Independent and Dependent Variables

Quantitative Results

To understand the concept of independent and dependent variables, one should understand the meaning of variables. We define variables as the properties or characteristics of certain events or objects.

Researchers manipulate independent variables and measure and compare their effects. The other name for independent variables is Predictor(s). They call independent variables as such because they predict or forecast the values of the dependent variable in the model.

The analysis also considers the other variable(s) as the dependent variable(s). Dependent variables measure the impact of independent variables on test units. Dependent variables rely entirely on independent variables. The other name for the dependent variable is the Predicted variable(s). We name dependent variables as such because independent variables predict or assume their values.

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 both 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, we designate them 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.