_test + liver_test + alc_heavy
SBC => 744.5433
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
liver_test 1 730.924 742.858 579.087 0.77136 0.75269
bcs 1 735.715 747.649 582.943 0.75015 0.72975
alc_heavy 1 747.181 759.114 592.362 0.69104 0.66582
pindex 1 750.782 762.716 595.377 0.66973 0.64277
enzyme_test 1 757.971 769.905 601.477 0.62270 0.59190
------------------------------------------------------------------------
Step => 4
Removed => liver_test
Model => y ~ bcs + pindex + enzyme_test + alc_heavy
SBC => 742.858
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_heavy 1 746.376 756.320 591.702 0.68413 0.66518
bcs 1 748.167 758.112 593.257 0.67347 0.65388
pindex 1 760.551 770.496 604.143 0.58930 0.56466
enzyme_test 1 778.574 788.519 620.390 0.42659 0.39218
------------------------------------------------------------------------
No more variables to be removed.
Variables Removed:
=> alc_mod
=> gender
=> age
=> liver_test
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
output from stepSBIC backward regression is as expected
Code
ols_step_backward_sbic(model)
Output
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
Code
ols_step_backward_sbic(model, progress = TRUE)
Output
Backward Elimination Method
---------------------------
Candidate Terms:
1. bcs
2. pindex
3. enzyme_test
4. liver_test
5. age
6. gender
7. alc_mod
8. alc_heavy
Variables Removed:
=> alc_mod
=> gender
=> age
=> liver_test
No more variables to be removed.
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
Code
ols_step_backward_sbic(model, details = TRUE)
Output
Backward Elimination 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 ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_mod + alc_heavy
SBIC => 586.6645
Initiating stepwise selection...
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_mod 1 734.407 752.308 584.276 0.78177 0.74856
gender 1 734.478 752.379 584.323 0.78148 0.74823
age 1 734.544 752.445 584.367 0.78121 0.74792
liver_test 1 735.878 753.779 585.255 0.77574 0.74162
bcs 1 741.677 759.577 589.203 0.75032 0.71233
alc_heavy 1 749.210 767.111 594.541 0.71294 0.66926
pindex 1 756.624 774.525 600.014 0.67070 0.62059
enzyme_test 1 763.557 781.458 605.318 0.62559 0.56861
------------------------------------------------------------------------
Step => 1
Removed => alc_mod
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_heavy
SBIC => 584.2758
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
gender 1 732.494 748.406 581.938 0.78142 0.75351
age 1 732.551 748.463 581.978 0.78119 0.75325
liver_test 1 733.921 749.833 582.951 0.77556 0.74691
bcs 1 739.677 755.589 587.106 0.75032 0.71845
alc_heavy 1 750.486 766.398 595.217 0.69499 0.65605
pindex 1 754.759 770.671 598.530 0.66987 0.62773
enzyme_test 1 761.595 777.507 603.950 0.62532 0.57749
------------------------------------------------------------------------
Step => 2
Removed => gender
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + alc_heavy
SBIC => 581.9383
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
age 1 730.620 744.543 579.638 0.78091 0.75808
liver_test 1 732.339 746.262 580.934 0.77382 0.75026
bcs 1 737.680 751.603 585.012 0.75030 0.72429
alc_heavy 1 748.486 762.409 593.500 0.69499 0.66322
pindex 1 752.777 766.700 596.959 0.66976 0.63536
enzyme_test 1 759.596 773.518 602.553 0.62532 0.58629
------------------------------------------------------------------------
Step => 3
Removed => age
Model => y ~ bcs + pindex + enzyme_test + liver_test + alc_heavy
SBIC => 579.6377
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
liver_test 1 730.924 742.858 579.087 0.77136 0.75269
bcs 1 735.715 747.649 582.943 0.75015 0.72975
alc_heavy 1 747.181 759.114 592.362 0.69104 0.66582
pindex 1 750.782 762.716 595.377 0.66973 0.64277
enzyme_test 1 757.971 769.905 601.477 0.62270 0.59190
------------------------------------------------------------------------
Step => 4
Removed => liver_test
Model => y ~ bcs + pindex + enzyme_test + alc_heavy
SBIC => 579.0865
Table: Removing Existing Variables
------------------------------------------------------------------------
Predictor DF AIC SBC SBIC R2 Adj. R2
------------------------------------------------------------------------
alc_heavy 1 746.376 756.320 591.702 0.68413 0.66518
bcs 1 748.167 758.112 593.257 0.67347 0.65388
pindex 1 760.551 770.496 604.143 0.58930 0.56466
enzyme_test 1 778.574 788.519 620.390 0.42659 0.39218
------------------------------------------------------------------------
No more variables to be removed.
Variables Removed:
=> alc_mod
=> gender
=> age
=> liver_test
Stepwise Summary
-------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-------------------------------------------------------------------------
0 Full Model 736.390 756.280 586.665 0.78184 0.74305
1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
2 gender 732.494 748.406 581.290 0.78142 0.75351
3 age 730.620 744.543 578.844 0.78091 0.75808
4 liver_test 730.924 742.858 578.678 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
bcs 81.439 17.781 0.329 4.580 0.000 45.706 117.171
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
alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152
------------------------------------------------------------------------------------------------
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