| Re: How to calculate 3SIGMA in Linfit! [message #80359] |
Tue, 12 June 2012 12:35 |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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On Tuesday, June 12, 2012 2:10:16 PM UTC-4, dave poreh wrote:
> On Tuesday, June 12, 2012 10:54:26 AM UTC-7, Craig Markwardt wrote:
>> On Tuesday, June 12, 2012 10:53:03 AM UTC-4, Craig Markwardt wrote:
>>> On Tuesday, June 12, 2012 3:07:40 AM UTC-4, dave poreh wrote:
>>>> On Monday, June 11, 2012 6:25:35 PM UTC+2, Craig Markwardt wrote:
>>>> > On Monday, June 11, 2012 3:51:50 AM UTC-4, dave poreh wrote:
>>>> > > Dear folks
>>>> > > hi,
>>>> > > i want to calculate 3sigma in linfit function. sigma function just give me the SD and i could not do 3*sigma to get 3sigma. As far as i understood first i need to transfer data to normal function and then i find SD and 3SD=3sigma.
>>>> >
>>>> > I'm assuming you want to calculate a 3 sigma confidence limit. But of what? The slope coefficient? Offset coefficient?
>>>> >
>>>> > As far as I understand, 3 sigma is indeed usually 3 times the 1 sigma error estimate. When your fitting function is non-linear it gets more complicated, but yours is not-nonlinear.
>>>> >
>>>> > Craig
>>>> I want to measure velocity of the time series that means i would have a velocity and +- 3sigma error.
>>
>> As a practical matter, I recommend that you subtract the average time value (or center-time value) from the time column of your samples.
>>
>> The result returned from LINFIT() will then be mean position at the center time, and the mean velocity at the center time.
>>
>> If you don't subtract the mean time value, then that can introduce some nasty correlations between the slope and offset coefficients.
>>
>> Craig
> Thanks
> I have noticed that, and i thought it is a statistical matter. Why it is like that. Is this thing (subtracting mean()) some kind of normalization or what?
It's a correlation between parameters.
A linear fit has a slope term and an offset term, which is measured at the origin of the X axis. If the origin of the X axis is very far from the measured data positions, then a very small error in the slope will trigger a large error in the offset, and vice versa.
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| Re: How to calculate 3SIGMA in Linfit! [message #80361 is a reply to message #80359] |
Tue, 12 June 2012 11:10  |
d.poreh
Messages: 406
Registered: October 2007
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Senior Member |
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On Tuesday, June 12, 2012 10:54:26 AM UTC-7, Craig Markwardt wrote:
> On Tuesday, June 12, 2012 10:53:03 AM UTC-4, Craig Markwardt wrote:
>> On Tuesday, June 12, 2012 3:07:40 AM UTC-4, dave poreh wrote:
>>> On Monday, June 11, 2012 6:25:35 PM UTC+2, Craig Markwardt wrote:
>>>> On Monday, June 11, 2012 3:51:50 AM UTC-4, dave poreh wrote:
>>>> > Dear folks
>>>> > hi,
>>>> > i want to calculate 3sigma in linfit function. sigma function just give me the SD and i could not do 3*sigma to get 3sigma. As far as i understood first i need to transfer data to normal function and then i find SD and 3SD=3sigma.
>>>>
>>>> I'm assuming you want to calculate a 3 sigma confidence limit. But of what? The slope coefficient? Offset coefficient?
>>>>
>>>> As far as I understand, 3 sigma is indeed usually 3 times the 1 sigma error estimate. When your fitting function is non-linear it gets more complicated, but yours is not-nonlinear.
>>>>
>>>> Craig
>>> I want to measure velocity of the time series that means i would have a velocity and +- 3sigma error.
>
> As a practical matter, I recommend that you subtract the average time value (or center-time value) from the time column of your samples.
>
> The result returned from LINFIT() will then be mean position at the center time, and the mean velocity at the center time.
>
> If you don't subtract the mean time value, then that can introduce some nasty correlations between the slope and offset coefficients.
>
> Craig
Thanks
I have noticed that, and i thought it is a statistical matter. Why it is like that. Is this thing (subtracting mean()) some kind of normalization or what?
Cheers,
Dave
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| Re: How to calculate 3SIGMA in Linfit! [message #80362 is a reply to message #80361] |
Tue, 12 June 2012 10:54 |
Craig Markwardt
Messages: 1869
Registered: November 1996
|
Senior Member |
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On Tuesday, June 12, 2012 10:53:03 AM UTC-4, Craig Markwardt wrote:
> On Tuesday, June 12, 2012 3:07:40 AM UTC-4, dave poreh wrote:
>> On Monday, June 11, 2012 6:25:35 PM UTC+2, Craig Markwardt wrote:
>>> On Monday, June 11, 2012 3:51:50 AM UTC-4, dave poreh wrote:
>>>> Dear folks
>>>> hi,
>>>> i want to calculate 3sigma in linfit function. sigma function just give me the SD and i could not do 3*sigma to get 3sigma. As far as i understood first i need to transfer data to normal function and then i find SD and 3SD=3sigma.
>>>
>>> I'm assuming you want to calculate a 3 sigma confidence limit. But of what? The slope coefficient? Offset coefficient?
>>>
>>> As far as I understand, 3 sigma is indeed usually 3 times the 1 sigma error estimate. When your fitting function is non-linear it gets more complicated, but yours is not-nonlinear.
>>>
>>> Craig
>> I want to measure velocity of the time series that means i would have a velocity and +- 3sigma error.
As a practical matter, I recommend that you subtract the average time value (or center-time value) from the time column of your samples.
The result returned from LINFIT() will then be mean position at the center time, and the mean velocity at the center time.
If you don't subtract the mean time value, then that can introduce some nasty correlations between the slope and offset coefficients.
Craig
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| Re: How to calculate 3SIGMA in Linfit! [message #80363 is a reply to message #80362] |
Tue, 12 June 2012 07:53 |
Craig Markwardt
Messages: 1869
Registered: November 1996
|
Senior Member |
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On Tuesday, June 12, 2012 3:07:40 AM UTC-4, dave poreh wrote:
> On Monday, June 11, 2012 6:25:35 PM UTC+2, Craig Markwardt wrote:
>> On Monday, June 11, 2012 3:51:50 AM UTC-4, dave poreh wrote:
>>> Dear folks
>>> hi,
>>> i want to calculate 3sigma in linfit function. sigma function just give me the SD and i could not do 3*sigma to get 3sigma. As far as i understood first i need to transfer data to normal function and then i find SD and 3SD=3sigma.
>>
>> I'm assuming you want to calculate a 3 sigma confidence limit. But of what? The slope coefficient? Offset coefficient?
>>
>> As far as I understand, 3 sigma is indeed usually 3 times the 1 sigma error estimate. When your fitting function is non-linear it gets more complicated, but yours is not-nonlinear.
>>
>> Craig
> I want to measure velocity of the time series that means i would have a velocity and +- 3sigma error.
Assuming:
* the errors are gaussian; (and uncorrelated)
* the data error bars are the correct size; and
* the linear function is a good model for the data;
then the formal parameter errors reported by LINFIT() will be an unbiased estimate of the true parameter errors. And the 3 sigma confidence limits will be the same as the 3 x (1 sigma) confidence limits.
If that is not occurring, then one of the assumptions above is not applicable.
Craig
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| Re: How to calculate 3SIGMA in Linfit! [message #80365 is a reply to message #80363] |
Tue, 12 June 2012 00:07 |
d.poreh
Messages: 406
Registered: October 2007
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Senior Member |
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On Monday, June 11, 2012 6:25:35 PM UTC+2, Craig Markwardt wrote:
> On Monday, June 11, 2012 3:51:50 AM UTC-4, dave poreh wrote:
>> Dear folks
>> hi,
>> i want to calculate 3sigma in linfit function. sigma function just give me the SD and i could not do 3*sigma to get 3sigma. As far as i understood first i need to transfer data to normal function and then i find SD and 3SD=3sigma.
>
> I'm assuming you want to calculate a 3 sigma confidence limit. But of what? The slope coefficient? Offset coefficient?
>
> As far as I understand, 3 sigma is indeed usually 3 times the 1 sigma error estimate. When your fitting function is non-linear it gets more complicated, but yours is not-nonlinear.
>
> Craig
I want to measure velocity of the time series that means i would have a velocity and +- 3sigma error.
Cheers,
Dave
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| Re: How to calculate 3SIGMA in Linfit! [message #80373 is a reply to message #80365] |
Mon, 11 June 2012 09:25 |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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On Monday, June 11, 2012 3:51:50 AM UTC-4, dave poreh wrote:
> Dear folks
> hi,
> i want to calculate 3sigma in linfit function. sigma function just give me the SD and i could not do 3*sigma to get 3sigma. As far as i understood first i need to transfer data to normal function and then i find SD and 3SD=3sigma.
I'm assuming you want to calculate a 3 sigma confidence limit. But of what? The slope coefficient? Offset coefficient?
As far as I understand, 3 sigma is indeed usually 3 times the 1 sigma error estimate. When your fitting function is non-linear it gets more complicated, but yours is not-nonlinear.
Craig
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