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What is the mathematical term used for saying if something increases/decreases it has no effect on another thing?

I was thinking along the lines of "X is not linear with Y" however it seems to give the sense that if X increase, Y will increase (though not linearly). This is not the idea I want to convey.

I want the reader to know that an increase/decrease in X does not necessarily mean an increase/decrease in Y.

Well, if you've read the above paragraph you know what I want, but I need the whole idea of that paragraph packed in a single phrase. (I'd have thought a mathematical term would be useful in this sense (since those words are cool), but that's not compulsory of course).

To be sure, I'm not asking for a mathematical term. I'm asking for a catchy term.

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5 Answers 5

up vote 4 down vote accepted

Orthogonal

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brilliant! btw how do i use it in a sentence.. X is orthogonal to Y.. X is orthogonal of Y..? –  Pacerier Jun 19 '11 at 20:22
    
X is orthogonal to Y, or X and Y are orthogonal. –  kindall Jun 19 '11 at 22:14
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"Is not dependent on" and "is independent of" are both common usage in statistics.

I'd also suggest "X and Y are not correlated." This is also a commonly used term in stats.

Alternatively, you could use "X and Y are uncorrelated" (as was suggested by Alain), which means the same thing, but might sound a bit more sophisticated.

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+1, that's the best word. Or better: X and Y are uncorrelated (just being nit-picky). –  Alain Pannetier Φ Jun 17 '11 at 20:53
    
If there isn't much of any association between X and Y, and you're not explaining the statistics, you might just say they're unrelated. "Cell phone minutes used and bananas consumed are unrelated." –  aedia λ Jun 17 '11 at 21:40
    
@aedia for me, unrelated is the best answer. Good one. –  Joe Blow Jun 17 '11 at 21:55
    
Uncorrelated is not only the correct mathematical term, it should also be understood by non-mathematicians. –  Peter Shor Jun 17 '11 at 22:22
    
@aedia, @Joe Blow: I agree with you, but evidently OP wants something "catchy" (by which I think he means he would like to sound technical and jargony, while still being understandable). For that, I have to admit that uncorrelated best fits the bill. Independent (which I also think is a fine choice) is perhaps somewhere in between. –  John Y Jun 17 '11 at 22:35
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I believe it's actually independent. X is an independent variable if it does not depend on Y.

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I would use depend, as in:

Y does not depend on X.

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I was thinking the other way around: X is independent of Y. I think these are both correct. –  KitFox Jun 17 '11 at 20:35
    
Y does not depend on X has zero catchyness.. –  Pacerier Jun 17 '11 at 20:40
    
@Pacerier But accurate and clear, right? –  KitFox Jun 17 '11 at 20:41
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There are many ways of expressing the relationship between two variables, including those in other answers. Another is with "proportional". Some examples of its use:

  • X is directly proportional to Y (i.e. as X increases or decreases, Y does so as well)
  • X is inversely proportional to Y (i.e. as X increases, Y decreases, or vice versa)
  • X is not proportional to Y (i.e. X and Y are unrelated)

This is probably the most precise way to describe two variables' relationship. There are many other types of proportionality.

Another expression is "direct variation", e.g.:

  • X is in direct variation with Y
  • X and Y vary directly (i.e. the value of Y depends on the value of X)
  • X is in not in direct variation with Y
  • X and Y do not vary directly (i.e. the value of Y does not depend on the value of X)
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