Does the independent variable need to be a specific quantifiable physical quantity? I was writing a paper for my school submission and I am not sure what the independent variable could be since there seems to be no trend for the original independent variable I chose. I will explain what I mean through an example.
Let's say we talk about the young's modulus of a material, so can I call the 'material used' the independent variable for this example and the young's modulus as a dependent variable? Or will I have to use a quantifiable physical quantity as an independent variable?
I did try searching up the meaning of an independent variable for better clarity but it seems my question is a little arbitrary for Google to answer.
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Thank you in advance!
 A: The Young's modulus is a physical property of a given material, and each given material will have a different Young's modulus.  To determine the value of the Young's modulus, you must construct a material with a known cross-sectional area, put a known tension on that material, and measure how much the material stretches under that known tension.  Thus, the variable that you would manipulate in such an experiment, also known as the independent variable, is tension (for the selected cross-sectional area).  The dependent variable is the amount of stretch that occurs due to that tension.
Regarding your confusion of whether or not a material can be declared as an independent variable, physical properties are determined via scientific experiments.  Scientific experiments MUST rely on measurements.  If you can't measure a particular variable, it is not a valid independent variable.  In other words, where would you find a "material meter", such that you would make some adjustment that allowed you to change your measured material from copper to brass to steel (as an example) by turning some knob on some device?  In effect, if you don't have the ability to directly manipulate a variable, it cannot be an independent variable.
A: Let $y = f(x)$ define a function $f$.  Using the functional relationship $f(x)$, $y$ is dependent on the independent variable $x$. If $f(x)$ is both one-to-one and onto, then the inverse function $x = f^{-1}(y)$ exists. Using the functional relationship $f^{-1}(y)$, $x$ is dependent on the independent variable $y$.
For your example of the Young's modulus, for every specific material there is a unique Young's modulus so the material can be considered an independent variable and the Young's modulus the dependent variable.  However, for a specific Young's modulus, more than one material can have the same Young's modulus, so the Young's modulus cannot be considered as the independent variable.
