How to use regression analysis to study the effects of multiple factors?

Regression analysis statistically models the relationship between a continuous dependent variable and multiple independent factors (predictors). This technique allows researchers to quantify the individual and combined effects of these factors on the outcome of interest while controlling for confounding variables. Effective application requires several key considerations. Firstly, careful variable selection is essential, choosing predictors based on theoretical rationale and potential causal links while avoiding multicollinearity. Secondly, assumptions including linearity, independence of errors, homoscedasticity, and normality of residuals must be checked; violations often require remedial actions like transformations or alternative models. Thirdly, the data must meet quality standards, be in an analyzable format, and represent a suitable sample size. The model's scope is inherently limited to the range of available data. Implementing regression involves distinct steps. Prepare the data: clean, code categorical predictors, consider interactions, and transform variables if needed. Specify and estimate the model using appropriate software. Rigorously test statistical assumptions and diagnose potential issues like outliers or influential points. Interpret the estimated coefficients, their significance (p-values), and model fit (e.g., R-squared). Finally, communicate findings, emphasizing the estimated effects of each factor on the outcome, while acknowledging uncertainty. This process provides actionable insights into factor influences for decision-making across fields.