How are regression and correlation analysis used to study relationships between variables?

Regression and correlation analysis are both used to study relationships between variables, though they serve different analytical purposes.1

Regression Analysis

Regression analysis identifies the relationship between a dependent variable and one or more independent variables. Researchers typically use the least squares method to estimate model parameters and develop an estimated regression equation. This equation allows analysts to predict the value of a dependent variable based on given values of independent variables. To ensure the model is reliable, statisticians conduct significance testing using tests such as the F-test.234

Correlation Analysis

Correlation analysis quantifies the strength and direction of a linear association between two variables. Pearson’s correlation coefficient (r) ranges from −1 to +1, where values closer to the extremes indicate stronger linear relationships. Unlike regression, correlation does not distinguish between dependent and independent variables.51

It is ethically and scientifically critical to note that neither method establishes cause-and-effect relationships. These tools only measure the extent of association; any causal conclusions must rely on the analyst's judgment.51