Testing Model Significance Using the F-Test

13 Pages Posted: 23 Jun 2009

See all articles by Phillip E. Pfeifer

Phillip E. Pfeifer

University of Virginia - Darden School of Business


This note introduces the F-statistic as a way to test the hypothesis that all (or some subset) of the coefficients in a linear model are equal to zero. An F-table is included.




With the multiple linear model

mean(Y) = a + bl(Xl) + b2(X2) + …bk(Xk)

each coefficient has an associated T-statistic and P-value, which measure the significance of that coefficient given all the others in the model. Statistical significance is a statement about the likelihood of seeing an estimated coefficient larger than that calculated if the underlying coefficient is actually zero. T-statistics help evaluate the incremental contribution of each term in the model towards explaining the dependent variable. As such, they each measure how much explanatory power would be lost if the associated independent variable were to be removed from the model.

Testing the significance of coefficients one at a time may be fine in many modeling situations, in which cases the individual T-statistics will suffice. However, it is sometimes useful to be able to test the significance of a group of coefficients. If the candidate model includes a set of dummy variables, for example, the relevant modeling question concerns the contribution of this set of variables as a whole. The set of dummy variables is usually looked at as a “package deal”; they are either all included or all removed from the model. To help make such a modeling decision, we need a procedure for simultaneously testing the significance of a group of model coefficients. This group might be either a subset of the model coefficients, or it might include all k of the coefficients in the model. In this latter case, the test can be looked at as an examination of the overall significance of the model.

. . .

Keywords: model evaluation, quantitative analysis, general, regression analysis, statistics

Suggested Citation

Pfeifer, Phillip E., Testing Model Significance Using the F-Test. Darden Case No. UVA-QA-0331, Available at SSRN: https://ssrn.com/abstract=1422917

Phillip E. Pfeifer (Contact Author)

University of Virginia - Darden School of Business ( email )

P.O. Box 6550
Charlottesville, VA 22906-6550
United States
434-924-4803 (Phone)

HOME PAGE: http://www.darden.virginia.edu/faculty/Pfeifer.htm

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