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tests/testthat/_snaps/step-backward-output.md
In olsrr: Tools for Building OLS Regression Models
output from stepwise backward regression is as expected
Code
ols_step_backward_p(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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
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_p(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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
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_p(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
R2 => 0.782
Initiating stepwise selection...
Step => 1
Removed => alc_mod
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_heavy
R2 => 0.78177
Step => 2
Removed => gender
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + alc_heavy
R2 => 0.78142
Step => 3
Removed => age
Model => y ~ bcs + pindex + enzyme_test + liver_test + alc_heavy
R2 => 0.78091
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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
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 stepwise backward hierarchical regression
Code
ols_step_backward_p(model, hierarchical = TRUE)
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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
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
------------------------------------------------------------------------------------------------
Code
ols_step_backward_p(model, hierarchical = TRUE, progress = TRUE)
Output
Backward Elimination Method
---------------------------
Candidate Terms:
1. bcs
2. alc_heavy
3. pindex
4. enzyme_test
5. liver_test
6. age
7. gender
8. alc_mod
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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
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
------------------------------------------------------------------------------------------------
Code
ols_step_backward_p(model, hierarchical = TRUE, details = TRUE)
Output
Backward Elimination 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 => 0.782
Initiating stepwise selection...
Significance Table
-----------------------
Predictor Pr(>|t|)
-----------------------
bcs 0.01426
alc_heavy 0.00047
pindex 2e-05
enzyme_test 0.00000
liver_test 0.26811
age 0.72123
gender 0.78727
alc_mod 0.90601
-----------------------
Step => 1
Removed => alc_mod
Model => y ~ bcs + alc_heavy + pindex + enzyme_test + liver_test + age + gender
R2 => 0.78177
Significance Table
-----------------------
Predictor Pr(>|t|)
-----------------------
bcs 0.01331
alc_heavy 9e-05
pindex 1e-05
enzyme_test 0.00000
liver_test 0.25860
age 0.72755
gender 0.78613
-----------------------
Step => 2
Removed => gender
Model => y ~ bcs + alc_heavy + pindex + enzyme_test + liver_test + age
R2 => 0.78142
Significance Table
-----------------------
Predictor Pr(>|t|)
-----------------------
bcs 0.01285
alc_heavy 8e-05
pindex 1e-05
enzyme_test 0.00000
liver_test 0.20745
age 0.74164
-----------------------
Step => 3
Removed => age
Model => y ~ bcs + alc_heavy + pindex + enzyme_test + liver_test
R2 => 0.78091
Significance Table
-----------------------
Predictor Pr(>|t|)
-----------------------
bcs 0.01248
alc_heavy 5e-05
pindex 1e-05
enzyme_test 0.00000
liver_test 0.15457
-----------------------
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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
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
------------------------------------------------------------------------------------------------
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output from stepwise backward regression is as expected
Code
ols_step_backward_p(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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
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_p(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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
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_p(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
R2 => 0.782
Initiating stepwise selection...
Step => 1
Removed => alc_mod
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + gender + alc_heavy
R2 => 0.78177
Step => 2
Removed => gender
Model => y ~ bcs + pindex + enzyme_test + liver_test + age + alc_heavy
R2 => 0.78142
Step => 3
Removed => age
Model => y ~ bcs + pindex + enzyme_test + liver_test + alc_heavy
R2 => 0.78091
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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
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 stepwise backward hierarchical regression
Code
ols_step_backward_p(model, hierarchical = TRUE)
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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
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
------------------------------------------------------------------------------------------------
Code
ols_step_backward_p(model, hierarchical = TRUE, progress = TRUE)
Output
Backward Elimination Method
---------------------------
Candidate Terms:
1. bcs
2. alc_heavy
3. pindex
4. enzyme_test
5. liver_test
6. age
7. gender
8. alc_mod
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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
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
------------------------------------------------------------------------------------------------
Code
ols_step_backward_p(model, hierarchical = TRUE, details = TRUE)
Output
Backward Elimination 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 => 0.782
Initiating stepwise selection...
Significance Table
-----------------------
Predictor Pr(>|t|)
-----------------------
bcs 0.01426
alc_heavy 0.00047
pindex 2e-05
enzyme_test 0.00000
liver_test 0.26811
age 0.72123
gender 0.78727
alc_mod 0.90601
-----------------------
Step => 1
Removed => alc_mod
Model => y ~ bcs + alc_heavy + pindex + enzyme_test + liver_test + age + gender
R2 => 0.78177
Significance Table
-----------------------
Predictor Pr(>|t|)
-----------------------
bcs 0.01331
alc_heavy 9e-05
pindex 1e-05
enzyme_test 0.00000
liver_test 0.25860
age 0.72755
gender 0.78613
-----------------------
Step => 2
Removed => gender
Model => y ~ bcs + alc_heavy + pindex + enzyme_test + liver_test + age
R2 => 0.78142
Significance Table
-----------------------
Predictor Pr(>|t|)
-----------------------
bcs 0.01285
alc_heavy 8e-05
pindex 1e-05
enzyme_test 0.00000
liver_test 0.20745
age 0.74164
-----------------------
Step => 3
Removed => age
Model => y ~ bcs + alc_heavy + pindex + enzyme_test + liver_test
R2 => 0.78091
Significance Table
-----------------------
Predictor Pr(>|t|)
-----------------------
bcs 0.01248
alc_heavy 5e-05
pindex 1e-05
enzyme_test 0.00000
liver_test 0.15457
-----------------------
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 734.407 752.308 584.276 0.78177 0.74856
2 gender 732.494 748.406 581.938 0.78142 0.75351
3 age 730.620 744.543 579.638 0.78091 0.75808
-------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-------------------------------------------------------------------
R 0.884 RMSE 184.276
R-Squared 0.781 MSE 38202.426
Adj. R-Squared 0.758 Coef. Var 27.839
Pred R-Squared 0.700 AIC 730.620
MAE 137.656 SBC 744.543
-------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
-----------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
-----------------------------------------------------------------------
Regression 6535804.090 5 1307160.818 34.217 0.0000
Residual 1833716.447 48 38202.426
Total 8369520.537 53
-----------------------------------------------------------------------
Parameter Estimates
------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
------------------------------------------------------------------------------------------------
(Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
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
------------------------------------------------------------------------------------------------
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