Overview
The olsrr package provides following tools for teaching and learning OLS regression using R:
- Comprehensive Regression Output
- Variable Selection Procedures
- Heteroskedasticity Tests
- Collinearity Diagnostics
- Model Fit Assessment
- Measures of Influence
- Residual Diagnostics
- Variable Contribution Assessment
Shiny App
Use ols_launch_app() to explore the package using a shiny app.
Quick Demo
olsrr is built with the aim of helping those users who are new to the R language. If you know how to write a formula or build models using lm, you will find olsrr very useful. Most of the functions use an object of class lm as input. So you just need to build a model using lm and then pass it onto the functions in olsrr. Below is a quick demo:
Regression
ols_regress(mpg ~ disp + hp + wt + qsec, data = mtcars)
#> Model Summary
#> --------------------------------------------------------------
#> R 0.914 RMSE 2.622
#> R-Squared 0.835 Coef. Var 13.051
#> Adj. R-Squared 0.811 MSE 6.875
#> Pred R-Squared 0.771 MAE 1.858
#> --------------------------------------------------------------
#> RMSE: Root Mean Square Error
#> MSE: Mean Square Error
#> MAE: Mean Absolute Error
#>
#> ANOVA
#> --------------------------------------------------------------------
#> Sum of
#> Squares DF Mean Square F Sig.
#> --------------------------------------------------------------------
#> Regression 940.412 4 235.103 34.195 0.0000
#> Residual 185.635 27 6.875
#> Total 1126.047 31
#> --------------------------------------------------------------------
#>
#> Parameter Estimates
#> ----------------------------------------------------------------------------------------
#> model Beta Std. Error Std. Beta t Sig lower upper
#> ----------------------------------------------------------------------------------------
#> (Intercept) 27.330 8.639 3.164 0.004 9.604 45.055
#> disp 0.003 0.011 0.055 0.248 0.806 -0.019 0.025
#> hp -0.019 0.016 -0.212 -1.196 0.242 -0.051 0.013
#> wt -4.609 1.266 -0.748 -3.641 0.001 -7.206 -2.012
#> qsec 0.544 0.466 0.161 1.166 0.254 -0.413 1.501
#> ----------------------------------------------------------------------------------------Stepwise Regression
Build regression model from a set of candidate predictor variables by entering and removing predictors based on p values, in a stepwise manner until there is no variable left to enter or remove any more.
Variable Selection
# stepwise regression
model <- lm(y ~ ., data = surgical)
ols_step_both_p(model)
#> Stepwise Selection Method
#> ---------------------------
#>
#> Candidate Terms:
#>
#> 1. bcs
#> 2. pindex
#> 3. enzyme_test
#> 4. liver_test
#> 5. age
#> 6. gender
#> 7. alc_mod
#> 8. alc_heavy
#>
#> We are selecting variables based on p value...
#>
#> Variables Entered/Removed:
#>
#> - liver_test added
#> - alc_heavy added
#> - enzyme_test added
#> - pindex added
#> - bcs added
#>
#> No more variables to be added/removed.
#>
#>
#> Final Model Output
#> ------------------
#>
#> Model Summary
#> -----------------------------------------------------------------
#> R 0.884 RMSE 195.454
#> R-Squared 0.781 Coef. Var 27.839
#> Adj. R-Squared 0.758 MSE 38202.426
#> Pred R-Squared 0.700 MAE 137.656
#> -----------------------------------------------------------------
#> RMSE: Root Mean Square Error
#> MSE: Mean Square Error
#> MAE: Mean Absolute Error
#>
#> ANOVA
#> -----------------------------------------------------------------------
#> Sum of
#> Squares DF Mean Square F Sig.
#> -----------------------------------------------------------------------
#> Regression 6535804.090 5 1307160.818 34.217 0.0000
#> Residual 1833716.447 48 38202.426
#> Total 8369520.537 53
#> -----------------------------------------------------------------------
#>
#> Parameter Estimates
#> ------------------------------------------------------------------------------------------------
#> model Beta Std. Error Std. Beta t Sig lower upper
#> ------------------------------------------------------------------------------------------------
#> (Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
#> liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
#> alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
#> enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
#> pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
#> bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
#> ------------------------------------------------------------------------------------------------
#>
#> Stepwise Selection Summary
#> ------------------------------------------------------------------------------------------
#> Added/ Adj.
#> Step Variable Removed R-Square R-Square C(p) AIC RMSE
#> ------------------------------------------------------------------------------------------
#> 1 liver_test addition 0.455 0.444 62.5120 771.8753 296.2992
#> 2 alc_heavy addition 0.567 0.550 41.3680 761.4394 266.6484
#> 3 enzyme_test addition 0.659 0.639 24.3380 750.5089 238.9145
#> 4 pindex addition 0.750 0.730 7.5370 735.7146 206.5835
#> 5 bcs addition 0.781 0.758 3.1920 730.6204 195.4544
#> ------------------------------------------------------------------------------------------Stepwise AIC Backward Regression
Build regression model from a set of candidate predictor variables by removing predictors based on Akaike Information Criteria, in a stepwise manner until there is no variable left to remove any more.
Variable Selection
# stepwise aic backward regression
model <- lm(y ~ ., data = surgical)
k <- ols_step_backward_aic(model)
#> Backward Elimination Method
#> ---------------------------
#>
#> Candidate Terms:
#>
#> 1 . bcs
#> 2 . pindex
#> 3 . enzyme_test
#> 4 . liver_test
#> 5 . age
#> 6 . gender
#> 7 . alc_mod
#> 8 . alc_heavy
#>
#>
#> Variables Removed:
#>
#> - alc_mod
#> - gender
#> - age
#>
#> No more variables to be removed.
k
#>
#>
#> Backward Elimination Summary
#> ---------------------------------------------------------------------------
#> Variable AIC RSS Sum Sq R-Sq Adj. R-Sq
#> ---------------------------------------------------------------------------
#> Full Model 736.390 1825905.713 6543614.824 0.78184 0.74305
#> alc_mod 734.407 1826477.828 6543042.709 0.78177 0.74856
#> gender 732.494 1829435.617 6540084.920 0.78142 0.75351
#> age 730.620 1833716.447 6535804.090 0.78091 0.75808
#> ---------------------------------------------------------------------------Breusch Pagan Test
Breusch Pagan test is used to test for herteroskedasticity (non-constant error variance). It tests whether the variance of the errors from a regression is dependent on the values of the independent variables. It is a \(\chi^{2}\) test.
model <- lm(mpg ~ disp + hp + wt + drat, data = mtcars)
ols_test_breusch_pagan(model)
#>
#> Breusch Pagan Test for Heteroskedasticity
#> -----------------------------------------
#> Ho: the variance is constant
#> Ha: the variance is not constant
#>
#> Data
#> -------------------------------
#> Response : mpg
#> Variables: fitted values of mpg
#>
#> Test Summary
#> ---------------------------
#> DF = 1
#> Chi2 = 1.429672
#> Prob > Chi2 = 0.231818Collinearity Diagnostics
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_coll_diag(model)
#> Tolerance and Variance Inflation Factor
#> ---------------------------------------
#> # A tibble: 4 x 3
#> Variables Tolerance VIF
#> <chr> <dbl> <dbl>
#> 1 disp 0.125 7.99
#> 2 hp 0.194 5.17
#> 3 wt 0.145 6.92
#> 4 qsec 0.319 3.13
#>
#>
#> Eigenvalue and Condition Index
#> ------------------------------
#> Eigenvalue Condition Index intercept disp hp
#> 1 4.721487187 1.000000 0.000123237 0.001132468 0.001413094
#> 2 0.216562203 4.669260 0.002617424 0.036811051 0.027751289
#> 3 0.050416837 9.677242 0.001656551 0.120881424 0.392366164
#> 4 0.010104757 21.616057 0.025805998 0.777260487 0.059594623
#> 5 0.001429017 57.480524 0.969796790 0.063914571 0.518874831
#> wt qsec
#> 1 0.0005253393 0.0001277169
#> 2 0.0002096014 0.0046789491
#> 3 0.0377028008 0.0001952599
#> 4 0.7017528428 0.0024577686
#> 5 0.2598094157 0.9925403056Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.