Dependent and Independent Variables

Basic Concepts

• Every experiment involves two types of variables; these include the dependent and independent variables.
• The independent variable (IV) is the variable that you, the researcher, control and change to test its effects on the dependent variable.
• The dependent variable (DV) is the outcome being measured. It is believed to depend on, or be caused by, the independent variable.
• In a mathematical model, the dependent variable is denoted by ‘y’ and the independent variable is denoted by ‘x’.

Analysis of Dependent and Independent Variables

• The relationship between these variables is captured in the equation of the fitting line in a scatter plot.
• This fitting line, often a straight line in simple cases, is given by y = mx + c, where ‘m’ is the gradient, and ‘c’ is the y-intercept.
• The correlation between the independent variable and the dependent variable shows the strength and direction of the relationship between them.
• The correlation coefficient (Pearson’s r) measures the linear relationship between the two variables. The closer this coefficient is to -1 or 1, the stronger the linear relationship.

Importance of Variable Definitions

• Being clear about which variable is the independent variable and which is the dependent variable is essential in regression analysis.
• A common error in correlation and regression analysis is swapping of the independent and dependent variables. It’s crucial to identify these correctly before performing any calculations.

Impact on Correlations

• The specific way in which the independent variable affects the dependent variable is measured by the coefficient of the independent variable in the regression analysis.
• When calculating the correlation coefficient, the selection of dependent and independent variables can affect the results.
• It’s essential to keep in mind that correlation is not causation. Although a strong correlation can be observed, it does not prove that changes in the independent variable cause changes in the dependent variable.

Application in Modelling

• Dependent and independent variables play a key role when modelling real-life scenarios.
• They help us to answer questions such as: “Is there a relationship?”, “How strong is that relationship?”, and “What can we predict?” Bearing in mind the dependent and independent variables can help to deduce conclusions from data analysis.