# Covariate Selection Based on a Assumpton-free Approach to Linear Regression with Exact Probabilities

@inproceedings{Davies2019CovariateSB, title={Covariate Selection Based on a Assumpton-free Approach to Linear Regression with Exact Probabilities}, author={Laurie Davies and Lutz Dumbgen}, year={2019} }

In this paper we give a completely new approach to the problem of covariate selection in linear regression. A covariate or a set of covariates is included only if it is better in the sense of least squares than the same number of Gaussian covariates consisting of i.i.d. N(0, 1) random variables. The Gaussian P-value is defined as the probability that the Gaussian covariates are better. It is given in terms of the Beta distribution, it is exact and it holds for all data. The covariate selection…

## One Citation

Linear Regression, Covariate Selection and the Failure of Modelling

- Mathematics
- 2021

It is argued that all model based approaches to the selection of covariates in linear regression have failed. This applies to frequentist approaches based on P-values and to Bayesian approaches…

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