Definition
Correlation measures the degree and direction of relationship between two variables; regression predicts the value of one variable based on another through a mathematical model.

Introduction
Human and social realities are interconnected: education influences income, advertising affects sales, and temperature determines crop yield. Correlation and regression are twin analytical techniques that quantify and predict these relationships.

Explanation
Correlation ranges from –1 to +1. A positive correlation (+) means both variables move together, a negative (–) means they move oppositely, and zero implies no relationship. However, correlation alone cannot prove causation.

Regression analysis goes a step further—it models the dependency between variables. In simple regression, one independent variable predicts a dependent variable:
Y = a + bX, where b indicates the slope (change in Y per unit change in X).
Multiple regression extends this to several predictors, disentangling their individual effects.

The strength of regression lies in its predictive capacity. Marketers, economists, and scientists use regression to forecast trends or test hypotheses about causality, always supported by diagnostic tests to ensure validity.

Key Takeaways
Correlation describes association; regression explains and predicts. Together they transform observation into quantifiable relationships.

Real-World Case
Housing economists use multiple regression to model how property prices depend on factors like location, size, and interest rates—helping banks and policymakers predict market movements.
Reference: https://www.nber.org