 # Dependent Variable

A variable that will change in conjunction with the changes in the value of another variable, called the independent variable

## What is a Dependent Variable?

A dependent variable is a variable whose value will change depending on the value of another variable, called the independent variable. In a scientific experiment, it is the variable being tested, and therefore, it is called the dependent variable. Dependent variables are also known as outcome variables, left-hand-side variables, or response variables. ### Summary

• A dependent variable is a variable whose value will change depending on the value of another variable, called the independent variable.
• Independent and dependent variables are common in statistical modeling and analysis, research, mathematics, and other experimental science fields. The term “dependent variable” is self-explanatory because dependent variables are said to be reliant on other variables and values.
• When looking at simulation, the dependent variable is a result of changes in the independent variables. Hence, the changes in the dependent variable are a direct response to the alterations in the values of the independent variables.

### Understanding Dependent and Independent Variables

Independent and dependent variables are common in statistical modeling and analysis, research, mathematics, and other experimental science fields. The term “dependent variable” is self-explanatory because dependent variables are said to be reliant on other variables and values.

Such a dependency is studied, observed, and determined through experiments and hypothesis testing methods. On the other hand, independent variables are said to not be dependent on the values of other variables, and it is also confirmed through experiments and hypothesis testing methods.

The variation of a dependent variable is usually the one being researched and studied between the two variable types (dependent and independent). It is done through regression and alteration of inputs and the development of regression models based on theoretical studies.

In statistics and other data experimental fields of study, the variable that a researcher or experimenter can manipulate – or that serves as part of the objective of the study – is considered to be the independent variable.

Through the experiments and studies, the relationship between dependent and independent variables is determined, the nature of the relationship (whether negative or positive) is determined, and the impact of the independent variables on dependent variables is determined. Independent variables can also be added to a model to account for possible complexities.

### Dependent and Independent Variables in Mathematics

A function is a rule in mathematics that implies that an output is derived from inputs. An independent variable, in a mathematical function, is a symbol that represents an observable input, whereas a symbol that represents an observable output is considered a dependent variable.

The most generally utilized symbol for inputs in mathematics is x, and the output is represented by y. Hence, a function is normally written as:

y = f(x)

A function may include multiple dependent and independent variables. An example would be the functions found in multivariable calculus. A common general function, in this case, is:

z = f(x,y)

Here, x and y are the independent variables in the function, and z is the dependent variable.

### Dependent and Independent Variables in Statistics

The independent variable in research studies or experiments is the variable that can be altered or manipulated by the researcher or person experimenting. The outcome or variable expected to change due to the alteration of the independent variable is known as the dependent variable.

### Dependent and Independent Variables in Modeling

Dependent variables are examined in mathematical modeling to see whether and to what extent they differ in conjunction with variations in the independent variables. Consider the stochastics linear equation:

yi = a + bxi + ei

The value “yi” is the value of the dependent variable, and “xi” denotes the value of the independent variable. To account for errors and potential inconsistencies in the dependent variable that cannot be explained through the independent variable, an error term “ei” is added to the equation/model.

### Dependent and Independent Variables in Simulation

When looking at simulation, the dependent variable is a result of changes in the independent variables. Hence, the changes in the dependent variable are a direct response to the alterations in the values of the independent variables.

### Practical Examples of Dependent and Independent Variables

The examples below consist of two different experiments with their dependent and independent variables highlighted for ease of understanding:

Example 1

Jane is experimenting with microwave popcorn. She would like to determine which brand provides the best value for money and produces the most popcorn (finished product). She tested as many brands as she could afford to try.

The dependent variable Jane will be working with is the number of popcorn kernels that popped per bag (from each separate brand). The independent variable would be the microwave popcorn brand.

Example 2

Steve loves gardening. He decides to experiment to help him determine which fertilizer would be ideal for faster plant growth. He added different brands of fertilizer to different plans and observed their growth over time.

The dependent variable Steve will be working with is the increase in the height of each plant (from each separate brand). The independent variable would be the fertilizer brand.