# output from stepwise forward regression is as expected Code ols_step_forward_p(model) Output Stepwise Summary -------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------- 0 Base Model 802.606 806.584 646.794 0.00000 0.00000 1 liver_test 771.875 777.842 616.009 0.45454 0.44405 2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975 3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854 4 pindex 735.715 747.649 582.943 0.75015 0.72975 5 bcs 730.620 744.543 579.638 0.78091 0.75808 -------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ------------------------------------------------------------------- R 0.884 RMSE 184.276 R-Squared 0.781 MSE 38202.426 Adj. R-Squared 0.758 Coef. Var 27.839 Pred R-Squared 0.700 AIC 730.620 MAE 137.656 SBC 744.543 ------------------------------------------------------------------- RMSE: Root Mean Square Error MSE: Mean Square Error MAE: Mean Absolute Error AIC: Akaike Information Criteria SBC: Schwarz Bayesian Criteria ANOVA ----------------------------------------------------------------------- Sum of Squares DF Mean Square F Sig. ----------------------------------------------------------------------- Regression 6535804.090 5 1307160.818 34.217 0.0000 Residual 1833716.447 48 38202.426 Total 8369520.537 53 ----------------------------------------------------------------------- Parameter Estimates ------------------------------------------------------------------------------------------------ model Beta Std. Error Std. Beta t Sig lower upper ------------------------------------------------------------------------------------------------ (Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746 liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779 alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878 enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077 pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559 bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230 ------------------------------------------------------------------------------------------------ --- Code ols_step_forward_p(model, progress = TRUE) Output Forward Selection Method ------------------------ Candidate Terms: 1. bcs 2. pindex 3. enzyme_test 4. liver_test 5. age 6. gender 7. alc_mod 8. alc_heavy Variables Entered: => liver_test => alc_heavy => enzyme_test => pindex => bcs No more variables to be added. Stepwise Summary -------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------- 0 Base Model 802.606 806.584 646.794 0.00000 0.00000 1 liver_test 771.875 777.842 616.009 0.45454 0.44405 2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975 3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854 4 pindex 735.715 747.649 582.943 0.75015 0.72975 5 bcs 730.620 744.543 579.638 0.78091 0.75808 -------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ------------------------------------------------------------------- R 0.884 RMSE 184.276 R-Squared 0.781 MSE 38202.426 Adj. R-Squared 0.758 Coef. Var 27.839 Pred R-Squared 0.700 AIC 730.620 MAE 137.656 SBC 744.543 ------------------------------------------------------------------- RMSE: Root Mean Square Error MSE: Mean Square Error MAE: Mean Absolute Error AIC: Akaike Information Criteria SBC: Schwarz Bayesian Criteria ANOVA ----------------------------------------------------------------------- Sum of Squares DF Mean Square F Sig. ----------------------------------------------------------------------- Regression 6535804.090 5 1307160.818 34.217 0.0000 Residual 1833716.447 48 38202.426 Total 8369520.537 53 ----------------------------------------------------------------------- Parameter Estimates ------------------------------------------------------------------------------------------------ model Beta Std. Error Std. Beta t Sig lower upper ------------------------------------------------------------------------------------------------ (Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746 liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779 alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878 enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077 pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559 bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230 ------------------------------------------------------------------------------------------------ --- Code ols_step_forward_p(model, details = TRUE) Output Forward Selection Method ------------------------ Candidate Terms: 1. bcs 2. pindex 3. enzyme_test 4. liver_test 5. age 6. gender 7. alc_mod 8. alc_heavy Step => 0 Model => y ~ 1 R2 => 0 Initiating stepwise selection... Selection Metrics Table ----------------------------------------------------------------- Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC ----------------------------------------------------------------- liver_test 0.00000 0.455 0.444 771.875 enzyme_test 0.00000 0.334 0.322 782.629 pindex 0.00155 0.177 0.161 794.100 alc_heavy 0.00172 0.174 0.158 794.301 bcs 0.01025 0.120 0.103 797.697 alc_mod 0.19286 0.032 0.014 802.828 gender 0.20972 0.030 0.011 802.956 age 0.39073 0.014 -0.005 803.834 ----------------------------------------------------------------- Step => 1 Selected => liver_test Model => y ~ liver_test R2 => 0.455 Selection Metrics Table ----------------------------------------------------------------- Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC ----------------------------------------------------------------- alc_heavy 0.00065 0.567 0.550 761.439 enzyme_test 0.00089 0.562 0.544 762.077 pindex 0.07087 0.489 0.469 770.387 alc_mod 0.10979 0.481 0.461 771.141 gender 0.79395 0.455 0.434 773.802 age 0.83908 0.455 0.434 773.831 bcs 0.93062 0.455 0.433 773.867 ----------------------------------------------------------------- Step => 2 Selected => alc_heavy Model => y ~ liver_test + alc_heavy R2 => 0.567 Selection Metrics Table ----------------------------------------------------------------- Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC ----------------------------------------------------------------- enzyme_test 0.00057 0.659 0.639 750.509 pindex 0.00961 0.622 0.599 756.125 bcs 0.55687 0.570 0.544 763.063 age 0.58269 0.569 0.544 763.110 alc_mod 0.91757 0.567 0.541 763.428 gender 0.93799 0.567 0.541 763.433 ----------------------------------------------------------------- Step => 3 Selected => enzyme_test Model => y ~ liver_test + alc_heavy + enzyme_test R2 => 0.659 Selection Metrics Table --------------------------------------------------------------- Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC --------------------------------------------------------------- pindex 1e-04 0.750 0.730 735.715 bcs 0.21294 0.670 0.643 750.782 alc_mod 0.75743 0.660 0.632 752.403 age 0.77290 0.660 0.632 752.416 gender 0.99197 0.659 0.631 752.509 --------------------------------------------------------------- Step => 4 Selected => pindex Model => y ~ liver_test + alc_heavy + enzyme_test + pindex R2 => 0.75 Selection Metrics Table --------------------------------------------------------------- Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC --------------------------------------------------------------- bcs 0.01248 0.781 0.758 730.620 age 0.86220 0.750 0.724 737.680 gender 0.96390 0.750 0.724 737.712 alc_mod 0.97040 0.750 0.724 737.713 --------------------------------------------------------------- Step => 5 Selected => bcs Model => y ~ liver_test + alc_heavy + enzyme_test + pindex + bcs R2 => 0.781 Selection Metrics Table --------------------------------------------------------------- Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC --------------------------------------------------------------- age 0.74164 0.781 0.754 732.494 gender 0.80666 0.781 0.753 732.551 alc_mod 0.94086 0.781 0.753 732.614 --------------------------------------------------------------- No more variables to be added. Variables Selected: => liver_test => alc_heavy => enzyme_test => pindex => bcs Stepwise Summary -------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------- 0 Base Model 802.606 806.584 646.794 0.00000 0.00000 1 liver_test 771.875 777.842 616.009 0.45454 0.44405 2 alc_heavy 761.439 769.395 605.506 0.56674 0.54975 3 enzyme_test 750.509 760.454 595.297 0.65900 0.63854 4 pindex 735.715 747.649 582.943 0.75015 0.72975 5 bcs 730.620 744.543 579.638 0.78091 0.75808 -------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ------------------------------------------------------------------- R 0.884 RMSE 184.276 R-Squared 0.781 MSE 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 ------------------------------------------------------------------------------------------------ # output from stepwise forward hierarchical regression Code ols_step_forward_p(model, 0.1, hierarchical = TRUE) Output Stepwise Summary -------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------- 0 Base Model 802.606 806.584 646.794 0.00000 0.00000 1 bcs 797.697 803.664 640.655 0.12010 0.10318 2 alc_heavy 791.701 799.657 633.668 0.24119 0.21144 3 pindex 778.574 788.519 620.390 0.42659 0.39218 4 enzyme_test 730.924 742.858 579.087 0.77136 0.75269 -------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ------------------------------------------------------------------- R 0.878 RMSE 188.249 R-Squared 0.771 MSE 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 alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152 pindex 10.131 1.622 0.431 6.246 0.000 6.871 13.390 enzyme_test 11.243 1.308 0.601 8.596 0.000 8.614 13.871 ------------------------------------------------------------------------------------------------ --- Code ols_step_forward_p(model, 0.1, hierarchical = TRUE, progress = TRUE) Output Forward Selection Method ------------------------ Candidate Terms: 1. bcs 2. alc_heavy 3. pindex 4. enzyme_test 5. liver_test 6. age 7. gender 8. alc_mod Variables Entered: => bcs => alc_heavy => pindex => enzyme_test No more variables to be added. Stepwise Summary -------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------- 0 Base Model 802.606 806.584 646.794 0.00000 0.00000 1 bcs 797.697 803.664 640.655 0.12010 0.10318 2 alc_heavy 791.701 799.657 633.668 0.24119 0.21144 3 pindex 778.574 788.519 620.390 0.42659 0.39218 4 enzyme_test 730.924 742.858 579.087 0.77136 0.75269 -------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ------------------------------------------------------------------- R 0.878 RMSE 188.249 R-Squared 0.771 MSE 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 alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152 pindex 10.131 1.622 0.431 6.246 0.000 6.871 13.390 enzyme_test 11.243 1.308 0.601 8.596 0.000 8.614 13.871 ------------------------------------------------------------------------------------------------ --- Code ols_step_forward_p(model, 0.1, hierarchical = TRUE, details = TRUE) Output Forward Selection Method ------------------------ Candidate Terms: 1. bcs 2. alc_heavy 3. pindex 4. enzyme_test 5. liver_test 6. age 7. gender 8. alc_mod Step => 0 Model => y ~ 1 R2 => 0 Initiating stepwise selection... Selection Metrics Table --------------------------------------------------------------- Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC --------------------------------------------------------------- bcs 0.01025 0.120 0.103 797.697 --------------------------------------------------------------- Step => 1 Selected => bcs Model => y ~ bcs R2 => 0.12 Selection Metrics Table --------------------------------------------------------------- Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC --------------------------------------------------------------- alc_heavy 0.00624 0.241 0.211 791.701 bcs 0.01025 0.120 0.103 797.697 --------------------------------------------------------------- Step => 2 Selected => alc_heavy Model => y ~ bcs + alc_heavy R2 => 0.241 Selection Metrics Table --------------------------------------------------------------- Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC --------------------------------------------------------------- pindex 2e-04 0.427 0.392 778.574 alc_heavy 0.00624 0.241 0.211 791.701 bcs 0.01025 0.120 0.103 797.697 --------------------------------------------------------------- Step => 3 Selected => pindex Model => y ~ bcs + alc_heavy + pindex R2 => 0.427 Selection Metrics Table ----------------------------------------------------------------- Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC ----------------------------------------------------------------- enzyme_test 0.00000 0.771 0.753 730.924 pindex 2e-04 0.427 0.392 778.574 alc_heavy 0.00624 0.241 0.211 791.701 bcs 0.01025 0.120 0.103 797.697 ----------------------------------------------------------------- Step => 4 Selected => enzyme_test Model => y ~ bcs + alc_heavy + pindex + enzyme_test R2 => 0.771 Selection Metrics Table ----------------------------------------------------------------- Predictor Pr(>|t|) R-Squared Adj. R-Squared AIC ----------------------------------------------------------------- enzyme_test 0.00000 0.771 0.753 730.924 pindex 2e-04 0.427 0.392 778.574 alc_heavy 0.00624 0.241 0.211 791.701 bcs 0.01025 0.120 0.103 797.697 liver_test 0.15457 0.781 0.758 730.620 ----------------------------------------------------------------- Variables Selected: => bcs => alc_heavy => pindex => enzyme_test Stepwise Summary -------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------- 0 Base Model 802.606 806.584 646.794 0.00000 0.00000 1 bcs 797.697 803.664 640.655 0.12010 0.10318 2 alc_heavy 791.701 799.657 633.668 0.24119 0.21144 3 pindex 778.574 788.519 620.390 0.42659 0.39218 4 enzyme_test 730.924 742.858 579.087 0.77136 0.75269 -------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ------------------------------------------------------------------- R 0.878 RMSE 188.249 R-Squared 0.771 MSE 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 alc_heavy 312.777 72.341 0.309 4.324 0.000 167.402 458.152 pindex 10.131 1.622 0.431 6.246 0.000 6.871 13.390 enzyme_test 11.243 1.308 0.601 8.596 0.000 8.614 13.871 ------------------------------------------------------------------------------------------------