Variables are defined as the properties or characteristics of some events that take on different values or amounts. There are basically two types of variables. They are as follows:
1. Independent variables
2. Dependent variables
Independent variables are those kinds of variables that are used for predicting the variation caused by the dependent variables in regression. Independent variables are also termed as predictors. Independent variables refer to the alternatives that are manipulated and are measured as well as compared. Independent variables are the type of variables that are not affected by any other variables, and are not changed by other variables abruptly. The concept of independent variables can be very well explained with the help of an example, like how the grades of a student can be affected by factors including how much time he devoted to studying, how many hours he slept, what his diet was, etc. These factors are independent variables as they are not at all affected by the grades of the students.
The second type of variable is the dependent variable. Like its name suggests, the dependent variables are always dependent on the independent variables. The variations caused by the dependent variables are generally explained by the independent variables in regression. The other name for dependent variables is predicted variables. The dependent variables are named the predicted variables because they are those types of variables that are predicted by the predictor variables or the independent variables. The other name for dependent variables is criterion variables. Considering the previous example, the score of the students, which are affected by several factors, is the dependent variable. Observing the relationship between the two things is used to find out what affects the dependent variable the most.
We shall now describe the dependent and the independent variables in the following cases:
For the case of the linear model, the general equation is described as the following:
So, in this model, the variable ‘Y’ is defined as the dependent variable, and the variable ‘X’ is defined as the independent variable.
In the regression model, the equation is given by the following:
The regressors called the βij (j=1, ,p) are defined as the independent variables, and the regressands Yi are defined as the dependent variables.
The independent variables are also called ‘ regressors’ and sometimes the independent variables are called the ‘control variables.’ This is because the independent variables are the ones that control the dependent variables. The other name for independent variables is ‘explanatory variables.’
