Why is the amount of fertilizer known as the independent variable?

You can think of an independent variable is the variable that is being varied by you the experimenter or scientist; it is the input/"cause"/the tunable variable. A dependent variable is the response/output/"effect".

There is also the control variable, which are variables that stay constant throughout. You generally have only one independent variable and many control variables so that you can properly disentangle cause and effect.

A simple example might be say you want to know if a certain brand of fertilizer helps your crops grow. You want to see how much fertilizer you need for optimal growth without using too much. What is the independent and dependent variable? (Highlight below for the answer!)

The independent variable is the amount of fertilizer you put on the crop. It is the variable that you, as the tester, vary yourself. The dependent variable is how much your crop grows. What about the control? It is the crop you choose to use the fertilizer on (e.g., corn, wheat, peas). Certainly, comparing the influence of fertilizer between corn and peas would not definitely tell you whether the fertilizer is effective; if you compared two different crops, you would have other confounding variables out of your control, so you want to test it only on one crop at a time.

I put cause and effect in quotes because you may run into one of many cause/effect fallacies (or mistaken beliefs). It is possible (and often happens in research) where you plot what you think is an independent and its dependent variable, but the reality is quite different! There are two common types- spurious relationships and spurious correlations. A spurious relationship is one in which a direct cause/effect relationship is concluded incorrectly when in fact there is a lurking or hidden variable unaccounted for. One commonly cited example is say you find an increase of death by drownings and ice cream sales. It would be incorrect to infer that eating more ice cream causes more drownings, or vice versa. The lurking variable that can explain both is hot weather (i.e., people eat more ice cream and go swimming more to cool down). A spurious correlation is incorrectly inferring the extent of how related two variables are (not necessarily a cause/effect relation, but something used often in statistics). Here is a website that illustrates quite ridiculous correlations (a pet project of a graduate student), emphasizing that correlation is not causation.