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.