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Multiple Linear Regression

Published online by Cambridge University Press:  23 January 2015

G. Grégoire
G. Grégoire*
Affiliation:
Laboratory LJK, Grenoble University, BP. 53, 38041 Grenoble Cedex 09, France
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Abstract

This chapter deals with the multiple linear regression. That is we investigate the situation where the mean of a variable depends linearly on a set of covariables. The noise is supposed to be gaussian.

We develop the least squared method to get the parameter estimators and estimates of their precisions. This leads to design confidence intervals, prediction intervals, global tests, individual tests and more generally tests of submodels defined by linear constraints.

Methods for model's choice and variables selection, measures of the quality of the fit, residuals study, diagnostic methods are presented. Finally identification of departures from the model's assumptions and the way to deal with these problems are addressed.

A real data set is used to illustrate the methodology with software R.

Note that this chapter is intended to serve as a guide for other regression methods, like logistic regression or AFT models and Cox regression.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 66: Statistics for Astrophysics Methods and Applications of the Regression , 2014 , pp. 45 - 72
Copyright
© EAS, EDP Sciences, 2015

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