Nothing
tests/testthat/_snaps/step-rsquared-output.md
In olsrr: Tools for Building OLS Regression Models
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
---------------------------------------------------------------------------------------
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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
---------------------------------------------------------------------------------------
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