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Re:Fitting data on a vertical line
*To*: mathgroup at christensen.cybernetics.net
*Subject*: [mg1596] Re:Fitting data on a vertical line
*From*: phpull at unix1.sncc.lsu.edu (Joe Wade Pulley)
*Date*: Tue, 4 Jul 1995 00:58:24 -0400
*Organization*: Louisiana State University
I am a bit amazed at the responses that people have given to my
question.
First, I would not have asked the program to fit the data had
I known that the points were all going to be on the same vertical
line. I knew that the x-coordinates of all the points were close,
but I did not know that they were identical.
Secondly, I DID plot the results, and because all of the
points were closely spaced vertically in the REAL application(not the
fabricated data I used to ask the question) I received a plot that
looked almost exactly like I expected.
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.
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.
Lastly, If you change one of the x coordinate values by even
an infinitesimal amount, the program returna a "correct" result.
While I understand the concept of minimizing things as Mr. Whithoff
says, I think that some real thought should be given to those
instances when the standard algorithm produces a result which is not
the standard answer.
P.S. I took the data to a simple linear least squares
fitting program which we use here in our laboratory classes to see
what result it gave. Though it is not as "smart" as mathematica, it
did realize that the data could not be fit with the y=mx+b form and
gave an indeterminate result. Is it too much to ask for Mathematica
to do the same?
Frustrated,
--
Joe Wade Pulley Department of Physics and Astronomy
Louisiana State University
Baton Rouge, LA 70803 phpull at unix1.sncc.lsu.edu
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