---
title: What Is the F-test of Overall Significance in Regression Analysis?
description: What Is the F-test of Overall Significance in Regression Analysis?
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# What Is the F-test of Overall Significance in Regression Analysis?
Minitab Blog Editor | 6/11/2015
Topics: [Regression Analysis](https://blog.minitab.com/en/blog/tag/regression-analysis)
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Previously, I’ve written about [how to interpret regression coefficients and their individual P values](https://blog.minitab.com/blog/adventures-in-statistics/how-to-interpret-regression-analysis-results-p-values-and-coefficients?hsLang=en).
I’ve also written about [how to interpret R-squared](https://blog.minitab.com/blog/adventures-in-statistics/regression-analysis-how-do-i-interpret-r-squared-and-assess-the-goodness-of-fit?hsLang=en) to assess the strength of the relationship between your model and the response variable.
Recently I've been asked, how does the F-test of the overall significance and its P value fit in with these other statistics? That’s the topic of this post!
In general, an F-test in regression compares the fits of different linear models. Unlike t-tests that can assess only one regression coefficient at a time, the F-test can assess multiple coefficients simultaneously.
The F-test of the overall significance is a specific form of the F-test. It compares a model with no predictors to the model that you specify. A regression model that contains no predictors is also known as an intercept-only model.
The hypotheses for the F-test of the overall significance are as follows:
- **Null hypothesis**: The fit of the intercept-only model and your model are equal.
- **Alternative hypothesis**: The fit of the intercept-only model is significantly reduced compared to your model.
In [Minitab statistical software](http://www.minitab.com/products/minitab/), you'll find the F-test for overall significance in the Analysis of Variance table.
If the P value for the F-test of overall significance test is less than your significance level, you can reject the null-hypothesis and conclude that your model provides a better fit than the intercept-only model.
Great! That set of terms you included in your model improved the fit!
Typically, if you don't have any significant P values for the individual coefficients in your model, the overall F-test won't be significant either. However, in a few cases, the tests could yield different results. For example, a significant overall F-test could determine that the coefficients are *jointly* not all equal to zero while the tests for individual coefficients could determine that all of them are *individually* equal to zero.
There are a couple of additional conclusions you can draw from a significant overall F-test.
In the intercept-only model, all of the fitted values equal the mean of the response variable. Therefore, if the P value of the overall F-test is significant, your regression model predicts the response variable better than the mean of the response.
While R-squared provides an estimate of the strength of the relationship between your model and the response variable, it does not provide a formal hypothesis test for this relationship. The overall F-test determines whether this relationship is statistically significant. If the P value for the overall F-test is less than your significance level, you can conclude that the R-squared value is significantly different from zero.
To see how the F-test works using concepts and graphs, see my post about [understanding the F-test](https://blog.minitab.com/blog/adventures-in-statistics/understanding-analysis-of-variance-anova-and-the-f-test?hsLang=en).
If your entire model is statistically significant, that's great news! However, be sure to [check the residual plots](https://blog.minitab.com/blog/adventures-in-statistics/why-you-need-to-check-your-residual-plots-for-regression-analysis?hsLang=en) so you can trust the results!
If you're learning about regression, read my [regression tutorial](https://blog.minitab.com/blog/adventures-in-statistics/regression-analysis-tutorial-and-examples?hsLang=en)!
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