How to use regression analysis to study the relationships between variables?

Regression analysis is a widely utilized statistical method for investigating and quantifying the relationships between a dependent variable and one or more independent variables. It determines if a statistically significant relationship exists and models its form and magnitude. Successful implementation requires identifying relevant variables, collecting suitable data, selecting the appropriate regression model (e.g., linear regression, logistic regression), and specifying the functional relationship. Key assumptions must be validated, including linearity (for linear models), independence of errors, homoscedasticity (constant error variance), and normality of residuals. Multicollinearity among predictors is a critical consideration requiring assessment. The method finds application across fields like economics, medicine, social sciences, and business intelligence. Regression analysis is extensively applied for prediction, forecasting future outcomes based on independent variable values, and for understanding causal mechanisms and effect sizes. Typical implementation involves defining the research question, data preparation, model fitting, rigorous diagnostic checking for assumption violations, interpretation of coefficients, significance testing, and model refinement. This process enables identifying key drivers of phenomena, evaluating interventions, and making informed predictions.