Re: hi...


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Re: hi...



Alex Boroda <jumpstart@GIS.NET> writes:

> hi.. i bought a ti-86 recently... i was just wondering if there is a way
> to give it a list of (x,y) coordinates and have it plot a graph... then
> give the equation of the graph... i read the manual that came with the
> calculator and searched the net but was unable to come up with anything.
> ...
> ...

That's an ill-defined problem, since there are _infinitely many_ functions
that take on given values at a particular finite set of inputs -- you could
draw all sorts of curves through a particular set of points.

Some more well-defined problems along this line _can_ be solved, though, and
the TI-86 can be very helpful in delivering quick results. For example, through
two given points there is only one straight line. Through three given points
there is only one vertical parabola that can be drawn. etc. etc. A matrix
calculation will quickly give you the coefficients of the polynomial function
in cases like these.

Through any given set of points there is one _best_ straight line that can be
drawn, in the sense that the line comes closest, overall, to all of the points
in the set. For a number of reasons, the criterion usually chosen here is the
straight line that minimizes the squares of the distances of the points
from the line. Finding this "best fit" line was a classic problem (the "least
squares method") until powerful calculators came along and trivialized the
computation. Nowadays you can go on and speculate that a parabola, or a third-
degree polynomial equation, or an exponential function, etc. might better fit
the particular set of data points that you have at hand, and ask your
calculator to give you the best fit in each of these cases -- and to further
give you an estimate of how close the fit is. It's a wonderful world we live
in...

This topic is called _regression_. I don't have my TI-86 manual at hand, but I
believe the process of calculating the different regression formulas are fairly
well explained in the manual. As with most everything, though, you've got to
be clear on what it is you want to do and why you want to do it before you can
properly address the question of _how_ to do it. Hope the background above
helped a bit.

RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623

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