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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Regression Models
verfasst von : Wolfgang Karl Härdle, Léopold Simar
Erschienen in: Applied Multivariate Statistical Analysis
Verlag: Springer Berlin Heidelberg
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The 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
,…,
x
p
)
⊤
. We have already introduced such models in Chapters
3
and
7
where linear models were written in (
3.50
) as
$$y={\mathcal{X}} \beta + \varepsilon,$$
where
y
(
n
×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
ε
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
${\mathcal{X}}$
.