Regression Assumptions

Statistics · Axiom Academy

Understanding the four key assumptions that must hold for linear regression to produce valid, reliable results The relationship between the independent variable(s) and the dependent variable must be linear . This means the expected value of the response changes at a constant rate with changes in the predictor. Residual plot: Plot residuals vs. fitted values. Look for random scatter around zero. Scatterplot: Plot Y vs. X to visually inspect the relationship. Component-residual plots: For multiple regression, examine partial relationships. Transform variables (log, square root, polynomial) Add polynomial terms (e.g., X²) Use non-linear regression models Consider generalized additive models (GAM) Observations must be independent of each other. The residual for one observation should not predict the residual for another observation. This assumption is often violated in time series or clustered data. Durbin-Watson test: Tests for autocorrelation in residuals (values near 2 indicate independence). Residual plots over time: For time series, plot residuals vs. time to look for patterns. ACF plots: Autocorrelation function plots reveal serial correlation. Study design review: Consider whether data collection could create dependencies. Use time series models (ARIMA, autoregressive models) Apply mixed-effects models for clustered/hierarchical data Use generalized estimating equations (GEE) Add lagged variables to account for temporal dependencies

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