Re:Fitting data on a vertical line

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1649] Re:Fitting data on a vertical line
• From: rubin at msu.edu (Paul A. Rubin)
• Date: Sat, 8 Jul 1995 05:05:34 -0400
• Organization: Michigan State University

```In article <3t2ips\$mie at news0.cybernetics.net>,
phpull at unix1.sncc.lsu.edu (Joe Wade Pulley) wrote:
[snip]
->	Thirdly, I did not mean to say that the slope of the line
->should have been +Infinity or -Infinity, just that the program should
->return some sort of inderminate result.  How do you define
->"mathematically correct"?  I believe that if you try a function which
->has an extremely large slope and intercept which is large and of
->opposite sign you will find that the sum of the square of the
->deviations approaches zero as the slope increases towards vertical.

Nope.  The sum of squared deviations cannot fall below the variance of the
dependent data (since the independent variable is the same in all
observations).  I suspect you may be thinking of the deviations as the
orthogonal distance from the points to the line.  They're not - they are
the _vertical_ distance.  No matter what slope you give the line (other
than vertical), the only point on the line which comes into play is the
point where it crosses the vertical line containing the sample.  (A
vertical fitted line is ruled out because it is not the plot of a
function.)

->It is of course impossible to accurately fit the data, but to fit it
->in this manner seems to me to be quite silly.  I think that in all
->cases the desire is to produce a fit which best fits the data.  In
->this case there is no line of the form y=mx+b which fits any more
->realistically than any other line.  Certainly you can minimize one
->parameter or other according to some scheme, but do you really have a
->good result when you get done?  There is a joke about a
->mathematician, an engineer and a physicist in a burning hotel, but I
->can't remember how it goes which is really appropriate here.
->Anyway, the result that was given may have been mathematically
->correct, but physically it was about as far off as could be and it
->cost me an entire week of work because it gave me an answer which
->was close to what I expected, but in the end, it wasn't worth
->anything.  Had the system given me an indertiminate result or said
->"you Idiot, you can't do that" or something, it would have been much
->better.

I agree that the package should warn that the solution is not unique (which
occurs iff the independent data is multicollinear, which happened here).

**************************************************************************
* Paul A. Rubin                                  Phone: (517) 432-3509   *
* Department of Management                       Fax:   (517) 432-1111   *
* Eli Broad Graduate School of Management        Net:   RUBIN at MSU.EDU    *
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Mathematicians are like Frenchmen:  whenever you say something to them,
they translate it into their own language, and at once it is something
entirely different.                                    J. W. v. GOETHE

```

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