Residual vs Fitted Values Plot
Plot to detect non-linearity, unequal error variances, and outliers.
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The olsrr package provides following tools for teaching and learning OLS regression using R:
This document is a quickstart guide to the tools offered by olsrr. Other vignettes provide more details on specific topics:
Residual Diagnostics: Includes plots to examine residuals to validate OLS assumptions
Variable selection: Differnt variable selection procedures such as all possible regression, best subset regression, stepwise regression, stepwise forward regression and stepwise backward regression
Heteroskedasticity: Tests for heteroskedasticity include bartlett test, breusch pagan test, score test and f test
Measures of influence: Includes 10 different plots to detect and identify influential observations
Collinearity diagnostics: VIF, Tolerance and condition indices to detect collinearity and plots for assessing mode fit and contributions of variables
## Model Summary
## ---------------------------------------------------------------
## R 0.914 RMSE 2.409
## R-Squared 0.835 MSE 6.875
## Adj. R-Squared 0.811 Coef. Var 13.051
## Pred R-Squared 0.771 AIC 159.070
## MAE 1.858 SBC 167.864
## ---------------------------------------------------------------
## 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 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
## ----------------------------------------------------------------------------------------In the presence of interaction terms in the model, the predictors are
scaled and centered before computing the standardized betas.
ols_regress() will detect interaction terms automatically
but in case you have created a new variable instead of using the inline
function *, you can indicate the presence of interaction
terms by setting iterm to TRUE.
Plot to detect non-linearity, unequal error variances, and outliers.
DFBETAs measure the difference in each parameter estimate with and
without the influential observation. dfbetas_panel creates
plots to detect influential observations using DFBETAs.
Plot to detect non-linearity, influential observations and outliers.
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.
##
## 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 = 0.231818## Tolerance and Variance Inflation Factor
## ---------------------------------------
## Variables Tolerance VIF
## 1 disp 0.1252279 7.985439
## 2 hp 0.1935450 5.166758
## 3 wt 0.1445726 6.916942
## 4 qsec 0.3191708 3.133119
##
##
## Eigenvalue and Condition Index
## ------------------------------
## Eigenvalue Condition Index intercept disp hp wt
## 1 4.721487187 1.000000 0.000123237 0.001132468 0.001413094 0.0005253393
## 2 0.216562203 4.669260 0.002617424 0.036811051 0.027751289 0.0002096014
## 3 0.050416837 9.677242 0.001656551 0.120881424 0.392366164 0.0377028008
## 4 0.010104757 21.616057 0.025805998 0.777260487 0.059594623 0.7017528428
## 5 0.001429017 57.480524 0.969796790 0.063914571 0.518874831 0.2598094157
## qsec
## 1 0.0001277169
## 2 0.0046789491
## 3 0.0001952599
## 4 0.0024577686
## 5 0.9925403056Build 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.
##
##
## Stepwise Summary
## ------------------------------------------------------------------------------
## Step Variable AIC SBC SBIC R2 Adj. R2
## ------------------------------------------------------------------------------
## 0 Base Model 802.606 806.584 646.794 0.00000 0.00000
## 1 liver_test (+) 771.875 777.842 616.009 0.45454 0.44405
## 2 alc_heavy (+) 761.439 769.395 605.506 0.56674 0.54975
## 3 enzyme_test (+) 750.509 760.454 595.297 0.65900 0.63854
## 4 pindex (+) 735.715 747.649 582.943 0.75015 0.72975
## 5 bcs (+) 730.620 744.543 579.638 0.78091 0.75808
## ------------------------------------------------------------------------------
##
## Final Model Output
## ------------------
##
## Model Summary
## -------------------------------------------------------------------
## R 0.884 RMSE 184.276
## R-Squared 0.781 MSE 38202.426
## Adj. R-Squared 0.758 Coef. Var 27.839
## Pred R-Squared 0.700 AIC 730.620
## MAE 137.656 SBC 744.543
## -------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
## AIC: Akaike Information Criteria
## SBC: Schwarz Bayesian Criteria
##
## ANOVA
## -----------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## -----------------------------------------------------------------------
## Regression 6535804.090 5 1307160.818 34.217 0.0000
## Residual 1833716.447 48 38202.426
## Total 8369520.537 53
## -----------------------------------------------------------------------
##
## Parameter Estimates
## ------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ------------------------------------------------------------------------------------------------
## (Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
## 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
## ------------------------------------------------------------------------------------------------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.
# stepwise aic backward regression
model <- lm(y ~ ., data = surgical)
k <- ols_step_backward_aic(model)
k##
##
## Stepwise Summary
## -------------------------------------------------------------------------
## Step Variable AIC SBC SBIC R2 Adj. R2
## -------------------------------------------------------------------------
## 0 Full Model 736.390 756.280 586.665 0.78184 0.74305
## 1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
## 2 gender 732.494 748.406 581.290 0.78142 0.75351
## 3 age 730.620 744.543 578.844 0.78091 0.75808
## -------------------------------------------------------------------------
##
## Final Model Output
## ------------------
##
## Model Summary
## -------------------------------------------------------------------
## R 0.884 RMSE 184.276
## R-Squared 0.781 MSE 38202.426
## Adj. R-Squared 0.758 Coef. Var 27.839
## Pred R-Squared 0.700 AIC 730.620
## MAE 137.656 SBC 744.543
## -------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
## AIC: Akaike Information Criteria
## SBC: Schwarz Bayesian Criteria
##
## ANOVA
## -----------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## -----------------------------------------------------------------------
## Regression 6535804.090 5 1307160.818 34.217 0.0000
## Residual 1833716.447 48 38202.426
## Total 8369520.537 53
## -----------------------------------------------------------------------
##
## Parameter Estimates
## ------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ------------------------------------------------------------------------------------------------
## (Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
## bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
## pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
## enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
## liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
## alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
## ------------------------------------------------------------------------------------------------These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.
