To understand the concept of independent and dependent variables, one should understand the meaning of variables. Variables are defined as the properties or kinds of characteristics of certain events or objects.
Independent variables are variables that are manipulated or are changed by researchers and whose effects are measured and compared. The other name for independent variables is Predictor(s). The independent variables are called as such because independent variables predict or forecast the values of the dependent variable in the model.
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The other variable(s) are also considered the dependent variable(s). The dependent variables refer to that type of variable that measures the affect of the independent variable(s) on the test units. We can also say that the dependent variables are the types of variables that are completely dependent on the independent variable(s). The other name for the dependent variable is the Predicted variable(s). The dependent variables are named as such because they are the values that are predicted or assumed by the predictor / independent variables. For example, a student’s score could be a dependent variable because it could change depending on several factors, such as how much he studied, how much sleep he got the night before he took the test, or even how hungry he was when he took it. Usually when one is looking for a relationship between two things, one is trying to find out what makes the dependent variable change the way it does.
Let us identify independent and dependent variables in the
following cases:
In the case of a linear model, we have the general equation as:
Here, Y is the variable dependent on X, therefore, X, is an independent variable.
Similarly, in cases of the regression model, we have
Here, the regressors, ßij (j=1, p) are the independent variables and the regressands Yi are the dependent variables.
Independent variables are also called “regressors,“ “controlled variable,” “manipulated variable,” “explanatory variable,” “exposure variable,” and/or “input variable.” Similarly, dependent variables are also called “response variable,” “regressand,” “measured variable,” “observed variable,” “responding variable,” “explained variable,” “outcome variable,” “experimental variable,” and/or “output variable.”
A few examples can highlight the importance and usage of dependent and independent variables in a broader sense.
If one wants to measure the influence of different quantities of nutrient intake on the growth of an infant, then the amount of nutrient intake can be the independent variable, with the dependent variable as the growth of an infant measured by height, weight or other factor(s) as per the requirements of the experiment.
If one wants to estimate the cost of living of an individual, then the factors such as salary, age, marital status, etc. are independent variables, while the cost of living of a person is highly dependent on such factors. Therefore, they are designated as the dependent variable.
In the case of time series analysis, forecasting a price value of a particular commodity is again dependent on various factors as per the study. Suppose we want to forecast the value of gold, for example. In this case the seasonal factor can be an independent variable on which the price value of gold will depend.
In the case of a poor performance of a student in an examination, the independent variables can be the factors like the student not attending classes regularly, poor memory, etc., and these will reflect the grade of the student. Here, the dependent variable is the test score of the student.
Recognize and Graph Independent and Dependent Variables
Updated on December 01, 2019
Both the independent variable and dependent variable are examined in an experiment using the scientific method, so it's important to know what they are and how to use them. Here are the definitions for independent and dependent variables, examples of each variable, and the explanation for how to graph them.
Independent Variable
The independent variable is the condition that you change in an experiment. It is the variable you control. It is called independent because its value does not depend on and is not affected by the state of any other variable in the experiment. Sometimes you may hear this variable called the "controlled variable" because it is the one that is changed. Do not confuse it with a "control variable," which is a variable that is purposely held constant so that it can't affect the outcome of the experiment.
Dependent Variable
The dependent variable is the condition that you measure in an experiment. You are assessing how it responds to a change in the independent variable, so you can think of it as depending on the independent variable. Sometimes the dependent variable is called the "responding variable."
Independent and Dependent Variable Examples
- In a study to determine whether how long a student sleeps affects test scores, the independent variable is the length of time spent sleeping while the dependent variable is the test score.
- You want to compare brands of paper towels, to see which holds the most liquid. The independent variable in your experiment would be the brand of paper towel. The dependent variable would be the amount of liquid absorbed by the paper towel.
- In an experiment to determine how far people can see into the infrared part of the spectrum, the wavelength of light is the independent variable and whether the light is observed (the response) is the dependent variable.
- If you want to know whether caffeine affects your appetite, the presence/absence of a given amount of caffeine would be the independent variable. How hungry you are would be the dependent variable.
- You want to determine whether a chemical is essential for rat nutrition, so you design an experiment. The presence/absence of the chemical is the independent variable. The health of the rat (whether it lives and can reproduce) is the dependent variable. If you determine the substance is necessary for proper nutrition, a follow-up experiment might determine how much of the chemical is needed. Here, the amount of chemical would be the independent variable and the rat health would be the dependent variable.
How to Tell the Independent and Dependent Variable Apart
If you are having a hard time identifying which variable is the independent variable and which is the dependent variable, remember the dependent variable is the one affected by a change in the independent variable. If you write out the variables in a sentence that shows cause and effect, the independent variable causes the effect on the dependent variable. If you have the variables in the wrong order, the sentence won't make sense.
Independent variable causes an effect on the dependent variable.
Example: How long you sleep (independent variable) affects your test score (dependent variable).
This makes sense, but:
Example: Your test score affects how long you sleep.
This doesn't really make sense (unless you can't sleep because you are worried you failed a test, but that would be a different experiment).
How to Plot Variables on a Graph
There is a standard method for graphing the independent and dependent variable. The x-axis is the independent variable, while the y-axis is the dependent variable. You can use the DRY MIX acronym to help remember how to graph variables:
DRY MIX
D = dependent variable
R = responding variable
Y = graph on the vertical or y-axis
M = manipulated variable
I = independent variable
X = graph on the horizontal or x-axis
Test your understanding with the scientific method quiz.