Re: Modeling Data...Linear or direct proportion?

[Phil Parker <PPARKER@TWSUVM.UC.TWSU.EDU>]

> Date:    Mon, 23 Nov 1998 00:10:16 -0500
> From:    David Simmons <dsimmon@UOFT02.UTOLEDO.EDU>
>
> [dele]
> nice linear data which they graph and model in the form y  =  mx + b.
> (F = mass x acceleration + friction). The y-intercept is the cart's
> friction. In talking about the straight line graph of a vs F, I used
> the term "directly proportional" to describe the relationship between
> F and a.
>
> My question is, what do I correctly call the relationship between F
> and 'a' as graphed[?] Is just "linear" the right term to use? Is there
> another name I should use?
The truly correct term is "affine," but "linear" is near-universal in
practice.
   In one dimension, strict linearity and direct proportion (or, much
less commonly or correctly, direct variation) are the same. But in
two or more dimensions, the additivity of (strict) linearity allows
more than just scalar multiples and they part company.
   Getting back to your equation again, in linear algebra one also uses
the term "inhomogeneous linear" for such equations. But then the others
become "homogeneous linear" and the general "linear" refers
indifferently to either.
   So it looks like the final answers are "affine," "yes," and "yes,"
respectively, to your questions I quoted above.

*************************
Phil Parker                            Email: pparker@twsuvm.uc.twsu.edu
Math. Dept., Wichita St. Univ.           Fax: 316-978-3748
   I find [in mathematics] a wonderful beauty. This is no science,
   this is art, where equations fall away to elements like resolving
   chords, and where always prevails a symmetry either explicit or
   multiplex, but always of a crystalline serenity.
                                      ---Turjan of Miir (Jack Vance)