Regression modelling is an important statistical tool frequently utilized by cardiothoracic surgeons. However, these models—including linear, logistic and Cox proportional hazards regression—rely on certain assumptions. If these assumptions are violated, then a very cautious interpretation of the fitted model should be taken. Here, we discuss several assumptions and report diagnostics that can be used to detect departures from these assumptions. Most of the diagnostics discussed are based on residuals: a measure of the difference between the observed and model fitted values. Reliable and generalizable results depend on correctly developed statistical models, and proper diagnostics should play an integral part in the model development.