# output from stepwise regression is as expected Code ols_step_both_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 38202.426 Adj. R-Squared 0.758 Coef. Var 27.839 Pred R-Squared 0.700 AIC 730.620 MAE 137.656 SBC 744.543 ------------------------------------------------------------------- RMSE: Root Mean Square Error MSE: Mean Square Error MAE: Mean Absolute Error AIC: Akaike Information Criteria SBC: Schwarz Bayesian Criteria ANOVA ----------------------------------------------------------------------- Sum of Squares DF Mean Square F Sig. ----------------------------------------------------------------------- Regression 6535804.090 5 1307160.818 34.217 0.0000 Residual 1833716.447 48 38202.426 Total 8369520.537 53 ----------------------------------------------------------------------- Parameter Estimates ------------------------------------------------------------------------------------------------ model Beta Std. Error Std. Beta t Sig lower upper ------------------------------------------------------------------------------------------------ (Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746 liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779 alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878 enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077 pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559 bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230 ------------------------------------------------------------------------------------------------ --- Code ols_step_both_p(model, progress = TRUE) Output Stepwise 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 Added/Removed: => liver_test added => alc_heavy added => enzyme_test added => pindex added => bcs added No more variables to be added or removed. Stepwise Summary ------------------------------------------------------------------------------ Step Variable AIC SBC SBIC R2 Adj. R2 ------------------------------------------------------------------------------ 0 Base Model 802.606 806.584 646.794 0.00000 0.00000 1 liver_test (+) 771.875 777.842 616.009 0.45454 0.44405 2 alc_heavy (+) 761.439 769.395 605.506 0.56674 0.54975 3 enzyme_test (+) 750.509 760.454 595.297 0.65900 0.63854 4 pindex (+) 735.715 747.649 582.943 0.75015 0.72975 5 bcs (+) 730.620 744.543 579.638 0.78091 0.75808 ------------------------------------------------------------------------------ Final Model Output ------------------ Model Summary ------------------------------------------------------------------- R 0.884 RMSE 184.276 R-Squared 0.781 MSE 38202.426 Adj. R-Squared 0.758 Coef. Var 27.839 Pred R-Squared 0.700 AIC 730.620 MAE 137.656 SBC 744.543 ------------------------------------------------------------------- RMSE: Root Mean Square Error MSE: Mean Square Error MAE: Mean Absolute Error AIC: Akaike Information Criteria SBC: Schwarz Bayesian Criteria ANOVA ----------------------------------------------------------------------- Sum of Squares DF Mean Square F Sig. ----------------------------------------------------------------------- Regression 6535804.090 5 1307160.818 34.217 0.0000 Residual 1833716.447 48 38202.426 Total 8369520.537 53 ----------------------------------------------------------------------- Parameter Estimates ------------------------------------------------------------------------------------------------ model Beta Std. Error Std. Beta t Sig lower upper ------------------------------------------------------------------------------------------------ (Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746 liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779 alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878 enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077 pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559 bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230 ------------------------------------------------------------------------------------------------ --- Code ols_step_both_p(model, details = TRUE) Output Stepwise 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... Step => 1 Selected => liver_test Model => y ~ liver_test R2 => 0.455 Step => 2 Selected => alc_heavy Model => y ~ liver_test + alc_heavy R2 => 0.567 Step => 3 Selected => enzyme_test Model => y ~ liver_test + alc_heavy + enzyme_test R2 => 0.659 Step => 4 Selected => pindex Model => y ~ liver_test + alc_heavy + enzyme_test + pindex R2 => 0.75 Step => 5 Selected => bcs Model => y ~ liver_test + alc_heavy + enzyme_test + pindex + bcs R2 => 0.781 No more variables to be added or removed. Stepwise Summary ------------------------------------------------------------------------------ Step Variable AIC SBC SBIC R2 Adj. R2 ------------------------------------------------------------------------------ 0 Base Model 802.606 806.584 646.794 0.00000 0.00000 1 liver_test (+) 771.875 777.842 616.009 0.45454 0.44405 2 alc_heavy (+) 761.439 769.395 605.506 0.56674 0.54975 3 enzyme_test (+) 750.509 760.454 595.297 0.65900 0.63854 4 pindex (+) 735.715 747.649 582.943 0.75015 0.72975 5 bcs (+) 730.620 744.543 579.638 0.78091 0.75808 ------------------------------------------------------------------------------ Final Model Output ------------------ Model Summary ------------------------------------------------------------------- R 0.884 RMSE 184.276 R-Squared 0.781 MSE 38202.426 Adj. R-Squared 0.758 Coef. Var 27.839 Pred R-Squared 0.700 AIC 730.620 MAE 137.656 SBC 744.543 ------------------------------------------------------------------- RMSE: Root Mean Square Error MSE: Mean Square Error MAE: Mean Absolute Error AIC: Akaike Information Criteria SBC: Schwarz Bayesian Criteria ANOVA ----------------------------------------------------------------------- Sum of Squares DF Mean Square F Sig. ----------------------------------------------------------------------- Regression 6535804.090 5 1307160.818 34.217 0.0000 Residual 1833716.447 48 38202.426 Total 8369520.537 53 ----------------------------------------------------------------------- Parameter Estimates ------------------------------------------------------------------------------------------------ model Beta Std. Error Std. Beta t Sig lower upper ------------------------------------------------------------------------------------------------ (Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746 liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779 alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878 enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077 pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559 bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230 ------------------------------------------------------------------------------------------------