| Regression fit and random noise [message #83691] |
Thu, 28 March 2013 11:27  |
kisCA
Messages: 78
Registered: January 2011
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Member |
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Hi there,
I am actually testing a multiple linear regression model by adding random noise to the original meteorological time series. When the noise/signal ratio become really high (20), the R2 value stabilize to 0.3-0.4. Is there any more explanation than that the maths "do their job" and will try to fit whatever it is with whatever you give the model to work with ? Is it an IDL thing ?
Thank you for your help
Cheers
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| Re: Regression fit and random noise [message #84722 is a reply to message #83691] |
Thu, 28 March 2013 14:50  |
Phillip Bitzer
Messages: 223
Registered: June 2006
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Senior Member |
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Not quite sure what you're asking here with such limited information. What routine are you using to do the fit? When you say noise/signal ratio, do you mean signal to noise ratio (SNR)? Do you have some sort of example data?
Regardless, consider the following "simple" linear regression, adapted from the IDL help:
PRO test_model
npts = 100
x = FINDGEN(npts)
noiseFactor = 0.
y = x + noiseFactor*(RANDOMU(seed, npts)-0.5)
plot, x, y, psym=2
result = REGRESS(X, Y, SIGMA=sigma, CONST=const, corr = r2, $
MEASURE_ERRORS=measure_errors)
PRINT, 'Constant: ', const
PRINT, 'Coefficients: ', result[*]
PRINT, 'Standard errors: ', sigma
PRINT, 'Correl Coeff: ', r2
END
Notice as you increase the noise factor, the correlation coefficient gets worse. This is entirely expected and is not a IDL-only thing. Basically, the "signal" gets swamped out by the "noise". You should get your hands on a good statistics book (e.g., Data Reduction and Error Analysis in the Physical Sciences by Bevington, Statistical Methods in the Atmospheric Sciences by Wilks) to better interpet what's going on "under the hood". For instance, according to regress.pro, the fit is done via chi squared minimization.
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