Math: independent and dependent variables

[kingwinner]

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! :hihi:

[jpittelo]

I'm not an expert in the anglic language, but if you put, or find, a causality that explain the correlation, maybe the order of A and B is important...maybe if you find a causality you should use "to"...and if it's just statistical "with" ??..I'm not sure...because if you think of EPRB, it is right that the tensor product is not commutative : A tensor B different that B tensor A, but the product of the eigenvalues (scalar) is...so...most of the time, correlated means the the mean value of AB is different than the mean value of A time the mean value of B, hence the mass (measure) of the correlation is :

 

C(A,:tongue:=<AB>-<A><B>. This definition is sometimes surprising...

 

If you think of fair coins with prob 1/2...then, it's obvious, that if the coins are not correlated, that the probability of having the same result is 2*1/2*1/2=1/2...but this indicate no correlation, only deviation from this are relevant..