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Re: Regression fit and random noise [message #83683 is a reply to message #83675]

Thu, 28 March 2013 18:16

Craig Markwardt
Messages: 1869
Registered: November 1996

Senior Member

On Thursday, March 28, 2013 7:37:34 PM UTC-4, kisCA wrote:

> I understand the process of "destroying" the correlation. What I don't get is why does the coefficient of determination (R2) reach a plateau value (0.3) and doesn't get closer to zero as I raise the noise_ratio a lot (like a hundred)...
>
>> "underlying statistics"

The little cut and paste example below should show that the correlation factors do indeed converge to zero as the noise value is increased. Of course an individual sample of random scale factors may not make a R^2 value that goes to zero. R^2 itself has sample variance.

Craig

x = randomu(seed,100) ;; Random X positions
ym = 0.3 - 0.7 * x ;; Pure Y model (no noise)
ye = 0.01 ;; Initial scatter
;; Sampled y value
ys = ym + randomn(seed,100)*ye
print, r_correlate(x, ys)

;; NOISE_FACTOR multiples
noise_factors = [1, 10, 100, 1000, 10000]

;; Try different noise factors
for i = 0, n_elements(noise_factors)-1 do begin & ys1 = ym + randomn(seed,100)*ye * noise_factors(i) & print, r_correlate(x, ys1)

;; EXAMPLE RUN:
;; i NOISE SPEARMAN SIGNIF
;; 0 1 -0.998248 0.00000
;; 1 10 -0.904374 5.05695e-38
;; 2 100 -0.175770 0.0802491
;; 3 1000 0.0576417 0.568917
;; 4 10000 -0.0107651 0.915328

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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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