Lack of Fit, in statistics, is a measure which tells us whether a regression model is a poor model of the data. This may be because we made a poor choice of variables, or it may be because important terms weren’t included. It can also be because of poor experimental design. If unusually large residuals or errors appear when fitting the model, we know we have lack-of-fit.

## Tests Used to Determine Lack of Fit

A variety of tests can be used to identify lack-of-fit in statistical models. These include:

- Goodness of fit
- Lack-of-fit F-Test/ sum of squares
- Ljung Box Test

## Correcting Lack of Fit

Correcting lack of fit in a model usually involves rewriting the model to fit the data better. This may be by adding a quadratic term, changing a linear regression model to a polynomial regression model, for instance.

Sometimes, what it points to is poor experimental design. This could suggest we redesign our experiment to get more accurate data or expand our sampling to get more data points that can provide a more complete picture. If the model was in fact an accurate description of the situation, a combination of these methods will change the fit to a good one.

## References

Christensen, Ronald. Chapter 8: Testing Lack-of-Fit. Unbalanced Analysis of Variance, Design, and Regression. Retrieved from http://www.math.unm.edu/~fletcher/SUPER/chap8.pdf on July 29, 2018.

Lack-of-Fit. Analyse-it Statistical Reference Guide. Retrieved from

https://analyse-it.com/docs/user-guide/fitmodel/linear/lackoffit on July 29, 2018

Ruczinski, Ingo. Chapter 6, Testing for Lack-of-Fit. Teaching Notes. Retrieved from http://www.biostat.jhsph.edu/~iruczins/teaching/jf/ch6.pdf on July 29, 2018

Statsoft Team. Lack-of-Fit. Statistica Help. Retrieved from http://documentation.statsoft.com/STATISTICAHelp.aspx?path=glossary/GlossaryTwo/L/LackofFit on July 29, 2018

Lack-of-Fit and Lack-of-Fit Tests

Retrieved from https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/regression/supporting-topics/regression-models/lack-of-fit-and-lack-of-fit-tests/ on July 29, 2018.

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