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gilmour (version 0.1.1)

The Interpretation of Adjusted Cp Statistic

Description

Several methods may be found for selecting a subset of regressors from a set of k candidate variables in multiple linear regression. One possibility is to evaluate all possible regression models and comparing them using Mallows's Cp statistic (Cp) according to Gilmour original study. Full model is calculated, all possible combinations of regressors are generated, adjusted Cp for each submodel are computed, and the submodel with the minimum adjusted value Cp (ModelMin) is calculated. To identify the final model, the package applies a sequence of hypothesis tests on submodels nested within ModelMin, following the approach outlined in Gilmour's original paper. For more details see the help of the function final_model() and the original study (1996) .

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Version

Install

install.packages('gilmour')

Version

0.1.1

License

GPL-3

Maintainer

Josef Dolejs

Last Published

July 10th, 2025

Functions in gilmour (0.1.1)

final_model

The function calculates all models and find final model according Gilmour
crit

This data contains critical values for testing at the significance level 5 Data published in the original article. Crit was taken from the original study (see Table2). Values in Crit were recalculated by Josef Dolejs for more possible steps of freedom
Gilmour9p

Ilustrative data published in the original article (House prices) Data with the practical meaning Gilmour9p was taken from the original study (see Table1).
Parks5p

number of visitors in parks, citation: Stemberk Josef, Josef Dolejs, Petra Maresova, Kamil Kuca. Factors affecting the number of Visitors in National Parks in the Czech Republic, Germany and Austria. International Journal of Geo-Information. ISPRS Int. J. Geo-Inf. 2018, 7(3), 124; doi:10.3390/ijgi7030124 data has real meaning
EU2019

illustrative econometric data from Eurostat for 5 variables in 17 countries in 2019 columns: Country, LifExp , HDP, Unempl, Obesity, APassangers remove the first column: rownames(EU2019)= EU2019[,1]; EU2019=EU2019[,-1] data has real meaning
Modified_Gilmour9p

special illustrative data if more than two tests are done in the loop in the function final_model() original Gilmour table was modified data has no real meaning
Patents5p

number of patents in universities, citation: Maresova Petra, Soukal Ivan, Stemberkova Ruzena, Selamat Ali Perspective and Suitable Research Area in Public Research-Patent Analysis of the Czech Public Universities Education and Urban Society, 54(7), Maresova Petra, Soukal Ivan, Stemberkova Ruzena, Selamat Ali data has real meaning
submodels

The function calculates all possible submodels and find model with the minimal value of Cp according Gilmour
T1

T1 contains simulated data without real meaning the null hypothesis is not rejected in the first test it illustrates the situation if full model is final model data has no real meaning
T2

T2 illustrates the situation if the loop of tests is finished by the Trivial model data has no practical meaning
Trivial

Trivial illustrates the situation if the Trivial model is model_min without testing process data has no real meaning