# output from stepAIC both direction regression is as expected when adding and removing variables Code ols_step_both_aic(model, progress = TRUE) Output Stepwise Selection Method ------------------------- Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Variables Added/Removed: => x6 added => x1 added => x3 added => x2 added => x6 removed => x4 added No more variables to be added or removed. Stepwise Summary -------------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------------- 0 Base Model 56988.482 57004.289 228.318 0.00000 0.00000 1 x6 (+) 33473.297 33497.007 -23285.069 0.69145 0.69143 2 x1 (+) 32931.758 32963.372 -23826.833 0.69972 0.69969 3 x3 (+) 31912.722 31952.239 -24845.827 0.71466 0.71462 4 x2 (+) 29304.296 29351.717 -27453.243 0.74958 0.74953 5 x6 (-) 29302.317 29341.835 -27455.223 0.74958 0.74954 6 x4 (+) 29300.814 29348.235 -27456.724 0.74962 0.74957 -------------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ----------------------------------------------------------------- R 0.866 RMSE 0.503 R-Squared 0.750 MSE 0.253 Adj. R-Squared 0.750 Coef. Var 6430.859 Pred R-Squared 0.749 AIC 29300.814 MAE 0.402 SBC 29348.235 ----------------------------------------------------------------- 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 15163.528 4 3790.882 14966.061 0.0000 Residual 5064.705 19995 0.253 Total 20228.233 19999 --------------------------------------------------------------------------- Parameter Estimates --------------------------------------------------------------------------------------- model Beta Std. Error Std. Beta t Sig lower upper --------------------------------------------------------------------------------------- (Intercept) -0.005 0.004 -1.496 0.135 -0.012 0.002 x1 0.255 0.003 0.362 84.140 0.000 0.249 0.261 x3 0.253 0.003 0.356 82.604 0.000 0.247 0.259 x2 0.249 0.003 0.346 80.544 0.000 0.243 0.255 x4 -0.007 0.004 -0.007 -1.872 0.061 -0.014 0.000 --------------------------------------------------------------------------------------- --- Code ols_step_both_aic(model, details = TRUE) Output Stepwise Selection Method ------------------------- Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Step => 0 Model => y ~ 1 AIC => 56988.48 Initiating stepwise selection... Table: Adding New Variables ------------------------------------------------------------------------------ Predictor DF AIC SBC SBIC R2 Adj. R2 ------------------------------------------------------------------------------ x1 1 43073.160 43096.870 -13686.868 0.50136 0.50133 x2 1 43561.884 43585.595 -13198.216 0.48902 0.48900 x3 1 43267.194 43290.904 -13492.863 0.49650 0.49647 x4 1 56989.595 57013.305 227.932 4e-05 -1e-05 x5 1 56990.439 57014.149 228.776 0.00000 -5e-05 x6 1 33473.297 33497.007 -23285.069 0.69145 0.69143 ------------------------------------------------------------------------------ Step => 1 Added => x6 Model => y ~ x6 AIC => 33473.3 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x1 1 32931.758 32963.372 -23826.833 0.69972 0.69969 x2 1 33033.295 33064.909 -23725.325 0.69819 0.69816 x3 1 32959.771 32991.385 -23798.829 0.69930 0.69927 x4 1 33470.717 33502.331 -23288.023 0.69152 0.69149 x5 1 33475.275 33506.889 -23283.467 0.69145 0.69142 ----------------------------------------------------------------------------- Step => 2 Added => x1 Model => y ~ x6 + x1 AIC => 32931.76 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 43073.160 43096.870 -13686.868 0.50136 0.50133 x1 1 33473.297 33497.007 -23285.069 0.69145 0.69143 ----------------------------------------------------------------------------- Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x2 1 32025.492 32065.010 -24733.099 0.71305 0.71301 x3 1 31912.722 31952.239 -24845.827 0.71466 0.71462 x4 1 32928.035 32967.552 -23830.887 0.69980 0.69976 x5 1 32933.735 32973.252 -23825.189 0.69972 0.69967 ----------------------------------------------------------------------------- Step => 3 Added => x3 Model => y ~ x6 + x1 + x3 AIC => 31912.72 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 34923.269 34954.883 -21835.862 0.66828 0.66825 x1 1 32959.771 32991.385 -23798.829 0.69930 0.69927 x3 1 32931.758 32963.372 -23826.833 0.69972 0.69969 ----------------------------------------------------------------------------- Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x2 1 29304.296 29351.717 -27453.243 0.74958 0.74953 x4 1 31908.533 31955.954 -24850.258 0.71475 0.71470 x5 1 31914.523 31961.944 -24844.270 0.71467 0.71461 ----------------------------------------------------------------------------- Step => 4 Added => x2 Model => y ~ x6 + x1 + x3 + x2 AIC => 29304.3 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 29302.317 29341.835 -27455.223 0.74958 0.74954 x1 1 32080.424 32119.941 -24678.188 0.71226 0.71222 x3 1 32025.492 32065.010 -24733.099 0.71305 0.71301 x2 1 31912.722 31952.239 -24845.827 0.71466 0.71462 ----------------------------------------------------------------------------- Step => 5 Removed => x6 Model => y ~ x1 + x3 + x2 AIC => 29302.32 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x4 1 29300.814 29348.235 -27456.724 0.74962 0.74957 x5 1 29304.253 29351.673 -27453.287 0.74958 0.74953 ----------------------------------------------------------------------------- Step => 6 Added => x4 Model => y ~ x1 + x3 + x2 + x4 AIC => 29300.81 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x1 1 35361.098 35400.615 -21398.670 0.66097 0.66092 x3 1 35170.915 35210.432 -21588.789 0.66418 0.66413 x2 1 34918.668 34958.185 -21840.951 0.66839 0.66834 x4 1 29302.317 29341.835 -27455.223 0.74958 0.74954 ----------------------------------------------------------------------------- Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x5 1 29302.751 29358.075 -27454.786 0.74962 0.74956 ----------------------------------------------------------------------------- No more variables to be added or removed. Variables Selected: => x1 => x3 => x2 => x4 Stepwise Summary -------------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------------- 0 Base Model 56988.482 57004.289 228.318 0.00000 0.00000 1 x6 (+) 33473.297 33497.007 -23285.069 0.69145 0.69143 2 x1 (+) 32931.758 32963.372 -23826.833 0.69972 0.69969 3 x3 (+) 31912.722 31952.239 -24845.827 0.71466 0.71462 4 x2 (+) 29304.296 29351.717 -27453.243 0.74958 0.74953 5 x6 (-) 29302.317 29341.835 -27455.223 0.74958 0.74954 6 x4 (+) 29300.814 29348.235 -27456.724 0.74962 0.74957 -------------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ----------------------------------------------------------------- R 0.866 RMSE 0.503 R-Squared 0.750 MSE 0.253 Adj. R-Squared 0.750 Coef. Var 6430.859 Pred R-Squared 0.749 AIC 29300.814 MAE 0.402 SBC 29348.235 ----------------------------------------------------------------- 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 15163.528 4 3790.882 14966.061 0.0000 Residual 5064.705 19995 0.253 Total 20228.233 19999 --------------------------------------------------------------------------- Parameter Estimates --------------------------------------------------------------------------------------- model Beta Std. Error Std. Beta t Sig lower upper --------------------------------------------------------------------------------------- (Intercept) -0.005 0.004 -1.496 0.135 -0.012 0.002 x1 0.255 0.003 0.362 84.140 0.000 0.249 0.261 x3 0.253 0.003 0.356 82.604 0.000 0.247 0.259 x2 0.249 0.003 0.346 80.544 0.000 0.243 0.255 x4 -0.007 0.004 -0.007 -1.872 0.061 -0.014 0.000 --------------------------------------------------------------------------------------- # output from stepSBC both direction regression is as expected when adding and removing variables Code ols_step_both_sbc(model, progress = TRUE) Output Stepwise Selection Method ------------------------- Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Variables Added/Removed: => x6 added => x1 added => x3 added => x2 added => x6 removed No more variables to be added or removed. Stepwise Summary -------------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------------- 0 Base Model 56988.482 57004.289 228.318 0.00000 0.00000 1 x6 (+) 33473.297 33497.007 -23285.069 0.69145 0.69143 2 x1 (+) 32931.758 32963.372 -23826.833 0.69972 0.69969 3 x3 (+) 31912.722 31952.239 -24845.827 0.71466 0.71462 4 x2 (+) 29304.296 29351.717 -27453.243 0.74958 0.74953 5 x6 (-) 29302.317 29341.835 -27455.223 0.74958 0.74954 -------------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ----------------------------------------------------------------- R 0.866 RMSE 0.503 R-Squared 0.750 MSE 0.253 Adj. R-Squared 0.750 Coef. Var 6431.262 Pred R-Squared 0.749 AIC 29302.317 MAE 0.402 SBC 29341.835 ----------------------------------------------------------------- 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 15162.641 3 5054.214 19951.084 0.0000 Residual 5065.592 19996 0.253 Total 20228.233 19999 --------------------------------------------------------------------------- Parameter Estimates --------------------------------------------------------------------------------------- model Beta Std. Error Std. Beta t Sig lower upper --------------------------------------------------------------------------------------- (Intercept) -0.005 0.004 -1.503 0.133 -0.012 0.002 x1 0.255 0.003 0.362 84.118 0.000 0.249 0.261 x3 0.253 0.003 0.356 82.597 0.000 0.247 0.259 x2 0.249 0.003 0.347 80.571 0.000 0.243 0.255 --------------------------------------------------------------------------------------- --- Code ols_step_both_sbc(model, details = TRUE) Output Stepwise Selection Method ------------------------- Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Step => 0 Model => y ~ 1 SBC => 57004.29 Initiating stepwise selection... Table: Adding New Variables ------------------------------------------------------------------------------ Predictor DF AIC SBC SBIC R2 Adj. R2 ------------------------------------------------------------------------------ x1 1 43073.160 43096.870 -13686.868 0.50136 0.50133 x2 1 43561.884 43585.595 -13198.216 0.48902 0.48900 x3 1 43267.194 43290.904 -13492.863 0.49650 0.49647 x4 1 56989.595 57013.305 227.932 4e-05 -1e-05 x5 1 56990.439 57014.149 228.776 0.00000 -5e-05 x6 1 33473.297 33497.007 -23285.069 0.69145 0.69143 ------------------------------------------------------------------------------ Step => 1 Added => x6 Model => y ~ x6 SBC => 33497.01 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x1 1 32931.758 32963.372 -23826.833 0.69972 0.69969 x2 1 33033.295 33064.909 -23725.325 0.69819 0.69816 x3 1 32959.771 32991.385 -23798.829 0.69930 0.69927 x4 1 33470.717 33502.331 -23288.023 0.69152 0.69149 x5 1 33475.275 33506.889 -23283.467 0.69145 0.69142 ----------------------------------------------------------------------------- Step => 2 Added => x1 Model => y ~ x6 + x1 SBC => 32963.37 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 43073.160 43096.870 -13686.868 0.50136 0.50133 x1 1 33473.297 33497.007 -23285.069 0.69145 0.69143 ----------------------------------------------------------------------------- Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x2 1 32025.492 32065.010 -24733.099 0.71305 0.71301 x3 1 31912.722 31952.239 -24845.827 0.71466 0.71462 x4 1 32928.035 32967.552 -23830.887 0.69980 0.69976 x5 1 32933.735 32973.252 -23825.189 0.69972 0.69967 ----------------------------------------------------------------------------- Step => 3 Added => x3 Model => y ~ x6 + x1 + x3 SBC => 31952.24 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 34923.269 34954.883 -21835.862 0.66828 0.66825 x1 1 32959.771 32991.385 -23798.829 0.69930 0.69927 x3 1 32931.758 32963.372 -23826.833 0.69972 0.69969 ----------------------------------------------------------------------------- Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x2 1 29304.296 29351.717 -27453.243 0.74958 0.74953 x4 1 31908.533 31955.954 -24850.258 0.71475 0.71470 x5 1 31914.523 31961.944 -24844.270 0.71467 0.71461 ----------------------------------------------------------------------------- Step => 4 Added => x2 Model => y ~ x6 + x1 + x3 + x2 SBC => 29351.72 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 29302.317 29341.835 -27455.223 0.74958 0.74954 x1 1 32080.424 32119.941 -24678.188 0.71226 0.71222 x3 1 32025.492 32065.010 -24733.099 0.71305 0.71301 x2 1 31912.722 31952.239 -24845.827 0.71466 0.71462 ----------------------------------------------------------------------------- Step => 5 Removed => x6 Model => y ~ x1 + x3 + x2 SBC => 29341.83 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x4 1 29300.814 29348.235 -27456.724 0.74962 0.74957 x5 1 29304.253 29351.673 -27453.287 0.74958 0.74953 ----------------------------------------------------------------------------- No more variables to be added or removed. Variables Selected: => x1 => x3 => x2 Stepwise Summary -------------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------------- 0 Base Model 56988.482 57004.289 228.318 0.00000 0.00000 1 x6 (+) 33473.297 33497.007 -23285.069 0.69145 0.69143 2 x1 (+) 32931.758 32963.372 -23826.833 0.69972 0.69969 3 x3 (+) 31912.722 31952.239 -24845.827 0.71466 0.71462 4 x2 (+) 29304.296 29351.717 -27453.243 0.74958 0.74953 5 x6 (-) 29302.317 29341.835 -27455.223 0.74958 0.74954 -------------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ----------------------------------------------------------------- R 0.866 RMSE 0.503 R-Squared 0.750 MSE 0.253 Adj. R-Squared 0.750 Coef. Var 6431.262 Pred R-Squared 0.749 AIC 29302.317 MAE 0.402 SBC 29341.835 ----------------------------------------------------------------- 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 15162.641 3 5054.214 19951.084 0.0000 Residual 5065.592 19996 0.253 Total 20228.233 19999 --------------------------------------------------------------------------- Parameter Estimates --------------------------------------------------------------------------------------- model Beta Std. Error Std. Beta t Sig lower upper --------------------------------------------------------------------------------------- (Intercept) -0.005 0.004 -1.503 0.133 -0.012 0.002 x1 0.255 0.003 0.362 84.118 0.000 0.249 0.261 x3 0.253 0.003 0.356 82.597 0.000 0.247 0.259 x2 0.249 0.003 0.347 80.571 0.000 0.243 0.255 --------------------------------------------------------------------------------------- # output from stepSBIC both direction regression is as expected when adding and removing variables Code ols_step_both_sbic(model, progress = TRUE) Output Stepwise Selection Method ------------------------- Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Variables Added/Removed: => x6 added => x1 added => x3 added => x2 added => x6 removed => x4 added No more variables to be added or removed. Stepwise Summary -------------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------------- 0 Base Model 56988.482 57004.289 228.318 0.00000 0.00000 1 x6 (+) 33473.297 33497.007 -23285.069 0.69145 0.69143 2 x1 (+) 32931.758 32963.372 -23826.833 0.69972 0.69969 3 x3 (+) 31912.722 31952.239 -24845.827 0.71466 0.71462 4 x2 (+) 29304.296 29351.717 -27453.243 0.74958 0.74953 5 x6 (-) 29302.317 29341.835 -27455.223 0.74958 0.74954 6 x4 (+) 29300.814 29348.235 -27456.724 0.74962 0.74957 -------------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ----------------------------------------------------------------- R 0.866 RMSE 0.503 R-Squared 0.750 MSE 0.253 Adj. R-Squared 0.750 Coef. Var 6430.859 Pred R-Squared 0.749 AIC 29300.814 MAE 0.402 SBC 29348.235 ----------------------------------------------------------------- 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 15163.528 4 3790.882 14966.061 0.0000 Residual 5064.705 19995 0.253 Total 20228.233 19999 --------------------------------------------------------------------------- Parameter Estimates --------------------------------------------------------------------------------------- model Beta Std. Error Std. Beta t Sig lower upper --------------------------------------------------------------------------------------- (Intercept) -0.005 0.004 -1.496 0.135 -0.012 0.002 x1 0.255 0.003 0.362 84.140 0.000 0.249 0.261 x3 0.253 0.003 0.356 82.604 0.000 0.247 0.259 x2 0.249 0.003 0.346 80.544 0.000 0.243 0.255 x4 -0.007 0.004 -0.007 -1.872 0.061 -0.014 0.000 --------------------------------------------------------------------------------------- --- Code ols_step_both_sbic(model, details = TRUE) Output Stepwise Selection Method ------------------------- Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Step => 0 Model => y ~ 1 SBIC => 230.9406 Initiating stepwise selection... Table: Adding New Variables ------------------------------------------------------------------------------ Predictor DF AIC SBC SBIC R2 Adj. R2 ------------------------------------------------------------------------------ x1 1 43073.160 43096.870 -13686.868 0.50136 0.50133 x2 1 43561.884 43585.595 -13198.216 0.48902 0.48900 x3 1 43267.194 43290.904 -13492.863 0.49650 0.49647 x4 1 56989.595 57013.305 227.932 4e-05 -1e-05 x5 1 56990.439 57014.149 228.776 0.00000 -5e-05 x6 1 33473.297 33497.007 -23285.069 0.69145 0.69143 ------------------------------------------------------------------------------ Step => 1 Added => x6 Model => y ~ x6 SBIC => -23285.07 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x1 1 32931.758 32963.372 -23826.833 0.69972 0.69969 x2 1 33033.295 33064.909 -23725.325 0.69819 0.69816 x3 1 32959.771 32991.385 -23798.829 0.69930 0.69927 x4 1 33470.717 33502.331 -23288.023 0.69152 0.69149 x5 1 33475.275 33506.889 -23283.467 0.69145 0.69142 ----------------------------------------------------------------------------- Step => 2 Added => x1 Model => y ~ x6 + x1 SBIC => -23826.83 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 43073.160 43096.870 -13686.868 0.50136 0.50133 x1 1 33473.297 33497.007 -23285.069 0.69145 0.69143 ----------------------------------------------------------------------------- Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x2 1 32025.492 32065.010 -24733.099 0.71305 0.71301 x3 1 31912.722 31952.239 -24845.827 0.71466 0.71462 x4 1 32928.035 32967.552 -23830.887 0.69980 0.69976 x5 1 32933.735 32973.252 -23825.189 0.69972 0.69967 ----------------------------------------------------------------------------- Step => 3 Added => x3 Model => y ~ x6 + x1 + x3 SBIC => -24845.83 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 34923.269 34954.883 -21835.862 0.66828 0.66825 x1 1 32959.771 32991.385 -23798.829 0.69930 0.69927 x3 1 32931.758 32963.372 -23826.833 0.69972 0.69969 ----------------------------------------------------------------------------- Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x2 1 29304.296 29351.717 -27453.243 0.74958 0.74953 x4 1 31908.533 31955.954 -24850.258 0.71475 0.71470 x5 1 31914.523 31961.944 -24844.270 0.71467 0.71461 ----------------------------------------------------------------------------- Step => 4 Added => x2 Model => y ~ x6 + x1 + x3 + x2 SBIC => -27453.24 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 29302.317 29341.835 -27455.223 0.74958 0.74954 x1 1 32080.424 32119.941 -24678.188 0.71226 0.71222 x3 1 32025.492 32065.010 -24733.099 0.71305 0.71301 x2 1 31912.722 31952.239 -24845.827 0.71466 0.71462 ----------------------------------------------------------------------------- Step => 5 Removed => x6 Model => y ~ x1 + x3 + x2 SBIC => -27455.22 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x4 1 29300.814 29348.235 -27456.724 0.74962 0.74957 x5 1 29304.253 29351.673 -27453.287 0.74958 0.74953 ----------------------------------------------------------------------------- Step => 6 Added => x4 Model => y ~ x1 + x3 + x2 + x4 SBIC => -27456.72 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x1 1 35361.098 35400.615 -21398.670 0.66097 0.66092 x3 1 35170.915 35210.432 -21588.789 0.66418 0.66413 x2 1 34918.668 34958.185 -21840.951 0.66839 0.66834 x4 1 29302.317 29341.835 -27455.223 0.74958 0.74954 ----------------------------------------------------------------------------- Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x5 1 29302.751 29358.075 -27454.786 0.74962 0.74956 ----------------------------------------------------------------------------- No more variables to be added or removed. Variables Selected: => x1 => x3 => x2 => x4 Stepwise Summary -------------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------------- 0 Base Model 56988.482 57004.289 228.318 0.00000 0.00000 1 x6 (+) 33473.297 33497.007 -23285.069 0.69145 0.69143 2 x1 (+) 32931.758 32963.372 -23826.833 0.69972 0.69969 3 x3 (+) 31912.722 31952.239 -24845.827 0.71466 0.71462 4 x2 (+) 29304.296 29351.717 -27453.243 0.74958 0.74953 5 x6 (-) 29302.317 29341.835 -27455.223 0.74958 0.74954 6 x4 (+) 29300.814 29348.235 -27456.724 0.74962 0.74957 -------------------------------------------------------------------------------- Final Model Output ------------------ Model Summary ----------------------------------------------------------------- R 0.866 RMSE 0.503 R-Squared 0.750 MSE 0.253 Adj. R-Squared 0.750 Coef. Var 6430.859 Pred R-Squared 0.749 AIC 29300.814 MAE 0.402 SBC 29348.235 ----------------------------------------------------------------- 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 15163.528 4 3790.882 14966.061 0.0000 Residual 5064.705 19995 0.253 Total 20228.233 19999 --------------------------------------------------------------------------- Parameter Estimates --------------------------------------------------------------------------------------- model Beta Std. Error Std. Beta t Sig lower upper --------------------------------------------------------------------------------------- (Intercept) -0.005 0.004 -1.496 0.135 -0.012 0.002 x1 0.255 0.003 0.362 84.140 0.000 0.249 0.261 x3 0.253 0.003 0.356 82.604 0.000 0.247 0.259 x2 0.249 0.003 0.346 80.544 0.000 0.243 0.255 x4 -0.007 0.004 -0.007 -1.872 0.061 -0.014 0.000 ---------------------------------------------------------------------------------------