2 years, 1 month ago
about Statistics
In regression analysis, what is the relationship between interaction and correlation?
This question is a follow up of a comment by @philipy
http://www.mahalo.com/answers/science-and-mathematics/how-do-you-explain-interaction-in-statistics-using-graphs
Can two variables that correlate by themselves do not have interaction via a third dependent variable?
Or conversely, two variables that have interaction in one situation, have a small correlation in other situation?
The question is open for discussion.
http://www.mahalo.com/answers/science-and-mathematics/how-do-you-explain-interaction-in-statistics-using-graphs
Can two variables that correlate by themselves do not have interaction via a third dependent variable?
Or conversely, two variables that have interaction in one situation, have a small correlation in other situation?
The question is open for discussion.
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M$1 Answer
If I understand correctly, this question refers to the transitivity of correlation relationship.
This is a good trap for intuition (see the study in the link).
So, no, the correlation is not preserved through correlation with a third variable, as a rule.
A counter-example can be built with X as a normal distribution.
X and exp(X) are correlated.
exp(x) and X^2 are correlated.
But X and X^2 are not correlated.
This is a good trap for intuition (see the study in the link).
So, no, the correlation is not preserved through correlation with a third variable, as a rule.
A counter-example can be built with X as a normal distribution.
X and exp(X) are correlated.
exp(x) and X^2 are correlated.
But X and X^2 are not correlated.
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
M$
the links are very interesting
I have tipped you half the value of the question
I was asking about the relation between correlation and interaction
http://en.wikipedia.org/wiki/Interaction_%28statistics%29