Overview
Regression analysis is one of the most powerful statistical tools and one of the most frequently misused. The primary misuse is presenting regression coefficients as causal effects when the design is observational — "for every one unit increase in X, Y increases by B units" implies a causal relationship when the design only establishes a predictive association. The second most common failure is publishing regression results without assumption verification: regression requires linearity, independence of errors, homoscedasticity, and normality of residuals — violating these produces coefficients that are biased or inefficient.
The Regression Hypothesis Testing Framework verifies assumptions before fitting models, interprets coefficients with appropriate causal qualification, applies incremental F-tests for model comparison, and reports model fit with both R² and adjusted R².