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Thread: Math: independent and dependent variables

  1. #1 Math: independent and dependent variables 
    Forum Sophomore
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    Given that A and B are either the independent variable or the dependent variable:

    1) "A is correlated with B"
    For this wording, does it mean that A is the independent variable and B is the dependent variable? (i.e. A affects B?) Or is it the other way around?

    2) "A is correlated to B"
    Is this meaning exactly the same thing as "A is correlated with B"? Or does it mean that A is the dependent variable and B is the independent variable? (i.e. B affects A?)

    3) "There is a strong postive linear correlation between A and B"
    "There is a strong postive linear correlation between B and A"
    Is there any difference between the two statements above? Does the order of stating A and B matter here? Does this wording give any clue to whether the first one or the second one is the independent variable?

    4) When it says "something vs something", should the independent variable listed first or second?


    Can anyone help me, please? I am really confused now!
    Thank you!


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  3. #2  
    Forum Radioactive Isotope mitchellmckain's Avatar
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    The terms independent variable and dependent variable has to do with functions, because functions are not necessarily invertable. For example,
    take the equality y = x^2 (where x is any real number) this can be written as a function y=f(x) with a domain over the whole real line, where y is the dependent variable and x is the independent variable. But this equality cannot be represented by a function with x as the dependent variable, because there are two values of x for every value of y. When we write x=sqrt(y) we chop off a part of the equality where the x can be negative.

    But often a functional relationship is reversible like that for the equality y = 2 x, which can be y = f(x) = 2 x or x = g(y) = y/2. These are equivalent. In which case, either can be the dependent variable

    A correlation is a statistical relationship between two types of measurements and though a functional relationship is possible it is not the usual case by any means. So the terms independent variable and dependent variable do not apply.

    A functional relationship between A and B implies that they are correlated.

    That A and B are correlated does not imply that there is a functional relationship between them.

    The most proper way to state a correlation is "There is a correlation between A and B" and the order has no significance.


    "A strong postive linear correlation between A and B" means that there is an approximately linear functional relationship between A and B with a positive slope.


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  4. #3 Case of a misconception. 
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    the defination of a function and correlation comes directly from a field of set theory and yes they are related.

    just like a function is invertable and noninvertable so are the correlation. although they donot possess an equation based relationship but the factor which needs to be considerd is that they are both of the same nature.

    Let me clearify.

    functions or equations are deterministic in nature therefore are dealt with greater considerations in the early years of educational years where as the correlation is a part of nondeterministic calculations i.e. statistics.

    comming to the original question, both of your statements are on the same weight.

    when you say that the enities are corelated you are actually comparing two sets of data, and are checking the relations between them either they are negatively correlated or are positivly. But in both cases the data is either indepadently or dependently gathered ( that is a differnet discussion).

    hope that clearfies the problem...

    if not do write back.

    Regards
    Rahim Ali[/quote]
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