Re: multiple regression (intercept)

illywhacker wrote: 
Hi Anon.

"Anon." <bob.ohara@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> a ,crit dans le message de
news: 42D629FE.9030201@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

illywhacker wrote:

"thierry" <colorado@xxxxxxxxxxxx> a écrit dans le message de news:
kAiBe.9900$qg1.786183@xxxxxxxxxxxxxxxxxxxxxxxx

I ask this question because I have a negative intercept in my equation (Y
= -2000 + 544*var1 + 1166*var2 - 487*var3), in my case intercept doesn't
mean anything.



Either way, if you know these things, you must impose the constraint,
otherwise you will end up with nonsense.


I think you're being excessive here: you can get nonsense if you impose a
constraint too.

One can fit a model without an intercept, but this is usually advised
against.  The model assumes that the response varies linearly with the
covariates.  This is probably not precisely true, but may well be good
enough over the range of the data. (as an aside: this should be checked,
e.g. by plotting the residuals against the covariates)  If there is
non-linearity outside the range of the data, it won't be picked up in the
analysis.  If you force the fit through the intercept, you can get a very
misleading model, that is wrong everywhere, rather than just at one point.



Well, the model with intercept is not just wrong at one point, but over a
range of values where the behaviour is nonlinear. In this case, it seems
that the OP is rather concerned with the region near the origin where the
behaviour may be nonlinear, in which case the linear model with intercept is
not of much use. Neither of course will the linear model without intercept
be of much use if it does not correspond well with the behaviour. The
solution is to use a better model, or several models, and to make model
choices.

I interpreted the OP's question as one where he had noticed something that seemed silly, but there was nothing in his comments to suggest that his data was anywhere near this region of the parameter space. If it's nowhere near, and the linear model seems to fit OK, then I would suggest not worrying about it. OTOH, if the linear model doesn't fit OK, or if the OP is intending to use the model near to the origin, then yes, he should improve the model. One problem is that if there's no data near the origin, then it's difficult to see how to select a better model: there's no information in the data in that part of the parameter space.

Bob

--
Bob O'Hara

Dept. of Mathematics and Statistics
P.O. Box 68 (Gustaf H„llstr”min katu 2b)
FIN-00014 University of Helsinki
Finland

Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax:  +358-9-191 51400
WWW:  http://www.RNI.Helsinki.FI/~boh/
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.

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