I'm new to this, and am struggling with the concept of how to determine what is the independent variable and what is the dependent variable.

Here's an example that I think would go a long way for me:

I'm studying baseball, specifically the home run rate for all players over the course of the season. Is the player the independent variable, and the home run rate dependent on the player?

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#### Best Answer

There are two sides to this question: the mathematical aspect, and the causal (inferential) aspect.

In the mathematical sense, a dependent variable y is a function f of an independent variable x: $y = f(x), f subset X times Y$. In this sense, the set X is the set of all players, and the set Y is the set of home run rates. The function f connects the chosen player and his (or her) home run rate. However, this relation can be inversed by use of the inverse function $f^{-1}$, in the sense of $y=f(x) Leftrightarrow x = f^{-1}(y)$

However, I understand your question as pertaining to the inferential structure. In terms of your question, what depends on what? Clearly, the home run rate depends on the player, because it is a function of some characteristics of the player – his speed, striking prowess, etc. In that sense, the data itself is imbued by a causal structure: if the player changed – say, went into heavy training or used enhancing drugs – he or she could improve performance.

I hope this goes somewhere in answering your question.

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