What is regression analysis and how is it applied to data analysis?

Regression analysis is a statistical method that examines the relationship between a dependent variable and one or more independent variables, primarily used for prediction or causal inference. It quantifies how changes in predictors are associated with changes in the outcome, enabling forecasting future outcomes based on known relationships. This technique relies on fundamental principles such as minimizing error terms (e.g., ordinary least squares) and assumes linearity, independence of errors, homoscedasticity, and normality of residuals. Key considerations include variable selection to avoid multicollinearity, model specification to capture true relationships, validation using holdout samples, and interpreting regression coefficients accurately. Its applicability spans economics, social sciences, engineering, and business analytics for understanding complex variable interactions. Regression supports evidence-based decision-making by predicting sales trends, estimating policy impacts, identifying key risk factors, or optimizing operational processes. Implemented effectively, it involves defining the research question, preparing data, selecting an appropriate model type (e.g., linear, logistic), fitting the model, rigorously assessing diagnostics, and validating predictive performance to derive actionable insights for strategic planning and resource allocation.