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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