| Multiple linear regression (MLR): significance of the calculated terms (2 sigma interval) [message #83769] |
Wed, 03 April 2013 12:27  |
kisCA
Messages: 78
Registered: January 2011
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Member |
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Hello,
I have been reading MLR results for a while now in published papers. They always talk about the significance of the calculated terms of the regression by saying "it's significant at a 2 sigma level". Is there any body here that would explain to me what it really means and how it is done ? Is it simply when 2sigma is largely superior to the calculated term ?
Thank you for your help
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| Re: Multiple linear regression (MLR): significance of the calculated terms (2 sigma interval) [message #83854 is a reply to message #83769] |
Wed, 03 April 2013 22:48  |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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On Wednesday, April 3, 2013 3:27:54 PM UTC-4, kisCA wrote:
>
> I have been reading MLR results for a while now in published papers. They always talk about the significance of the calculated terms of the regression by saying "it's significant at a 2 sigma level". Is there any body here that would explain to me what it really means and how it is done ? Is it simply when 2sigma is largely superior to the calculated term ?
A quick and dirty way to do it is calculate the T-value which is
T = (fitted parameter value) / (uncertainty of fitted parameter)
and call that a gaussian sigma. Example, a regression coefficient is reported as 4.5 units and the uncertainty is 1.5 units, so the regression coefficient is significant at (4.5)/(1.5) = 3 sigma. Quick and dirty of course.
The following course indicates to use the Student T test to test for parameter significance....
http://www.stat.yale.edu/Courses/1997-98/101/linmult.htm
IDL has a standard library routine TM_TEST which doesn't quite do what you want. If you peek at how it works, it computes significance from the T value as computed above. The formula is,
P = IBETA(0.5*DOF, 0.5, DOF/(DOF + T^2))
where DOF is number of degrees of freedom (number of data points minus number of regression coefficients).
The preference in my field of work is to use an F-test. (see my MPFTEST)
People usually use a shorthand statement. If something is 2-sigma significant, they usually mean that they calculated the significance (P-value) from the Student T test or F test, and then gave the gaussian "sigma" value that produced the same significance.
Example: your significance test produces a P-value of 0.0025 (in other words such a large regresssion coefficient would happen by random chance 0.0025 x 100 = 0.25% of the time). For the probability of a gaussian variable x to be less than 0.25%, the random variable must be |x|>3.02, so that would be a "3.02-sigma" result. (use GAUSS_CVF(0.0025/2))
Craig
MPFTEST download
http://www.physics.wisc.edu/~craigm/idl/fitting.html#MPFIT
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