[R] Terminology: Multiple Regression versus multivariate Reg

[(Ted Harding)]

On 24-Apr-09 08:14:34, strinz at freenet.de wrote:
> Hello R-Members,
> can anyone explain the difference between
> multiple and multivariate regression to me 
> in terms of the terminology and eventually 
> its respect to the mathematical foundation 
> respectively ?
> 
> Is multiple regression perhaps more related to GLM
> and multivariate Regression rather applied,
> if there are no explizit numeric factor levels ?
> 
> Thanks for elucidations on that topic.
> 
> Many thanks and best regrads
> Bjoern

This is indeed a question of terminology and usage, and there
is a degree of variability in it.

As far as I am concerned (and others, though not all), "multivariate
regression" refers to regression where the dependent ("outcome")
variable is mutltivariate:

  Y ~ X

where each instance of Y is a multivariate observation. For example,
suppose G (growth) consists of two pieces of data: height and weight,
and A is Age. Then a multivariate regression model would look like

  G ~ A  or  (Ht,Wt) ~ Age

(two variables on the left, one variable on the right). This allows
for correlation between Ht and Wt to be part of the model.

What is generally meant by "multiple regression" is regression
of a single variable (on the left) on more than one variable
(on the right), for example

  Wt ~ Ht + Age

If you must make a distinction, there is the term "simple regression"
(nowadays rarely used) for when there is only one variable on the right:

  Wt ~ Age

Whether this is a linear model (use lm()) or a generalised linear
model (use glm()) has nothing to do with the termonology.

There is an unfortunate (in my view) tendency for people to use
"multivariate regression" whden talking about what I call "multiple
regression" above (i.e. more than 1 independent variable). I think
this should be reserved for regression where the left-hand side is
multivariate.

But maybe I'm in a minority ...
Ted.

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Date: 24-Apr-09                                       Time: 10:00:23
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