# output from rsquared forward regression is as expected Code ols_step_forward_r2(model) Output 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 x4 29302.797 29358.121 -27454.740 0.74962 0.74956 6 x5 29304.734 29367.962 -27452.802 0.74962 0.74955 -------------------------------------------------------------------------------- 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 6431.168 Pred R-Squared 0.749 AIC 29304.734 MAE 0.402 SBC 29367.962 ----------------------------------------------------------------- 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 15163.548 6 2527.258 9976.429 0.0000 Residual 5064.685 19993 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 x6 0.000 0.004 -0.002 -0.129 0.897 -0.007 0.007 x1 0.256 0.005 0.363 54.591 0.000 0.247 0.265 x3 0.253 0.005 0.356 53.997 0.000 0.244 0.262 x2 0.249 0.005 0.347 52.766 0.000 0.240 0.258 x4 -0.007 0.004 -0.007 -1.870 0.062 -0.014 0.000 x5 -0.001 0.004 -0.001 -0.250 0.802 -0.008 0.006 --------------------------------------------------------------------------------------- --- Code ols_step_forward_r2(model, progress = TRUE) Output Forward Selection Method ------------------------ Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Variables Entered: => x6 => x1 => x3 => x2 => x4 => x5 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 x4 29302.797 29358.121 -27454.740 0.74962 0.74956 6 x5 29304.734 29367.962 -27452.802 0.74962 0.74955 -------------------------------------------------------------------------------- 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 6431.168 Pred R-Squared 0.749 AIC 29304.734 MAE 0.402 SBC 29367.962 ----------------------------------------------------------------- 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 15163.548 6 2527.258 9976.429 0.0000 Residual 5064.685 19993 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 x6 0.000 0.004 -0.002 -0.129 0.897 -0.007 0.007 x1 0.256 0.005 0.363 54.591 0.000 0.247 0.265 x3 0.253 0.005 0.356 53.997 0.000 0.244 0.262 x2 0.249 0.005 0.347 52.766 0.000 0.240 0.258 x4 -0.007 0.004 -0.007 -1.870 0.062 -0.014 0.000 x5 -0.001 0.004 -0.001 -0.250 0.802 -0.008 0.006 --------------------------------------------------------------------------------------- --- Code ols_step_forward_r2(model, details = TRUE) Output Forward Selection Method ------------------------ Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Step => 0 Model => y ~ 1 R2 => 0 Initiating stepwise selection... Table: Adding New Variables ------------------------------------------------------------------------------ Predictor DF AIC SBC SBIC R2 Adj. R2 ------------------------------------------------------------------------------ x6 1 33473.297 33497.007 -23285.069 0.69145 0.69143 x1 1 43073.160 43096.870 -13686.868 0.50136 0.50133 x3 1 43267.194 43290.904 -13492.863 0.49650 0.49647 x2 1 43561.884 43585.595 -13198.216 0.48902 0.48900 x4 1 56989.595 57013.305 227.932 4e-05 -1e-05 x5 1 56990.439 57014.149 228.776 0.00000 -5e-05 ------------------------------------------------------------------------------ Step => 1 Added => x6 Model => y ~ x6 R2 => 0.69145 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x1 1 32931.758 32963.372 -23826.833 0.69972 0.69969 x3 1 32959.771 32991.385 -23798.829 0.69930 0.69927 x2 1 33033.295 33064.909 -23725.325 0.69819 0.69816 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 R2 => 0.69972 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x3 1 31912.722 31952.239 -24845.827 0.71466 0.71462 x2 1 32025.492 32065.010 -24733.099 0.71305 0.71301 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 R2 => 0.71466 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 R2 => 0.74958 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x4 1 29302.797 29358.121 -27454.740 0.74962 0.74956 x5 1 29306.232 29361.556 -27451.307 0.74958 0.74952 ----------------------------------------------------------------------------- Step => 5 Added => x4 Model => y ~ x6 + x1 + x3 + x2 + x4 R2 => 0.74962 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x5 1 29304.734 29367.962 -27452.802 0.74962 0.74955 ----------------------------------------------------------------------------- Variables Selected: => x6 => x1 => x3 => x2 => x4 => x5 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 x4 29302.797 29358.121 -27454.740 0.74962 0.74956 6 x5 29304.734 29367.962 -27452.802 0.74962 0.74955 -------------------------------------------------------------------------------- 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 6431.168 Pred R-Squared 0.749 AIC 29304.734 MAE 0.402 SBC 29367.962 ----------------------------------------------------------------- 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 15163.548 6 2527.258 9976.429 0.0000 Residual 5064.685 19993 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 x6 0.000 0.004 -0.002 -0.129 0.897 -0.007 0.007 x1 0.256 0.005 0.363 54.591 0.000 0.247 0.265 x3 0.253 0.005 0.356 53.997 0.000 0.244 0.262 x2 0.249 0.005 0.347 52.766 0.000 0.240 0.258 x4 -0.007 0.004 -0.007 -1.870 0.062 -0.014 0.000 x5 -0.001 0.004 -0.001 -0.250 0.802 -0.008 0.006 --------------------------------------------------------------------------------------- # output from adjusted rsquared forward regression is as expected Code ols_step_forward_adj_r2(model) Output 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 x4 29302.797 29358.121 -27454.740 0.74962 0.74956 -------------------------------------------------------------------------------- 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 6431.017 Pred R-Squared 0.749 AIC 29302.797 MAE 0.402 SBC 29358.121 ----------------------------------------------------------------- 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 15163.532 5 3032.706 11972.264 0.0000 Residual 5064.701 19994 0.253 Total 20228.233 19999 --------------------------------------------------------------------------- Parameter Estimates --------------------------------------------------------------------------------------- model Beta Std. Error Std. Beta t Sig lower upper --------------------------------------------------------------------------------------- (Intercept) -0.005 0.004 -1.497 0.135 -0.012 0.002 x6 0.000 0.004 -0.002 -0.129 0.897 -0.007 0.007 x1 0.256 0.005 0.363 54.592 0.000 0.247 0.265 x3 0.253 0.005 0.356 53.998 0.000 0.244 0.262 x2 0.249 0.005 0.347 52.769 0.000 0.240 0.258 x4 -0.007 0.004 -0.007 -1.870 0.061 -0.014 0.000 --------------------------------------------------------------------------------------- --- Code ols_step_forward_adj_r2(model, progress = TRUE) Output Forward Selection Method ------------------------ Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Variables Entered: => x6 => x1 => x3 => x2 => x4 No more variables to be added. 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 x4 29302.797 29358.121 -27454.740 0.74962 0.74956 -------------------------------------------------------------------------------- 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 6431.017 Pred R-Squared 0.749 AIC 29302.797 MAE 0.402 SBC 29358.121 ----------------------------------------------------------------- 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 15163.532 5 3032.706 11972.264 0.0000 Residual 5064.701 19994 0.253 Total 20228.233 19999 --------------------------------------------------------------------------- Parameter Estimates --------------------------------------------------------------------------------------- model Beta Std. Error Std. Beta t Sig lower upper --------------------------------------------------------------------------------------- (Intercept) -0.005 0.004 -1.497 0.135 -0.012 0.002 x6 0.000 0.004 -0.002 -0.129 0.897 -0.007 0.007 x1 0.256 0.005 0.363 54.592 0.000 0.247 0.265 x3 0.253 0.005 0.356 53.998 0.000 0.244 0.262 x2 0.249 0.005 0.347 52.769 0.000 0.240 0.258 x4 -0.007 0.004 -0.007 -1.870 0.061 -0.014 0.000 --------------------------------------------------------------------------------------- --- Code ols_step_forward_adj_r2(model, details = TRUE) Output Forward Selection Method ------------------------ Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Step => 0 Model => y ~ 1 Adj. R2 => 0 Initiating stepwise selection... Table: Adding New Variables ------------------------------------------------------------------------------ Predictor DF AIC SBC SBIC R2 Adj. R2 ------------------------------------------------------------------------------ x6 1 33473.297 33497.007 -23285.069 0.69145 0.69143 x1 1 43073.160 43096.870 -13686.868 0.50136 0.50133 x3 1 43267.194 43290.904 -13492.863 0.49650 0.49647 x2 1 43561.884 43585.595 -13198.216 0.48902 0.48900 x4 1 56989.595 57013.305 227.932 4e-05 -1e-05 x5 1 56990.439 57014.149 228.776 0.00000 -5e-05 ------------------------------------------------------------------------------ Step => 1 Added => x6 Model => y ~ x6 Adj. R2 => 0.69143 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x1 1 32931.758 32963.372 -23826.833 0.69972 0.69969 x3 1 32959.771 32991.385 -23798.829 0.69930 0.69927 x2 1 33033.295 33064.909 -23725.325 0.69819 0.69816 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 Adj. R2 => 0.69969 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x3 1 31912.722 31952.239 -24845.827 0.71466 0.71462 x2 1 32025.492 32065.010 -24733.099 0.71305 0.71301 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 Adj. R2 => 0.71462 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 Adj. R2 => 0.74953 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x4 1 29302.797 29358.121 -27454.740 0.74962 0.74956 x5 1 29306.232 29361.556 -27451.307 0.74958 0.74952 ----------------------------------------------------------------------------- Step => 5 Added => x4 Model => y ~ x6 + x1 + x3 + x2 + x4 Adj. R2 => 0.74956 Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x5 1 29304.734 29367.962 -27452.802 0.74962 0.74955 ----------------------------------------------------------------------------- No more variables to be added. Variables Selected: => x6 => 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 x4 29302.797 29358.121 -27454.740 0.74962 0.74956 -------------------------------------------------------------------------------- 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 6431.017 Pred R-Squared 0.749 AIC 29302.797 MAE 0.402 SBC 29358.121 ----------------------------------------------------------------- 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 15163.532 5 3032.706 11972.264 0.0000 Residual 5064.701 19994 0.253 Total 20228.233 19999 --------------------------------------------------------------------------- Parameter Estimates --------------------------------------------------------------------------------------- model Beta Std. Error Std. Beta t Sig lower upper --------------------------------------------------------------------------------------- (Intercept) -0.005 0.004 -1.497 0.135 -0.012 0.002 x6 0.000 0.004 -0.002 -0.129 0.897 -0.007 0.007 x1 0.256 0.005 0.363 54.592 0.000 0.247 0.265 x3 0.253 0.005 0.356 53.998 0.000 0.244 0.262 x2 0.249 0.005 0.347 52.769 0.000 0.240 0.258 x4 -0.007 0.004 -0.007 -1.870 0.061 -0.014 0.000 --------------------------------------------------------------------------------------- # output from rsquared backward regression is as expected Code ols_step_backward_r2(model) Output [1] "No variables have been removed from the model." --- Code ols_step_backward_r2(model, progress = TRUE) Output Backward Elimination Method --------------------------- Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Variables Removed: No more variables to be removed. [1] "No variables have been removed from the model." --- Code ols_step_backward_r2(model, details = TRUE) Output Backward Elimination Method --------------------------- Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Step => 0 Model => y ~ x1 + x2 + x3 + x4 + x5 + x6 R2 => 0.749623 Initiating stepwise selection... Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 29302.751 29358.075 -27454.786 0.74962 0.74956 x5 1 29302.797 29358.121 -27454.740 0.74962 0.74956 x4 1 29306.232 29361.556 -27451.307 0.74958 0.74952 x2 1 31910.339 31965.663 -24848.695 0.71476 0.71468 x3 1 32025.383 32080.708 -24733.714 0.71311 0.71304 x1 1 32081.673 32136.998 -24677.455 0.71230 0.71223 ----------------------------------------------------------------------------- No more variables to be removed. [1] "No variables have been removed from the model." # output from adjusted rsquared backward regression is as expected Code ols_step_backward_adj_r2(model) Output Stepwise Summary -------------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------------- 0 Full Model 29304.734 29367.962 -27452.802 0.74962 0.74955 1 x6 29302.751 29358.075 -27454.787 0.74962 0.74956 2 x5 29300.814 29348.235 -27456.725 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 x2 0.249 0.003 0.346 80.544 0.000 0.243 0.255 x3 0.253 0.003 0.356 82.604 0.000 0.247 0.259 x4 -0.007 0.004 -0.007 -1.872 0.061 -0.014 0.000 --------------------------------------------------------------------------------------- --- Code ols_step_backward_adj_r2(model, progress = TRUE) Output Backward Elimination Method --------------------------- Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Variables Removed: => x6 => x5 No more variables to be removed. Stepwise Summary -------------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------------- 0 Full Model 29304.734 29367.962 -27452.802 0.74962 0.74955 1 x6 29302.751 29358.075 -27454.787 0.74962 0.74956 2 x5 29300.814 29348.235 -27456.725 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 x2 0.249 0.003 0.346 80.544 0.000 0.243 0.255 x3 0.253 0.003 0.356 82.604 0.000 0.247 0.259 x4 -0.007 0.004 -0.007 -1.872 0.061 -0.014 0.000 --------------------------------------------------------------------------------------- --- Code ols_step_backward_adj_r2(model, details = TRUE) Output Backward Elimination Method --------------------------- Candidate Terms: 1. x1 2. x2 3. x3 4. x4 5. x5 6. x6 Step => 0 Model => y ~ x1 + x2 + x3 + x4 + x5 + x6 Adj. R2 => 0.7495478 Initiating stepwise selection... Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 29302.751 29358.075 -27454.786 0.74962 0.74956 x5 1 29302.797 29358.121 -27454.740 0.74962 0.74956 x4 1 29306.232 29361.556 -27451.307 0.74958 0.74952 x2 1 31910.339 31965.663 -24848.695 0.71476 0.71468 x3 1 32025.383 32080.708 -24733.714 0.71311 0.71304 x1 1 32081.673 32136.998 -24677.455 0.71230 0.71223 ----------------------------------------------------------------------------- Step => 1 Removed => x6 Model => y ~ x1 + x2 + x3 + x4 + x5 Adj. R2 => 0.74956 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x5 1 29300.814 29348.235 -27456.724 0.74962 0.74957 x4 1 29304.253 29351.673 -27453.287 0.74958 0.74953 x2 1 34920.175 34967.596 -21839.933 0.66840 0.66833 x3 1 35172.737 35220.158 -21587.475 0.66418 0.66412 x1 1 35363.070 35410.491 -21397.220 0.66097 0.66090 ----------------------------------------------------------------------------- Step => 2 Removed => x5 Model => y ~ x1 + x2 + x3 + x4 Adj. R2 => 0.74957 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x4 1 29302.317 29341.835 -27455.223 0.74958 0.74954 x2 1 34918.668 34958.185 -21840.951 0.66839 0.66834 x3 1 35170.915 35210.432 -21588.789 0.66418 0.66413 x1 1 35361.098 35400.615 -21398.670 0.66097 0.66092 ----------------------------------------------------------------------------- No more variables to be removed. Variables Removed: => x6 => x5 Stepwise Summary -------------------------------------------------------------------------------- Step Variable AIC SBC SBIC R2 Adj. R2 -------------------------------------------------------------------------------- 0 Full Model 29304.734 29367.962 -27452.802 0.74962 0.74955 1 x6 29302.751 29358.075 -27454.787 0.74962 0.74956 2 x5 29300.814 29348.235 -27456.725 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 x2 0.249 0.003 0.346 80.544 0.000 0.243 0.255 x3 0.253 0.003 0.356 82.604 0.000 0.247 0.259 x4 -0.007 0.004 -0.007 -1.872 0.061 -0.014 0.000 --------------------------------------------------------------------------------------- # output from rsquared both direction regression is as expected Code ols_step_both_r2(model) Output 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 x4 (+) 29302.797 29358.121 -27454.740 0.74962 0.74956 6 x5 (+) 29304.734 29367.962 -27452.802 0.74962 0.74955 -------------------------------------------------------------------------------- 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 6431.168 Pred R-Squared 0.749 AIC 29304.734 MAE 0.402 SBC 29367.962 ----------------------------------------------------------------- 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 15163.548 6 2527.258 9976.429 0.0000 Residual 5064.685 19993 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 x6 0.000 0.004 -0.002 -0.129 0.897 -0.007 0.007 x1 0.256 0.005 0.363 54.591 0.000 0.247 0.265 x3 0.253 0.005 0.356 53.997 0.000 0.244 0.262 x2 0.249 0.005 0.347 52.766 0.000 0.240 0.258 x4 -0.007 0.004 -0.007 -1.870 0.062 -0.014 0.000 x5 -0.001 0.004 -0.001 -0.250 0.802 -0.008 0.006 --------------------------------------------------------------------------------------- --- Code ols_step_both_r2(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 => x4 added => x5 added 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 x4 (+) 29302.797 29358.121 -27454.740 0.74962 0.74956 6 x5 (+) 29304.734 29367.962 -27452.802 0.74962 0.74955 -------------------------------------------------------------------------------- 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 6431.168 Pred R-Squared 0.749 AIC 29304.734 MAE 0.402 SBC 29367.962 ----------------------------------------------------------------- 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 15163.548 6 2527.258 9976.429 0.0000 Residual 5064.685 19993 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 x6 0.000 0.004 -0.002 -0.129 0.897 -0.007 0.007 x1 0.256 0.005 0.363 54.591 0.000 0.247 0.265 x3 0.253 0.005 0.356 53.997 0.000 0.244 0.262 x2 0.249 0.005 0.347 52.766 0.000 0.240 0.258 x4 -0.007 0.004 -0.007 -1.870 0.062 -0.014 0.000 x5 -0.001 0.004 -0.001 -0.250 0.802 -0.008 0.006 --------------------------------------------------------------------------------------- --- Code ols_step_both_r2(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 R2 => 0 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 R2 => 0.69145 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 R2 => 0.69972 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 R2 => 0.71466 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 R2 => 0.74958 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 ----------------------------------------------------------------------------- Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x4 1 29302.797 29358.121 -27454.740 0.74962 0.74956 x5 1 29306.232 29361.556 -27451.307 0.74958 0.74952 ----------------------------------------------------------------------------- Step => 5 Added => x4 Model => y ~ x6 + x1 + x3 + x2 + x4 R2 => 0.74962 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 29300.814 29348.235 -27456.724 0.74962 0.74957 x1 1 32079.710 32127.131 -24679.159 0.71230 0.71224 x3 1 32023.390 32070.811 -24735.453 0.71311 0.71305 x2 1 31908.533 31955.954 -24850.258 0.71475 0.71470 x4 1 29304.296 29351.717 -27453.243 0.74958 0.74953 ----------------------------------------------------------------------------- Table: Adding New Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x5 1 29304.734 29367.962 -27452.802 0.74962 0.74955 ----------------------------------------------------------------------------- Step => 6 Added => x5 Model => y ~ x6 + x1 + x3 + x2 + x4 + x5 R2 => 0.74962 Table: Removing Existing Variables ----------------------------------------------------------------------------- Predictor DF AIC SBC SBIC R2 Adj. R2 ----------------------------------------------------------------------------- x6 1 29302.751 29358.075 -27454.786 0.74962 0.74956 x1 1 32081.673 32136.998 -24677.455 0.71230 0.71223 x3 1 32025.383 32080.708 -24733.714 0.71311 0.71304 x2 1 31910.339 31965.663 -24848.695 0.71476 0.71468 x4 1 29306.232 29361.556 -27451.307 0.74958 0.74952 x5 1 29302.797 29358.121 -27454.740 0.74962 0.74956 ----------------------------------------------------------------------------- Variables Selected: => x6 => x1 => x3 => x2 => x4 => x5 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 x4 (+) 29302.797 29358.121 -27454.740 0.74962 0.74956 6 x5 (+) 29304.734 29367.962 -27452.802 0.74962 0.74955 -------------------------------------------------------------------------------- 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 6431.168 Pred R-Squared 0.749 AIC 29304.734 MAE 0.402 SBC 29367.962 ----------------------------------------------------------------- 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 15163.548 6 2527.258 9976.429 0.0000 Residual 5064.685 19993 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 x6 0.000 0.004 -0.002 -0.129 0.897 -0.007 0.007 x1 0.256 0.005 0.363 54.591 0.000 0.247 0.265 x3 0.253 0.005 0.356 53.997 0.000 0.244 0.262 x2 0.249 0.005 0.347 52.766 0.000 0.240 0.258 x4 -0.007 0.004 -0.007 -1.870 0.062 -0.014 0.000 x5 -0.001 0.004 -0.001 -0.250 0.802 -0.008 0.006 --------------------------------------------------------------------------------------- # output from adjusted rsquared both direction regression is as expected Code ols_step_both_adj_r2(model) Output 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_adj_r2(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_adj_r2(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 Adj. R2 => 0 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 Adj. R2 => 0.69143 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 Adj. R2 => 0.69969 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 Adj. R2 => 0.71462 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 Adj. R2 => 0.74953 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 Adj. R2 => 0.74954 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 Adj. R2 => 0.74957 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 ---------------------------------------------------------------------------------------