Re: Fitting Data

Robert wrote:
"John D'Errico" <woodchips@xxxxxxxxxxxxxxxx> wrote in
message <fhfiha$lro$1@xxxxxxxxxxxxxxxxxx>...
"Robert " <robert.sochon@xxxxxxxxxxxxxxxxxx> wrote in
message <fhfgen
$nif$1@xxxxxxxxxxxxxxxxxx>...
I have some noisy(ish) data from an experiment, I would like
to plot this data and plot a line of best fit through it! -
easyish - I think!

My data is long and messy, but It should follow the
equation,
y = k * x ^ (3/2)

The problem is the 3/2 and the fact that it should lack a
constant. polyfit gives me hassle, but I think I have
managed it. I have tried logging the data too, and this just
only confuses me.
If x and y are columns, and x is non-negative

k = (x.^(3/2)) \ y;

John


Sorry - I'm confused, I can calculate 'k' just that deciding
when K deviates from the data is now the problem, I suppose
you could write the question as "what is the data sample
length that fits the curve y =k*x(3/2)?" - this leaves two
unknows! - "k" and a the length of "x".

My curve starts off with a curving section upwards, and then
turns to a straight line, by plotting R i can work out when
the curve ceases to be a straight line (downwards from the
top), but working upwards to where the curve stops fitting
the initial equation and turns to the transition region is
proving more difficult.

Sorry... I think my question wasn't clear enough!

That would be an iterative procedure then -- if you don't need to have it fully automated, I'd start by plotting the data to visually select a starting breakpoint.

After that, you would have to fit the two sections, compute the overall residual, and move the breakpoint one direction or the other and repeat until you locate a minimum.

There are procedures for this, whether any are implemented in the Matlab Statistic and/or Curve Fitting toolbox(es) or not, I don't know; or, of course, whether you have either. A common-enough problem that might have some code at the Code Exchange, too.

--
.

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