Good message, Alan --
As you indicate, the model is LINEAR in the coefficients b0, b1, b2, b3
and in the 4-D space of y,x1,x2,x3(i.e., x1*x2) the function lies in a PLANE.
But in the 3-D space of y,x1,x2 the surface is TWISTED ( not in
a PLANE).
-- Joe
----- Original Message -----
From: Alan McLean <[EMAIL PROTECTED]>
To: Wen-Feng Hsiao <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>
Sent: Sunday, April 16, 2000 4:01 PM
Subject: Re: linear model or interactive model?
| The model
|
| y = b0 + b1 * x1 + b2 * x2 + b3 * x1*x2
|
| is a nonlinear model, just as in engineering. However, it is 'linear in the
| variables'. In statistics this is useful, because in estimating the model from a
| data set, one can define a 'new' variable x3 = x2*x2 and apply, for example, a
| linear regression algorithm.
|
| But in interpreting the results you have to remember that the model is nonlinear!
|
| Regards,
| Alan
|
|
|
|
|
| Wen-Feng Hsiao wrote:
|
| > Dear Hartig,
| >
| > Thanks for your reply. I am sorry for my poor knowledge in statistics.
| > But I wonder why the definition of 'linearity' of statistics is different
| > from that of engineering mathematics, which defines 'linear' as:
| >
| > Each unknown xj appears to the first power only, and that there are no
| > cross product terms xi*xj with i!=j.
| >
| > Wen-Feng
| >
| > In article <[EMAIL PROTECTED]>,
| > [EMAIL PROTECTED] says...
| > > Generally, you can include an interaction (or moderator) term in a linear
| > > model, like
| > > y = b0 + b1 * x1 + b2 * x2 + b3 * x1*x2,
| > > and the model still is linear. If you decide not to include x1 and x2, like
| > > y = b0 + b1 * x1*x2,
| > > you still have a linear model.
| >
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|
| --
| Alan McLean ([EMAIL PROTECTED])
| Department of Econometrics and Business Statistics
| Monash University, Caulfield Campus, Melbourne
| Tel: +61 03 9903 2102 Fax: +61 03 9903 2007
|
|
|
|
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===========================================================================
This list is open to everyone. Occasionally, less thoughtful
people send inappropriate messages. Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.
For information about this list, including information about the
problem of inappropriate messages and information about how to
unsubscribe, please see the web page at
http://jse.stat.ncsu.edu/
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