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Calculate spline using points, with error bars

Posted on 2007-11-15
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Last Modified: 2008-02-01
I have a set of points and I want to draw a curve through it.
I can use a spline (y = ax^3 + by^2 + cx + d) to do that.

Each point has a error bar associated with it (+/- some value).
Can this (or should this) be used in calculation of the spline?
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Question by:allelopath
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12 Comments
 
LVL 27

Expert Comment

by:d-glitch
ID: 20290513
You should probably just plot the spline curve and include the error bars.
This is pretty standard practice.

You might plot three curves:  nominal, max, and min.
This is not standard.

What is your data?  And what are you trying to prove?
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LVL 1

Author Comment

by:allelopath
ID: 20290625
A question about including the error bar with the spline.

Suppose a data point of (3,4) with error of +/- 1
(so a valid point is anywhere from (3,3) to (3,5) )
Then the spline is estimated and at that point the curve goes through (3,4.5)
So then (3,4.5) +/- 1 is between (3,3.5) and (3,5.5)
This doesn't seem right in that the 5.5 is beyond the 5
or is this just the way it works?
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LVL 27

Expert Comment

by:d-glitch
ID: 20291101
What is your data?  Not the numbers, but the meaning of the numbers.

Where do the error bars come from?  

Do you really have the same +/- 1 errors on both the x- and y-axis??
That is a little unusual.  
Wouldn't that give you a unit circle around (3, 4) rather than a square?

A spline should actually go through what ever points you specify -- (3, 4) not (3, 4.5).
Your error bars (or circle) should apply to the original data, not the fitted curve.
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by:allelopath
ID: 20292039
>>A spline should actually go through what ever points you specify -- (3, 4) not (3, 4.5).
Oh, you're right. duh.
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Accepted Solution

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d-glitch earned 450 total points
ID: 20292206
You might try to fit a line (or some other curve) to your data using a least squares regression.

In that case, it is possible for the curve to miss the data point and the error bar entirely.  

This would suggest

EITHER  
Your error bars are too small.  ==>  You don't understand the limits of your measurement.

OR
You have chose the wrong type of fit.  ==>  You don't understand the underlying process.
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LVL 1

Author Comment

by:allelopath
ID: 20292228
Ok, so I think there is smoothing and there is interpolation. With interpolation (as in a cubic spline) the curve will go through the data points, with smoothing, the curve may miss the data point. Correct?
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LVL 27

Expert Comment

by:d-glitch
ID: 20292366
Smoothing implies some sort of fitting or averaging of the data.
And yes, the resultant curve may not hit any of the data points.

Curve fitting implies something else.  Perhaps assuming some kind of relationship among the data points.
And a fitted curve need not pass though any of the data either.

With interpolation (linear or cubic), the curve hits all the data points and you make assumptions between points.
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LVL 84

Assisted Solution

by:ozo
ozo earned 50 total points
ID: 20292646
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LVL 1

Author Comment

by:allelopath
ID: 20293629
Another semantics/terminology question
Does 'spline' imply interpolation (curve hits all data points)
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LVL 84

Expert Comment

by:ozo
ID: 20293752
this is what I understand "spline" to mean
http://en.wikipedia.org/wiki/Spline_(mathematics)
for
y = ax^3 + by^2 + cx + d
I would use
http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html
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LVL 84

Expert Comment

by:ozo
ID: 20293780
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LVL 27

Expert Comment

by:d-glitch
ID: 20294020
>>  Another semantics/terminology question
 >>  Does 'spline' imply interpolation (curve hits all data points)

A cubic spline hits all the data points AND matches the slopes between segments.

http://www.physics.utah.edu/~detar/phys6720/handouts/cubic_spline/cubic_spline/node1.html
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