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Model-free Study of Ordinary Least Squares Linear Regression
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In this article, a unified viewpoint on the implications of misspecification of OLS linear regression is presented, with the aim of making the various implications of missing covariates stand out.Abstract:
Ordinary least squares (OLS) linear regression is one of the most basic statistical techniques for data analysis. In the main stream literature and the statistical education, the study of linear regression is typically restricted to the case where the covariates are fixed, errors are mean zero Gaussians with variance independent of the (fixed) covariates. Even though OLS has been studied under misspecification from as early as the 1960's, the implications have not yet caught up with the main stream literature and applied sciences. The present article is an attempt at a unified viewpoint that makes the various implications of misspecification stand out.read more
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TL;DR: In the presence of heteroscedasticity, ordinary least squares (OLS) estimates are unbiased, but the usual tests of significance are generally inappropriate and their use can lead to incorrect inferences.