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The Difference Between Independent and Dependent Variables
Independent vs. Dependent Variables is one of those concepts that will follow you to almost every math class you take, to college and beyond, so it’s important that you learn it well the first time and don’t have any confusion. That being said, if you’re having trouble understanding the concept, never fear. We’ll walk you through everything you need to know.
What is an Independent Variable?
The independent variable, also referred to as the X variable or the causal variable, is the variable that doesn’t change as a result of the experiment that you’re running. It’s the variable that you change in order to see the resulting effect on the dependent variable (more on that later). In other words, the change in the independent variable will cause a change in the dependent variable.
Here are some examples of independent variables in various scenarios in which it may come up:
In equation form: Y = X +3
In this case, the “X” is the independent variable. If you increase X from 1 to 2, Y would change from 4 to 5. Note that you can’t change Y and see how it changes X.
In an experiment:
A common experiment is to determine the effect of different fertilizers on plant growth. In this experiment, you would put different fertilizers on otherwise identical plants and measure the growth of each plant over time. The type of fertilizer is the independent variable because you’re changing the fertilizer type in order to determine the desired effect.
In a graph:
When graphing a function, the independent variable always goes on the X axis, or the horizontal axis.
What is a Dependent Variable?
The dependent variable, also referred to as the Y variable or the effect variable, is the variable that changes as a result of the experiment that you’re running. It’s the variable that you are trying to measure through the experiment, and it’s the variable that you don’t ever directly change. In other words, this is the variable that changes as a result of manipulating the independent variable.
For clarity, here are some examples of a dependent variable being used in scenarios you may encounter:
In equation form: Y = 2X + 4
In this case, the Y is the dependent variable. Notice that you cannot change Y and still have an accurate result. You can only change Y by manipulating X.
In an experiment:
If we were to run an experiment that measured the effect of altitude on temperature, we would only change our observations based on changes in altitude. We would not manipulate temperature in any way; therefore, the temperature is the dependent variable.
In a graph:
When graphing a function, the dependent variable always goes on the Y-axis, or the vertical axis.
Bonus: Control Variables and Multivariable Equations
Okay, so the concept of independent and dependent variables is simple enough when you are dealing with equations or experiments that only have one independent and dependent variable. Things get more complicated when you are dealing with multiple independent variables.
Note: At the high school level, and in many cases on the college level as well, you will likely never deal with a situation with multiple dependent variables, so don’t worry about those situations.
If there are multiple independent variables, however, the equation will look something like this:
Y = 2X + 3Z + 7U
X, Z, and U are all independent variables in this case. This is called a multivariable equation.
Graphing such an equation would lead to a multi-dimensional graph, which you would only ever attempt to model at the college level.
In addition, you may see an independent variable that doesn’t change as a result of the experiment and is never manipulated. So is it an independent or dependent variable? It’s neither actually. It’s called a control variable. These variables are often included to account for external factors that might alter the results of the experiment.
For example, in the fertilizer example from above, the type of plant, climate, and soil quality could all be control variables. In the altitude example, the time of day that temperature was measured would be a control variable.
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