On 13 Jul 2001, Jonty Tuffin wrote:
> Hi, I'm trying to represent the data of a simple bar graph as a single,
> curved line. How do I do this?
See Chapter 5 of Draper & Smith, Applied Regression Analysis (2nd ed.),
and references therein. They deal explicitly only with representing a
function as a series of joined straight lines, but they give a number
of references (in the back of the book) that deal with more complex
kinds of splines.
Before entering upon intricate means of fitting curves to data, you
might usefully ask yourself why you want to do this, and whether it is
appropriate to try to do it with the data you have.
Here are some questions you should address before you proceed further:
1. How many bars are there in the graph? (If there are only 3 or 4,
no curvilinear function is going to be estimated very precisely, and
this is particularly true of empirical spline-type functions. If
there are a dozen or a score or more, you can be a more optimistic.)
2. How many data values are represented in the data set?
(This affects how precisely you know the length of the bars, and
therefore what kind of noise level is associated with any empirical
-- or theoretical, for that matter -- functions.)
3. How are the different bars related to each other? (If they are
only categories, the whole enterprise is meaningless. If they are
ordinal, but arguably not interval, the enterprise _may_ be suspect,
although perhaps not entirely meaningless. If they are of interval or
ratio scale, fitting a curve may be a sensible thing to attempt.)
4. Are piecewise linear fits inadequate or unacceptable?
(And are you _sure_ about that?)
5. Is there perhaps some reason, although you haven't mentioned one,
for wanting to fit a particular kind of function to the data?
(If so, you should try to fit such a function directly, and avoid
purely empirical approaches (e.g., splines) like the plague.)
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
184 Nashua Road, Bedford, NH 03110 603-471-7128
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