# Regression Diagnostic Test

A Regression Diagnostic Test is a statistical test that assesses the validity of a regression model and statistical significance of the estimated parameters.

**Example(s):**- A goodness of fit test.
- A t-test.
- A F-test.
- …

**Counter-Example(s):****See:**Statistical Hypothesis Test, Statistics, Regression Analysis, Statistical Assumption, Dependent And Independent Variables, Outlier.

## References

### 2017a

- (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Regression_diagnostic Retrieved:2017-9-9.
- In statistics, a
**regression diagnostic**is one of a set of procedures available for regression analysis that seek to assess the validity of a model in any of a number of different ways.^{[1]}This assessment may be an exploration of the model's underlying statistical assumptions, an examination of the structure of the model by considering formulations that have fewer, more or different explanatory variables, or a study of subgroups of observations, looking for those that are either poorly represented by the model (outliers) or that have a relatively large effect on the regression model's predictions.A regression diagnostic may take the form of a graphical result, informal quantitative results or a formal statistical hypothesis test,

^{[2]}each of which provides guidance for further stages of a regression analysis.

- In statistics, a

- ↑ Everitt, B.S. (2002) The Cambridge Dictionary of Statistics, CUP. ISBN 0-521-81099-X (entry for Regression diagnostics)
- ↑ Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9

### 2017b

- (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Regression_analysis#Diagnostics Retrieved:2017-9-9.
- 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 residuals and hypothesis testing. Statistical significance can be checked by an F-test of the overall fit, followed by t-tests of individual parameters.
Interpretations of these diagnostic tests rest heavily on the model 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.

- 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 residuals and hypothesis testing. Statistical significance can be checked by an F-test of the overall fit, followed by t-tests of individual parameters.