Independent Variable
The independent variable is the one factor an investigator deliberately changes in an experiment to see its effect.
Definition
The independent variable is the one thing you change on purpose in an experiment, and you pick its values before you start. It is the factor the investigator manipulates to test its effect on the dependent variable, plotted on the horizontal axis of a graph, and a fair test changes exactly one of them while holding everything else constant. The range and spacing of its levels determine what the experiment can reveal: too few levels cannot show curvature, and too narrow a range may miss the effect entirely. In multi-factor designs more than one independent variable can be tested, but each must be crossed systematically so its effect can be separated from the others.
Example
Testing how ramp height affects how far a cart rolls, the independent variable is ramp height, set at $10\ \text{cm}$, $20\ \text{cm}$, and $30\ \text{cm}$. In a salt-dissolving investigation it is water temperature at $10^\circ\text{C}$, $30^\circ\text{C}$, and $50^\circ\text{C}$, with salt mass, water volume, and stirring rate held constant. A group studying ramp angle chooses five levels from $10^\circ$ to $50^\circ$ rather than two, so they can tell whether speed rises linearly or follows the $\sqrt{\sin\theta}$ pattern that energy conservation predicts; with only two angles the two patterns would be indistinguishable.
Key Insight
Think "I" for independent: it is the variable I change, and there should be only one. It is a cause you are deliberately testing, not just anything that happens to vary; room temperature drifts during the day, but unless you set it on purpose it is something to control rather than the independent variable. Choosing its levels is a modeling decision, because the levels you pick decide which hypotheses your data can distinguish.