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Re: Regression fit and random noise [message #83688 is a reply to message #83687]

Thu, 28 March 2013 16:18

Phillip Bitzer
Messages: 223
Registered: June 2006

Senior Member

The (linear) correlation coefficient, r, is a measure how well the independent/dependent variables are correlated. For perfectly correlated data, r = 1, and the data plots as a straight line with positive slope. Perfectly anit-correlated data has a r=-1, and the data plots as a straight line with negative slope. Uncorrelated data has r=0; in this case, the best fit line has a slope of zero (imagine data points that are scattered with no perceptible trend). (You're dealing with the multiple correlation coefficient, but the concept is similar. There's a nice discussion in Bevington, among other places. BTW, the multiple correlation coefficient can be shown to be a linear combination of the linear correlation coefficients for each variable x_i. Further, the linear correlation coefficient can be used to assess the usefulness of a predictor in the model.)

In your case, setting noise ratio = 0 should provide the same value as if no noise was present because no (artificial) noise is present! As you increase noise_ratio, you're essentially "destroying" the correlation, in a manner of speaking. I bet if you crank up noise_ratio far enough you can get essentially uncorrelated data.

Be careful when you speak of a "good fit" - there ways to qualify what is a good fit (for example, using the chi squared value to test the null hypothesis). Depending on the SNR, the model will still be a "good fit" to the (noisy) data.

Ultimately, the answer to your question lies in the underlying statistics - there isn't (shouldn't be?) anything wonky going on in IDL.

Hope this helps!

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[Message index]

		Re: Regression fit and random noise By: kisCA on Fri, 29 March 2013 10:24
		Re: Regression fit and random noise By: Craig Markwardt on Thu, 28 March 2013 18:16
		Re: Regression fit and random noise By: Phillip Bitzer on Thu, 28 March 2013 16:40
		Re: Regression fit and random noise By: kisCA on Thu, 28 March 2013 16:37
		Re: Regression fit and random noise By: Mats Löfdahl on Thu, 28 March 2013 16:26
		Re: Regression fit and random noise By: Phillip Bitzer on Thu, 28 March 2013 16:18
		Re: Regression fit and random noise By: kisCA on Thu, 28 March 2013 15:26
		Re: Regression fit and random noise By: Phillip Bitzer on Thu, 28 March 2013 14:51
		Re: Regression fit and random noise By: Craig Markwardt on Fri, 29 March 2013 16:39

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