Correlation and Regression: A Comprehensive Review of Statistical Relationships and Predictive Modeling

Abstract: Correlation and regression are among the most important statistical techniques used in mathematics, economics, business, and data science for analyzing relationships between variables. Correlation measures the strength and direction of association between variables, while regression establishes predictive relationships and quantifies the effect of independent variables on dependent variables. This review paper discusses the theoretical foundations, types, methods, assumptions, applications, similarities, and differences between correlation and regression analysis. The study further explains how these techniques are applied in forecasting, decision-making, econometrics, and financial analysis. The paper concludes that correlation identifies associations, whereas regression provides predictive and explanatory insights for practical applications.

Keywords: Correlation, Regression, Pearson Correlation, Linear Regression, Statistical Analysis, Predictive Modeling, Econometrics.