A tutorial on employing StepReg for stepwise regression analysis with four well-known datasets namely the mtcars, remission, lung, and CreditCard. The guild showcases the utility of StepReg across four well-known datasets, employing it for different regression models such as linear, logistic, Cox proportional hazard, and Poisson regression. The vignette elucidates the stepwise process with distinct parameters, offering users a clear understanding of how to effectively utilize StepReg for exploratory data analysis and model building in various regression scenarios.
StepReg 1.5.0
Stepwise regression is a widely employed data-mining technique aimed at identifying a valuable subset of predictors for utilization in a multiple regression model. To facilitate this process, we have developed the R package StepReg. Depending on the nature of the response variable, StepReg facilitates users in conducting linear regression for continuous outcomes, logistic regression for binary outcomes, Cox regression for time-to-event outcomes, and Poisson regression for count outcomes, incorporating popular selection criteria. It provides a versatile set of stop rules available in forward selection, backward elimination, both-direction, and best subset methods.
Here, we applied the StepReg package to four well-established and diverse datasets—mtcars, remission, lung, and CreditCard—utilizing distinct parameters across various regression scenarios. These datasets provide robust test cases for showcasing the capabilities and versatility of the StepReg package in real-world applications. Through practical demonstrations, we illustrated the application of linear stepwise regression for continuous outcomes, logistic stepwise regression for binary outcomes, Cox stepwise regression for time-to-event outcomes, and Poisson stepwise regression for count outcomes. These examples offer users valuable insights into the effective utilization of StepReg for variable selection in different regression scenarios, providing a comprehensive guide for those seeking proficiency in incorporating StepReg into their analytical toolkit.
A breif introduction for four datasets is descripted as below,
mtcars: the mtcars dataset is a classic automotive dataset that provides information on various car models and their performance attributes. With 32 observations and 11 variables, it includes details such as miles per gallon (mpg), horsepower, and the number of cylinders.
remission: the remission dataset is relevant in the context of medical research, specifically in oncology. It captures data related to the remission status of leukemia patients. The dataset includes variables such as cellularity of the marrow clot section, the highest temperature before the start of treatment, and remission status (1 for remission and 0 for non-remission).
lung: the lung dataset is a dataset in the survival analysis domain, containing information related to the survival times of 228 patients with advanced lung cancer. It includes variables such as the patient’s age, the type of treatment received, and survival status.
CreditCard: the CreditCard dataset is associated with credit risk analysis and financial research. It contains information about credit card transactions, including details such as the amount spent, credit limit, and payment status.
A list containing multiple tables will be returned. Names and descriptions of each table are outlined as follows:
Table 1. Summary of Parameters
: This table presents the parameters utilized in stepwise regression along with their default or user-specified values.
Table 2. Variables and Types
: This table outlines the variables and their respective types utilized in the dataset.
Table names prefixed with Table. Selection Process
: This table details overview of the variable selection process. Variables are selected based on information criteria rules, such as AIC, BIC, SBC, IC(1), HQ, etc., where lower values indicate better model fit. The significance levels include SLE for the entry of variables in forward selection and SLS for staying in backward elimination. For Rsq or adjusted R-squared, higher values indicate a better model fit.
Tabel names prefixed with Table. Parameter Estimates
: This table provides summary information for the optimal models.
This section provides 9 examples utilizing distinct parameters across various regression scenarios with the above 4 datasets.
mtcars
Example1: In this analysis, we used
mpg
as the response variable, with all other variables serving as predictors, employing a strategy offorward
and a metric ofAIC
for linear stepwise regression. The analysis involved enforcingdisp
andcyl
to be included in all models.
library(StepReg)
data(mtcars)
formula <- mpg ~ .
exam1 <- stepwise(formula = formula,
data = mtcars,
type = "linear",
include = c("disp","cyl"),
strategy = "forward",
metric = "AIC")
exam1
## Table 1. Summary of Parameters
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Parameter Value
## ——————————————————————————————————————————
## included variable disp cyl
## strategy forward
## metric AIC
## tolerance of multicollinearity 1e-07
## multicollinearity variable NULL
## intercept 1
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 2. Type of Variables
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable type Variable name Variable class
## ——————————————————————————————————————————————
## Dependent mpg numeric
## Independent cyl numeric
## Independent disp numeric
## Independent hp numeric
## Independent drat numeric
## Independent wt numeric
## Independent qsec numeric
## Independent vs numeric
## Independent am numeric
## Independent gear numeric
## Independent carb numeric
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 3. Selection Process under AIC
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect NumberEffectIn NumberParmsIn AIC
## —————————————————————————————————————————————————————————————————————————————————————
## 0 1 0 1 149.943449990894
## 0 disp cyl -2 3 108.33357089067
## 1 wt 3 4 98.7462938182664
## 2 hp 4 5 97.5255371708581
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 4. Parameter Estimates for mpg under AIC
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate Std. Error t value Pr(>|t|)
## ——————————————————————————————————————————————————————————————————————————————————————————————
## (Intercept) 40.8285367422432 2.75746792810596 14.8065318642844 1.76140221350856e-14
## disp 0.0115992393009777 0.0117268091002486 0.989121525030348 0.331385561864358
## cyl -1.29331972351378 0.655876754872712 -1.97189443581482 0.0589468066844992
## wt -3.85390352303833 1.01547364107822 -3.79517829625422 0.000758947039357617
## hp -0.020538376368824 0.0121467704321512 -1.69085078898512 0.102379131471602
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Visulization of the selection process using information criteron
AIC
.
plot(exam1)
Example2: In this illustration, we maintained
mpg
as the response variable, while designating the other variables as predictors. The chosen strategy wasbidirectional
withAIC
,AICc
,BIC
,HQ
,HQc
,SBC
, andSL
as the stopping criterion, and the significance levels for entry (sle
) and stay (sls
) were both set to 0.05 parallelly. The analysis involved removingintercept
from the model. The specific characteristics of the data and the goals of the analysis in each subject area require users to choose different stepwise regression method and selection criteria. Users can compare all metics through the output list or the plots.
formula <- mpg ~ . + 0
exam2 <- stepwise(formula = formula,
data = mtcars,
type = "linear",
strategy = "bidirection",
metric = c("AIC","SBC","SL","AICc","BIC","HQ","HQc"),
sle = 0.05,
sls = 0.05)
exam2
## Table 1. Summary of Parameters
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Parameter Value
## ————————————————————————————————————————————————————————————————————————
## included variable NULL
## strategy bidirection
## metric AIC & SBC & SL & AICc & BIC & HQ & HQc
## entry significance level (sle) 0.05
## stay significance level (sls) 0.05
## test method F
## tolerance of multicollinearity 1e-07
## multicollinearity variable NULL
## intercept 0
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 2. Type of Variables
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable type Variable name Variable class
## ——————————————————————————————————————————————
## Dependent mpg numeric
## Independent cyl numeric
## Independent disp numeric
## Independent hp numeric
## Independent drat numeric
## Independent wt numeric
## Independent qsec numeric
## Independent vs numeric
## Independent am numeric
## Independent gear numeric
## Independent carb numeric
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 3. Selection Process under AIC
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect NumberEffectIn NumberParmsIn AIC
## —————————————————————————————————————————————————————————————————————————————————————
## 0 0 0 0 Inf
## 1 drat 1 1 131.940615397799
## 2 carb 2 2 112.874977003721
## 3 gear 3 3 105.767914676203
## 4 hp 4 4 105.399654906399
## 5 qsec 5 5 105.277861812131
## 6 wt 6 6 100.437613232709
## 7 hp 5 5 98.4440186423183
## 8 am 6 6 97.8009315992234
## 9 gear 5 5 96.5751826224886
## 10 carb 4 4 96.0485980614551
## 11 drat 3 3 95.418690850739
## 12 disp 4 4 95.3954043177414
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 4. Selection Process under SBC
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect NumberEffectIn NumberParmsIn SBC
## —————————————————————————————————————————————————————————————————————————————————————
## 0 0 0 0 Inf
## 1 drat 1 1 99.4063513005992
## 2 carb 2 2 81.8064488093206
## 3 gear 3 3 76.1651223846019
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 5. Selection Process under SL
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect NumberEffectIn NumberParmsIn SL
## —————————————————————————————————————————————————————————————————————————————————————————
## 0 0 0 0 1
## 1 drat 1 1 2.44913223058495e-22
## 2 carb 2 2 1.03775546495333e-05
## 3 gear 3 3 0.00438861027007104
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 6. Selection Process under AICc
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect NumberEffectIn NumberParmsIn AICc
## —————————————————————————————————————————————————————————————————————————————————————
## 0 0 0 0 Inf
## 1 drat 1 1 132.354408501248
## 2 carb 2 2 113.732119860864
## 3 gear 3 3 107.249396157684
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 7. Selection Process under BIC
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect NumberEffectIn NumberParmsIn BIC
## —————————————————————————————————————————————————————————————————————————————————————
## 0 0 0 0 Inf
## 1 drat 1 1 97.7553842586695
## 2 carb 2 2 79.2794817092699
## 3 gear 3 3 72.9946131788242
## 4 hp 4 4 72.9415244192211
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 8. Selection Process under HQ
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect NumberEffectIn NumberParmsIn HQ
## —————————————————————————————————————————————————————————————————————————————————————
## 0 0 0 0 Inf
## 1 drat 1 1 96.0182982097902
## 2 carb 2 2 75.0303426277027
## 3 gear 3 3 66.0009631121751
## 4 hp 4 4 63.7103861543619
## 5 qsec 5 5 61.6662758720848
## 6 wt 6 6 54.9037101046532
## 7 hp 5 5 54.8324327022722
## 8 am 6 6 52.2670284711681
## 9 disp 7 7 51.5596073775111
## 10 hp 8 8 50.5198981811353
## 11 carb 7 7 50.5007045958875
## 12 cyl 8 8 50.3437098642926
## 13 carb 9 9 50.2608086854785
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 9. Selection Process under HQc
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect NumberEffectIn NumberParmsIn HQc
## —————————————————————————————————————————————————————————————————————————————————————
## 0 0 0 0 Inf
## 1 drat 1 1 96.0263343627548
## 2 carb 2 2 75.052537716843
## 3 gear 3 3 66.0441202299477
## 4 hp 4 4 63.7820933654303
## 5 qsec 5 5 61.7750318088718
## 6 wt 6 6 55.0590757286348
## 7 hp 5 5 54.9411886390593
## 8 am 6 6 52.4223940951496
## 9 disp 7 7 51.7723907320945
## 10 hp 8 8 50.802381133829
## 11 carb 7 7 50.713487950471
## 12 cyl 8 8 50.6261928169863
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 10. Parameter Estimates for mpg under AIC
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate Std. Error t value Pr(>|t|)
## ———————————————————————————————————————————————————————————————————————————————————————————
## qsec 1.70550996283541 0.127485704584404 13.3780486870687 1.09964868080962e-13
## wt -4.61279456246674 1.15817323630342 -3.98281916545536 0.000440008628764359
## am 4.18085430467977 1.01361607335742 4.12469219320039 0.000300527233592535
## disp 0.0120200576653963 0.0088914542638529 1.35186633240215 0.187238258962162
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 11. Parameter Estimates for mpg under SBC
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate Std. Error t value Pr(>|t|)
## —————————————————————————————————————————————————————————————————————————————————————————
## drat 3.85142334610757 1.0678868653112 3.6065836852345 0.00115059878350687
## carb -2.36055514388328 0.350142761922923 -6.74169339077442 2.12967212881877e-07
## gear 3.4883542511301 1.12895206584177 3.08990466174409 0.00438861027007103
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 12. Parameter Estimates for mpg under SL
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate Std. Error t value Pr(>|t|)
## —————————————————————————————————————————————————————————————————————————————————————————
## drat 3.85142334610757 1.0678868653112 3.6065836852345 0.00115059878350687
## carb -2.36055514388328 0.350142761922923 -6.74169339077442 2.12967212881877e-07
## gear 3.4883542511301 1.12895206584177 3.08990466174409 0.00438861027007103
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 13. Parameter Estimates for mpg under AICc
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate Std. Error t value Pr(>|t|)
## —————————————————————————————————————————————————————————————————————————————————————————
## drat 3.85142334610757 1.0678868653112 3.6065836852345 0.00115059878350687
## carb -2.36055514388328 0.350142761922923 -6.74169339077442 2.12967212881877e-07
## gear 3.4883542511301 1.12895206584177 3.08990466174409 0.00438861027007103
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 14. Parameter Estimates for mpg under BIC
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate Std. Error t value Pr(>|t|)
## ————————————————————————————————————————————————————————————————————————————————————————————
## drat 4.30273288409265 1.09158280873171 3.94173749318379 0.000491150652824566
## carb -1.73804836219828 0.54597600366577 -3.18337866596471 0.00355127557199684
## gear 3.17367474781416 1.12779616721381 2.81404994987227 0.00885014913869611
## hp -0.0155479574747606 0.0106015597450293 -1.46657264107297 0.153634601937481
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 15. Parameter Estimates for mpg under HQ
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate Std. Error t value Pr(>|t|)
## ————————————————————————————————————————————————————————————————————————————————————————————
## drat 1.24018628116636 1.43081088945576 0.866771626009983 0.395019989028695
## gear 1.05507041373944 1.31730971553748 0.800928135042981 0.431369721203034
## qsec 1.21092335916019 0.39825927287781 3.0405402752084 0.00580910211687029
## wt -3.8393173477773 1.81635802262831 -2.11374481239207 0.0455922405971267
## am 2.78900560523413 1.87631320367996 1.48642859825542 0.15074627783938
## disp 0.013377487347384 0.0171483102637304 0.780105278108835 0.443283496072846
## hp -0.0200206683398262 0.0202056393976394 -0.990845572655583 0.332071276534613
## cyl 0.314427335966453 0.637410972654929 0.493288238601867 0.626486125552571
## carb -0.269382366878572 0.791924966403595 -0.340161477800012 0.736822040562188
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 16. Parameter Estimates for mpg under HQc
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate Std. Error t value Pr(>|t|)
## ————————————————————————————————————————————————————————————————————————————————————————————
## drat 1.15464081893128 1.38234393696422 0.835277522515128 0.411799846499336
## gear 0.86861885215473 1.17558240530996 0.738883848747045 0.467142793848725
## qsec 1.30385655642974 0.28438801586838 4.58478024275534 0.000119371208464951
## wt -4.28678423131556 1.22920122659441 -3.48745521772087 0.00190040875483783
## am 2.83676935913337 1.83625846165786 1.54486387312394 0.135464286600943
## disp 0.0173369535398226 0.0123585220697692 1.40283388595724 0.173471044902963
## hp -0.0236106906721794 0.0169099008757928 -1.39626428597101 0.175416642765162
## cyl 0.25167003723096 0.598781514963363 0.420303618167569 0.678003000841066
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Visulization of the selection process using
bidirection
strategy under information criteronAIC
,AICc
,BIC
,HQ
,HQc
,SBC
, andSL
withsle
=0.05 andsls
=0.05.
plot(exam2)