Editing Regression analysis (section)

===Diagnostics===
{{main|Regression diagnostics}}
{{Category see also|Regression diagnostics}}
Once a regression model has been constructed, it may be important to confirm the [[goodness of fit]] of the model and the [[statistical significance]] of the estimated parameters. Commonly used checks of goodness of fit include the [[R-squared]], analyses of the pattern of [[errors and residuals in statistics|residuals]] and hypothesis testing. Statistical significance can be checked by an [[F-test]] of the overall fit, followed by [[t-test]]s of individual parameters.

Interpretations of these diagnostic tests rest heavily on the model's assumptions. Although examination of the residuals can be used to invalidate a model, the results of a [[t-test]] or [[F-test]] are sometimes more difficult to interpret if the model's assumptions are violated. For example, if the error term does not have a normal distribution, in small samples the estimated parameters will not follow normal distributions and complicate inference. With relatively large samples, however, a [[central limit theorem]] can be invoked such that hypothesis testing may proceed using asymptotic approximations.