# 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 ------------------------------------------------------------------------------------------------