Regression Models

Wolfgang Karl Härdle () and Leopold Simar
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Wolfgang Karl Härdle: Humboldt-Universität zu Berlin, Ladislaus von Bortkiewicz Chair of Statistics

Chapter Chapter 8 in Applied Multivariate Statistical Analysis, 2019, pp 233-259 from Springer

Abstract: Abstract The main aim of regression models is to model the variation of a quantitative response variable y in terms of the variation of one or several explanatory variables $$(x_1,\ldots ,x_p)^{\top }$$. We have already introduced such models in Chap. 3 and 7 , where linear models were written in ( 3.50 ) as $$y=\mathcal{{X}} \beta + \varepsilon ,$$where $$y (n\times 1)$$ is the vector of observation for the response variable, $$\mathcal{{X}} (n\times p)$$ is the data matrix of the p explanatory variables and $$\varepsilon $$ are the errors. Linear models are not restricted to handle only linear relationships between y and x. Curvature is allowed by including appropriate higher order terms in the design matrix $$\mathcal{{X}}$$.

Date: 2019
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DOI: 10.1007/978-3-030-26006-4_8

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