one of the components of a partition of the sum of squares of residuals in an analysis of variance, used in the numerator in an F-test of the null hypothesis that says that a proposed model fits well.

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1. The hypothesis that the means of a given set of normally distributed populations, all having the same standard deviation, are equal. This is perhaps the best-known F-test, and plays an important role in the analysis of variance (ANOVA).
2.  Lack-of-fit sum of squares: The hypothesis that a proposed regression model fits the data well. 
3.  The hypothesis that a data set in a regression analysis follows the simpler of two proposed linear models that are nested within each other.

Common examples of f-tests

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

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