Hi Paul, William et al.--
This may be ANOTHER GOOD TIME TO COMMENT ON
THE COMMUNICATION PROBLEMS OF STATISTICS (AND OTHER AREAS, TOO).
I suggest that when we use the terms LINEAR and NONLINEAR that we
tell the reader what the SENDER means by those terms.
When I write:
Y = b1*X1 + b2*X2 + ... + bp*Xp + E
where bi (i = 1,2,...p) are least-squares regression coefficients, I
will refer to this as a LINEAR MODEL.
The Xs can be any numbers that I choose-- log(z), ln(z), z^3, cos(z), 1/z, binary
(1or 0), ...
If a person writes the form:
Y = a0 + a1*X + a2*X^2 + a3*X ^3 + E
then they might say that this is a NONLINEAR model.
As long as the reader knows exactly what the model is-- then we are communicating.
In these days of fancy 3D graphic displays, it is interesting to picture the function:
Y = a0 + a1*X + a2*X^2
in the 2D space of Y and X -- which appears as a CURVE.
and then picture the function in the 3D space of Y, X and X^2 or
re-designating X^2 as Z
Y = a0 + a1*X + a2*Z
We notice that the 3D function lies in a PLANE -- reminding us that
we have a "LINEAR MODEL".
If we hurriedly say to someone that "this function is NONLINEAR in the 2D space of Y
and X, but
LINEAR in the 3D space of Y,X and Z", then we might even cause more frustration. :-(
"COMMUNICATION" IS A PROBLEM EVERYWHERE!
DO WILLIAM AND PAUL HAVE THE SAME MEANING FOR "NONLINEAR"?
:-)
--- Joe
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----- Original Message -----
From: Paul Velleman <[EMAIL PROTECTED]>
To: William J. Larson <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>
Sent: Friday, May 05, 2000 6:43 AM
Subject: Re: R sq vs r sq
| At 11:18 AM +0200 05/05/2000, William J. Larson wrote:
| >
| >It appears that R sq is some sort of generalization of r sq
| >for nonlinear cases. True?
| >
| Not really. common convention is to capitalize the R for multiple
| correlation. The R sqr reported in regressions allows for the
| generalization of simple regression to a multiple regression (2 or
| more predictors). In both cases R sqr is the squared correlation
| between y and y-hat. Y-hat represents the best (in the least squares
| sense) fit to y among all linear combinations of the x's. All of
| these are statistics for linear models. It is dangerous to apply them
| to nonlinear models.
|
| -- Paul
| --
| Paul F. Velleman
| Cornell University Data Description, Inc.
| 358 Ives Hall Box 4555
| Ithaca, NY 14853 Ithaca, NY 14852-4555
| (607) 255-4411 (607) 257-1000
| (607) 255-8484 fax (607) 257-4146 fax
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