Wen-Feng-
The term LINEAR is a difficult term.
As I mentioned to you in an earlier message (included for
reference as the end of this message),
a LINEAR STATISTICAL MODEL is "LINEAR" in the unknown
coefficients, a1, a2,... ap in the model:
Y = a1*X1 + a2*X2 + ... + ap*Xp + E
The X predictors can be ANY NUMBERS THAT WE LIKE.
If we write --
Y = a1*U + a2*X + a2*X^2 + E
where
U = 1
X = a continuous predictor
X^2 = X*X
E = error or residual
we might say that the function is NON-LINEAR in the two-dimensional, Y-X plane,
but it is LINEAR in the three dimensional space of Y-X-X^2. With 3-D displays that we
can rotate as we would like, it is enlightening to observe that the CURVE seen in the
two-dimensional
space lies in a PLANE in the three-dimensional space of Y-X-X^2.
-- Joe
************************************************************************
* Joe Ward Health Careers High School *
* 167 East Arrowhead Dr 4646 Hamilton Wolfe *
* San Antonio, TX 78228-2402 San Antonio, TX 78229 *
* Phone: 210-433-6575 Phone: 210-617-5400 *
* Fax: 210-433-2828 Fax: 210-617-5423 *
* [EMAIL PROTECTED] *
* http://www.ijoa.org/joeward/wardindex.html *
************************************************************************
----- Original Message -----
From: Wen-Feng Hsiao <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Saturday, April 15, 2000 5:14 AM
Subject: Re: linear model or interactive model?
| 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.
|
============================
----- Original Message -----
From: Joe Ward <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>; Wen-Feng Hsiao <[EMAIL PROTECTED]>
Sent: Thursday, April 13, 2000 10:30 AM
Subject: Re: linear model or interactive model?
----- Original Message -----
From: Wen-Feng Hsiao <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Thursday, April 13, 2000 3:06 AM
Subject: linear model or interactive model?
| Dear all,
|
| Suppose I have an aggregation model which is in the following form:
| Y = c1*(X11 * X12) + c2*(X21 * X22)?
|
| This model could be thought as an aggregation of two knowledge, namely
| X1. and X2.. Each knowledge contains two pieces of information
| (attributes). For example, X1 contains X11 ans X12. Now if X.1 is the
| height, and X.2 is the weight of a person. Then, the aggregation of any
| two persons, say, Student1(height=170cm, weight=60kg),
| Student2(height=180cm, weight=68kg) can be represented by
|
| Y = 170*60+180*68=22440.
|
| My question: a model as the above form is linear or interactive? I doubt
| it is not a linear model. Since it is not in this form: Y= c1 X1 + c2 X2,
| where c1 and c2 are constant. I doubt it is not a pure interactive form,
| since X.1 and X.2 are dependent. Sorry for this stupid question.
|
| Wen-Feng
|
==== Joe Ward writes|
===========================================================================
Wen-Feng---
Your model --
Y = X11 * X12 + X21 * X22.
does not have any unknowns.
Did you mean to write:
Y = c1*(X11 * X12) + c2*(X21 * X22)?
All models of the form:
Y = c1*X1 + c2*X2 + ... + cp*Xp + E
are LINEAR MODELS.
It does not matter what NUMBERS are included in the Xs.
Y = c1*X1 + c2*X2 + c3*(X1*X2) + c4*(X1^2) + c5*(lnX1) + E
is LINEAR in the unknown coefficients c1, c2, ...
The most useful Xs are the BINARY( 1 or 0) predictors.
--- Joe
************************************************************************
* Joe Ward Health Careers High School *
* 167 East Arrowhead Dr 4646 Hamilton Wolfe *
* San Antonio, TX 78228-2402 San Antonio, TX 78229 *
* Phone: 210-433-6575 Phone: 210-617-5400 *
* Fax: 210-433-2828 Fax: 210-617-5423 *
* [EMAIL PROTECTED] *
* http://www.ijoa.org/joeward/wardindex.html *
************************************************************************
===========================================================================
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/
===========================================================================
