| Explanation for keywords of POLY_FIT? [message #63085] |
Tue, 28 October 2008 09:41  |
Karlo Janos
Messages: 31
Registered: July 2008
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Hello everybody,
I am looking for an explanation for some of the keywords of POLY_FIT.
I understand SIGMA. But what are YERROR and YBAND in the mathematical
sense? How are these values calculated? And how does MEASUREMENT_ERROR
influence these output values?
Regards
Karlo
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| Re: Explanation for keywords of POLY_FIT? [message #63240 is a reply to message #63085] |
Thu, 30 October 2008 04:48  |
Jeremy Bailin
Messages: 618
Registered: April 2008
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Senior Member |
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>> If your data points are X, Y and the fit is X, YFIT, then YERROR =
>> stddev(Y - YFIT).
>
> That is not correct (as I found out now), but you gave me the hint for
> finding the correct answer!
>
> YERROR is the "Root Mean Squared Error" aka the "fit standard error".
> Dr. Google gives the definition. ;)
Aha! Yeah, that makes more sense anyways.
>> MEASUREMENT_ERROR only influences these via changes to YFIT, but the
>> form is complicated and depends on the degree of the polynomial... if
>> you need the detailed expression, I'd just follow the NR derivation
>> for linear least squares fit with whatever degree polynomial you need.
>
> I assume that this is "weighted linear least squares", when using
> MEASUREMENT_ERROR.
Yup, that should be right. Some of the fitting procedures
alternatively let you use a WEIGHT keyword instead, so you can
directly weight the data points instead (depricated, since it's not a
great idea, but can be convenient to explicitly set some to zero), but
it looks like POLY_FIT isn't one of them.
-Jeremy.
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| Re: Explanation for keywords of POLY_FIT? [message #63247 is a reply to message #63137] |
Thu, 30 October 2008 01:06 |
Karlo Janos
Messages: 31
Registered: July 2008
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Member |
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> If your data points are X, Y and the fit is X, YFIT, then YERROR =
> stddev(Y - YFIT).
That is not correct (as I found out now), but you gave me the hint for
finding the correct answer!
YERROR is the "Root Mean Squared Error" aka the "fit standard error".
Dr. Google gives the definition. ;)
> MEASUREMENT_ERROR only influences these via changes to YFIT, but the
> form is complicated and depends on the degree of the polynomial... if
> you need the detailed expression, I'd just follow the NR derivation
> for linear least squares fit with whatever degree polynomial you need.
I assume that this is "weighted linear least squares", when using
MEASUREMENT_ERROR.
Thanks for your help!
Karlo
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